
R. Stricker, M. Meth, L. Postler, C. Edmunds, Christopher Ferrie, Rainer Blatt, Philipp Schindler, Thomas Monz, R. Kueng, M. Ringbauer Experimental singlesetting quantum state tomography,
Phys. Rev. X Quantum 3 40310 (20221210),
http://dx.doi.org/10.1103/PRXQuantum.3.040310 doi:10.1103/PRXQuantum.3.040310 (ID: 720910)

R. Stricker, D. Vodola, A. Erhardt, L. Postler, M. Meth, M. Ringbauer, Philipp Schindler, Rainer Blatt, Markus Müller, Thomas Monz Characterizing Quantum Instruments: From Nondemolition Measurements to Quantum Error Correction,
Phys. Rev. X Quantum 3 30318 (20221210),
http://dx.doi.org/10.1103/PRXQuantum.3.030318 doi:10.1103/PRXQuantum.3.030318 (ID: 720911)

M. Ringbauer, M. Meth, L. Postler, R. Stricker, Rainer Blatt, Philipp Schindler, Thomas Monz A universal qudit quantum processor with trapped ions,
Nature Phys. 18 1053 (20221210),
http://dx.doi.org/10.1038/s41567022016580 doi:10.1038/s41567022016580 (ID: 720912)

Lukas Gerster, F. MartinezGarcia, P. Hrmo, Martin van Mourik, Benjamin Wilhelm, D. Vodola, Markus Müller, Rainer Blatt, Philipp Schindler, Thomas Monz Experimental Bayesian calibration of trapped ion entangling operations,
Phys. Rev. X Quantum 3 20350 (20221210),
http://dx.doi.org/10.1103/PRXQuantum.3.020350 doi:10.1103/PRXQuantum.3.020350 (ID: 720913)

L. Postler, S. Heußen, I. Pogorelov, M. Rispler, T. Feldker, M. Meth, C. Marciniak, M. Ringbauer, R. Stricker, Rainer Blatt, Philipp Schindler, Markus Müller, Thomas Monz Demonstration of faulttolerant universal quantum gate operations,
Nature 605 675 (20221210),
http://dx.doi.org/10.1038/s41586022047211 doi:10.1038/s41586022047211 (ID: 720914)

M. van Mourik, P. Hrmo, Lukas Gerster, Benjamin Wilhelm, Rainer Blatt, Philipp Schindler, Thomas Monz rfinduced heating dynamics of noncrystallized trapped ions,
Phys. Rev. A 105 33101 (20221210),
http://dx.doi.org/10.1103/PhysRevA.105.033101 doi:10.1103/PhysRevA.105.033101 (ID: 720915)

Amit K. Pal, Philipp Schindler, A. Erhardt, A. Rivas, M. A. MartinDelgado, Rainer Blatt, Thomas Monz, Markus Müller Relaxation times do not capture logical qubit dynamics,
Quantum 6 632 (20221210),
http://dx.doi.org/10.22331/q20220124632 doi:10.22331/q20220124632 (ID: 720916)

F. Kranzl, M. K. Joshi, C. Maier, T. Brydges, J. Franke, R. Blatt, C. F. Roos Controlling long ion strings for quantum simulation and precision measurements,
Phys. Rev. A 105 52426 (20220518),
http://dx.doi.org/10.1103/PhysRevA.105.052426 doi:10.1103/PhysRevA.105.052426 (ID: 720726)
Toggle Abstract
Scaling a trappedion based quantum simulator to a large number of ions creates a fullycontrollable quantum system that becomes inaccessible to numerical methods. When highly anisotropic trapping potentials are used to confine the ions in the form of a long linear string, several challenges have to be overcome to achieve highfidelity coherent control of a quantum system extending over hundreds of micrometers. In this paper, we describe a setup for carrying out manyion quantum simulations including singleion coherent control that we use for demonstrating entanglement in 50ion strings. Furthermore, we present a set of experimental techniques probing ionqubits by Ramsey and CarrPurcellMeiboomGill (CPMG) pulse sequences that enable detection (and compensation) of powerlinesynchronous magneticfield variations, measurement of path length fluctuations, and of the wavefronts of elliptical laser beams coupling to the ion string.

M. K. Joshi, F. Kranzl, A. Schuckert, I. Lovas, C. Maier, R. Blatt, M. Knap, C. F. Roos Observing emergent hydrodynamics in a longrange quantum magnet,
Science 376 720 (20220502),
http://dx.doi.org/10.1126/science.abk2400 doi:10.1126/science.abk2400 (ID: 720666)
Toggle Abstract
Identifying universal properties of nonequilibrium quantum states is a major challenge in modern physics. A fascinating prediction is that classical hydrodynamics emerges universally in the evolution of any interacting quantum system. Here, we experimentally probe the quantum dynamics of 51 individually controlled ions, realizing a longrange interacting spin chain. By measuring spacetime resolved correlation functions in an infinite temperature state, we observe a whole family of hydrodynamic universality classes, ranging from normal diffusion to anomalous superdiffusion, that are described by L\'evy flights. We extract the transport coefficients of the hydrodynamic theory, reflecting the microscopic properties of the system. Our observations demonstrate the potential for engineered quantum systems to provide key insights into universal properties of nonequilibrium states of quantum matter.

M. Meth, V. Kuzmin, Rick van Bijnen, L. Postler, R. Stricker, Rainer Blatt, M. Ringbauer, Thomas Monz, Pietro Silvi, Philipp Schindler Probing phases of quantum matter with an iontrap tensornetwork quantum eigensolver,
Phys. Rev. X 12 41035 (20220328),
http://dx.doi.org/10.1103/PhysRevX.12.041035 doi:10.1103/PhysRevX.12.041035 (ID: 720826)
Toggle Abstract
TensorNetwork (TN) states are efficient parametric representations of ground states of local quantum Hamiltonians extensively used in numerical simulations. Here we encode a TN ansatz state directly into a quantum simulator, which can potentially offer an exponential advantage over purely numerical simulation. In particular, we demonstrate the optimization of a quantumencoded TN ansatz state using a variational quantum eigensolver on an iontrap quantum computer by preparing the ground states of the extended SuSchriefferHeeger model. The generated states are characterized by estimating the topological invariants, verifying their topological order. Our TN encoding as a trapped ion circuit employs only singlesite addressing optical pulses  the native operations naturally available on the platform. We reduce nearestneighbor crosstalk by selecting different magnetic sublevels with wellseparated transition frequencies to encode even and odd qubits.

C. Marciniak, T. Feldker, I. Pogorelov, C. R. Kaubrügger, D. Vasilyev, R. van Bijnen, P. Schindler, P. Zoller, R. Blatt, T. Monz Optimal metrology with variational quantum circuits on trapped ions,
Nature 603 604 (20220323),
http://dx.doi.org/10.1038/s41586022044354 doi:10.1038/s41586022044354 (ID: 720667)
Toggle Abstract
Cold atoms and ions exhibit unparalleled performance in frequency metrology epitomized in the atomic clock. More recently, such atomic systems have been used to implement programmable quantum computers and simulators with highest reported operational fidelities across platforms. Their strength in metrology and quantum information processing offers the opportunity to utilize tailored, programmable entanglement generation to approach the `optimal quantum sensor' compatible with quantum mechanics. Here we report quantum enhancement in metrology beyond squeezing through lowdepth, variational quantum circuits searching for optimal input states and measurement operators in a trapped ion platform. We perform entanglementenhanced Ramsey interferometry finding optimal parameters for variational quantum circuits using a Bayesian approach to stochastic phase estimation tailored to the sensor platform capabilities and finite dynamic range of the interferometer. We verify the performance by both directly using theory predictions of optimal parameters, and performing online quantumclassical feedback optimization to `selfcalibrate' the variational parameters. In both cases we find that variational circuits outperform classical and direct spin squeezing strategies under realistic noise and imperfections. With 26 ions we achieve 2.02(8) dB of metrological gain over classical interferometers.

S. Auchter , C. Axline, C. Decaroli, M. Valentini, L. Purwin, R. Oswald, R. Matt, Elmar Aschauer, Y. Colombe, Philip Holz, Thomas Monz, Rainer Blatt, Philipp Schindler, C. Rössler, J. Home Industrially Microfabricated Ion Trap with 1 eV Trap Depth,
Quantum Sci. Technol. 7 35015 (20220217),
http://dx.doi.org/10.1088/20589565/ac7072 doi:10.1088/20589565/ac7072 (ID: 720813)
Toggle Abstract
Scaling trappedion quantum computing will require robust trapping of at least hundreds of ions over long periods, while increasing the complexity and functionality of the trap itself. Symmetric 3D structures enable high trap depth, but microfabrication techniques are generally better suited to planar structures that produce less ideal conditions for trapping. We present an ion trap fabricated on stacked 8inch wafers in a largescale MEMS microfabrication process that provides reproducible traps at a large volume. Electrodes are patterned on the surfaces of two opposing wafers bonded to a spacer, forming a 3D structure with 2.5 micrometer standard deviation in alignment across the stack. We implement a design achieving a trap depth of 1 eV for a calcium40 ion held at 200 micrometers from either electrode plane. We characterize traps, achieving measurement agreement with simulations to within +/5% for mode frequencies spanning 0.63.8 MHz, and evaluate stray electric field across multiple trapping sites. We measure motional heating rates over an extensive range of trap frequencies, and temperatures, observing 40 phonons/s at 1 MHz and 185 K. This fabrication method provides a highly scalable approach for producing a new generation of 3D ion traps.

F. Kranzl, Stefan Birnkammer, Manoj K. Joshi, Alvise Bastianello, Rainer Blatt, Michael Knap, C. F. Roos Observation of magnon bound states in the longrange, anisotropic Heisenberg model ,
(20221209),
arXiv:2212.03899 arXiv:2212.03899 (ID: 720909)
Toggle Abstract
Over the recent years coherent, timeperiodic modulation has been established as a versatile tool for realizing novel Hamiltonians. Using this approach, known as Floquet engineering, we experimentally realize a longranged, anisotropic Heisenberg model with tunable interactions in a trapped ion quantum simulator. We demonstrate that the spectrum of the model contains not only single magnon excitations but also composite magnon bound states. For the longrange interactions with the experimentally realized powerlaw exponent, the group velocity of magnons is unbounded. Nonetheless, for sufficiently strong interactions we observe bound states of these unconventional magnons which possess a nondiverging group velocity. By measuring the configurational mutual information between two disjoint intervals, we demonstrate the implications of the bound state formation on the entanglement dynamics of the system. Our observations provide key insights into the peculiar role of composite excitations in the nonequilibrium dynamics of quantum manybody systems.

H. Hainzer, D. Kiesenhofer, T. Ollikainen, Matthias Bock, F. Kranzl, Manoj K. Joshi, Goni Yoeli, Rainer Blatt, Tuvia Gefen, C. F. Roos Correlation spectroscopy with multiqubitenhanced phase estimation,
(20220325),
arXiv:2203.12656 arXiv:2203.12656 (ID: 720825)
Toggle Abstract
Precision spectroscopy on trappedion crystals subject to correlated dephasing can reveal a multitude of information in the absence of any singleparticle coherences. We use correlation spectroscopy for measuring ionion distances and transition frequency shifts in one and twodimensional ion crystals by analyzing multiparticle correlations of up to N=91 qubits, each of which is encoded in a single ion. Additionally we carry out singleshot measurements of the laserion detuning and of pathlength fluctuations. We show that the information contained in Nparticle correlations reduces the measurement uncertainty as compared to the case where only twoparticle correlations are analyzed. We derive quantum precision limits for this problem. While for a pair of qubits entanglement can reduce the measurement uncertainty, entanglementfree correlation spectroscopy becomes asymptotically optimal in the limit of N→∞ when the measurement goal is the determination of all phase differences between the qubits.

R. Stricker, J. Carrasco, M. Ringbauer, L. Postler, M. Meth, C. Edmunds, Philipp Schindler, Rainer Blatt, Peter Zoller, Barbara Kraus, Thomas Monz Towards experimental classical verification of quantum computation,
(20220314),
arXiv:2203.07395 arXiv:2203.07395 (ID: 720821)
Toggle Abstract
With today's quantum processors venturing into regimes beyond the capabilities of classical devices [13], we face the challenge to verify that these devices perform as intended, even when we cannot check their results on classical computers [4,5]. In a recent breakthrough in computer science [68], a protocol was developed that allows the verification of the output of a computation performed by an untrusted quantum device based only on classical resources. Here, we follow these ideas, and demonstrate in a first, proofofprinciple experiment a verification protocol using only classical means on a small trappedion quantum processor. We contrast this to verification protocols, which require trust and detailed hardware knowledge, as in gatelevel benchmarking [9], or additional quantum resources in case we do not have access to or trust in the device to be tested [5]. While our experimental demonstration uses a simplified version [10] of Mahadev's protocol [6] we demonstrate the necessary steps for verifying fully untrusted devices. A scaledup version of our protocol will allow for classical verification, requiring no hardware access or detailed knowledge of the tested device. Its security relies on postquantum secure trapdoor functions within an interactive proof [11]. The conceptually straightforward, but technologically challenging scaledup version of the interactive proofs, considered here, can be used for a variety of additional tasks such as verifying quantum advantage [8], generating [12] and certifying quantum randomness [7], or composable remote state preparation [13].

G. cerchiari, L. Dania, D. Bykov, R. Blatt, T. E. Northup Position measurement of a dipolar scatterer via selfhomodyne detection,
Phys. Rev. A 104 53523 (20211119),
http://dx.doi.org/10.1103/PhysRevA.104.053523 doi:10.1103/PhysRevA.104.053523 (ID: 720734)
Toggle Abstract
We describe a technique to measure the position of a dipolar scatterer based on selfhomodyne detection of the scattered light. The method can theoretically reach the Heisenberg limit, at which information gained about the position is constrained only by the back action of the scattered light. The technique has applications in the fields of levitated optomechanics and trapped ions and is generally applicable to the position determination of confined light scatterers.

C. Greganti, T. F. Demarie, M. Ringbauer, J. A. Jones, V. Saggio, I. A. Calafell, L. A. Rozema, A. Erhard, M. Meth, L. Postler, R. Stricker, P. Schindler, R. Blatt, T. Monz, P. Walther, J. F. Fitzsimons Verification of independent quantum devices,
Phys. Rev. X 11 31049 (20210901),
http://dx.doi.org/10.1103/PhysRevX.11.031049 doi:10.1103/PhysRevX.11.031049 (ID: 720502)
Toggle Abstract
Quantum computers are on the brink of surpassing the capabilities of even the most powerful classical computers. This naturally raises the question of how one can trust the results of a quantum computer when they cannot be compared to classical simulation. Here we present a verification technique that exploits the principles of measurementbased quantum computation to link quantum circuits of different input size, depth, and structure. Our approach enables consistency checks of quantum computations within a device, as well as between independent devices. We showcase our protocol by applying it to five stateoftheart quantum processors, based on four distinct physical architectures: nuclear magnetic resonance, superconducting circuits, trapped ions, and photonics, with up to 6 qubits and 200 distinct circuits.

G. cerchiari, G. Araneda, L. Podhora, L. Slodicka, Y. Colombe, R. Blatt Measuring ion oscillations at the quantum level with fluorescence light,
Phys. Rev. Lett. 127 63603 (20210804),
http://dx.doi.org/10.1103/PhysRevLett.127.063603 doi:10.1103/PhysRevLett.127.063603 (ID: 720535)
Toggle Abstract
We demonstrate an optical method for detecting the mechanical oscillations of an atom with singlephonon sensitivity. The measurement signal results from the interference between the light scattered by a single trapped atomic ion and that of its mirror image. The motion of the atom modulates the interference path length and hence the photon detection rate. We detect the oscillations of the atom in the Doppler cooling limit and reconstruct average trajectories in phase space. We demonstrate singlephonon sensitivity near the ground state of motion after EIT cooling. These results could be applied for motion detection of other light scatterers of fundamental interest, such as trapped nanoparticles.

I. Pogorelov, T. Feldker, C. Marciniak, G. Jacob, V. Podlesnic, M. Meth, V. Negnevitsky, M. Stadler, K. Lakhmanskiy, R. Blatt, P. Schindler, T. Monz A compact iontrap quantum computing demonstrator,
PRX Quantum 2 20342 (20210617),
http://dx.doi.org/10.1103/PRXQuantum.2.020343 doi:10.1103/PRXQuantum.2.020343 (ID: 720642)
Toggle Abstract
Quantum information processing is steadily progressing from a purely academic discipline towards applications throughout science and industry. Transitioning from labbased, proofofconcept experiments to robust, integrated realizations of quantum information processing hardware is an important step in this process. However, the nature of traditional laboratory setups does not offer itself readily to scaling up system sizes or allow for applications outside of laboratorygrade environments. This transition requires overcoming challenges in engineering and integration without sacrificing the stateoftheart performance of laboratory implementations. Here, we present a 19inch rack quantum computing demonstrator based on 40Ca+ optical qubits in a linear Paul trap to address many of these challenges. We outline the mechanical, optical, and electrical subsystems. Further, we describe the automation and remote access components of the quantum computing stack. We conclude by describing characterization measurements relevant to digital quantum computing including entangling operations mediated by the MolmerSorenson interaction. Using this setup we produce maximallyentangled GreenbergerHorneZeilinger states with up to 24 ions without the use of postselection or error mitigation techniques; on par with wellestablished conventional laboratory setups.

M. Teller, D. Fioretto, P. Holz, P. Schindler, V. Messerer, K. Schüppert, Y. Zou, R. Blatt, J. Chiaverini, J. Sage, T. E. Northup Heating of a Trapped Ion Induced by Dielectric Materials,
126 230505 (20210614),
http://dx.doi.org/10.1103/PhysRevLett.126.230505 doi:10.1103/PhysRevLett.126.230505 (ID: 720661)
Toggle Abstract
Electricfield noise due to surfaces disturbs the motion of nearby trapped ions, compromising the fidelity of gate operations that are the basis for quantum computing algorithms. We present a method that predicts the effect of dielectric materials on the ion’s motion. Such dielectrics are integral components of ion traps. Quantitative agreement is found between a model with no free parameters and measurements of a trapped ion in proximity to dielectric mirrors. We expect that this approach can be used to optimize the design of iontrapbased quantum computers and network nodes.

P. Holz, K. Lakhmanskiy, D. Rathje, P. Schindler, Y. Colombe, R. Blatt Electric field noise in a hightemperature superconducting surface ion trap,
Phys. Rev. B 104 64513 (20210609),
http://dx.doi.org/10.1103/PhysRevB.104.064513 doi:10.1103/PhysRevB.104.064513 (ID: 720658)
Toggle Abstract
Scaling up trappedion quantum computers requires new trap materials to be explored. Here, we present experiments with a surface ion trap made from the hightemperature superconductor YBCO, a promising material for future trap designs. We show that voltage noise from superconducting electrode leads is negligible within the sensitivity SV=9×10−20V2Hz−1 of our setup, and for lead dimensions typical for advanced trap designs. Furthermore, we investigate the frequency and temperature dependence of electric field noise above a YBCO surface. We find a 1/f spectral dependence of the noise and a nontrivial temperature dependence, with a plateau in the noise stretching over roughly 60K. The onset of the plateau coincides with the superconducting transition, indicating a connection between the dominant noise and the YBCO trap material. We exclude the YBCO bulk as origin of the noise and suggest further experiments to decide between the two remaining options explaining the observed temperature dependence: noise screening within the superconducting phase, or surface noise activated by the YBCO bulk through some unknown mechanism.

G. cerchiari, G. Araneda, L. Podhora, L. Slodicka, Y. Colombe, R. Blatt Motion analysis of a trapped ion chain by single photon selfinterference,
Appl. Phys. Lett. 119 24003 (20210416),
http://dx.doi.org/10.1063/5.0052099 doi:10.1063/5.0052099 (ID: 720641)
Toggle Abstract
We present an optical scheme to detect the oscillations of a twoion string confined in a linear Paul trap. The motion is detected by analyzing the intensity correlations in the fluorescence light emitted by one or two ions in the string. We present measurements performed under continuous Doppler cooling and under pulsed illumination. We foresee several direct applications of this detection method, including motional analysis of multiion species or coupled mechanical oscillators, and sensing of mechanical correlations.

M. I. Hussain, D. Heinrich, M. GuevaraBertsch, E. Torrontegui, J. J. GarciaRipoll, C. F. Roos, R. Blatt Ultraviolet Laser Pulses with Multigigahertz Repetition Rate and Multiwatt Average Power for Fast TrappedIon Entanglement Operations,
Phys. Rev. Applied 15 24054 (20210223),
http://dx.doi.org/10.1103/PhysRevApplied.15.024054 doi:10.1103/PhysRevApplied.15.024054 (ID: 720517)
Toggle Abstract
The conventional approach to perform twoqubit gate operations in trapped ions relies on exciting the ions on motional sidebands with laser light, which is an inherently slow process. One way to implement a fast entangling gate protocol requires a suitable pulsed laser to increase the gate speed by orders of magnitude. However, the realization of such a fast entangling gate operation presents a big technical challenge, as such the required laser source is not available offtheshelf. For this, we have engineered an ultrafast entangling gate source based on a frequency comb. The laser generates bursts of several hundred modelocked pulses with pulse energy ∼800 pJ at 5 GHz repetition rate at 393.3 nm and complies with all requirements for implementing a fast twoqubit gate operation. To verify the applicability and projected performance we run simulations based on our source parameters. The gate time can be faster than a trap period with an error approaching 10^(−4).

A. Erhard, H. Poulsen Nautrup, M. Meth, L. Postler, R. Stricker, M. Ringbauer, P. Schindler, H. J. Briegel, R. Blatt, N. Friis, T. Monz Entangling logical qubits with lattice surgery,
Nature 589 224 (20210113),
http://dx.doi.org/10.1038/s41586020030796 doi:10.1038/s41586020030796 (ID: 720515)
Toggle Abstract
Future quantum computers will require quantum error correction for faithful operation. The correction capabilities come with an overhead for performing faulttolerant logical operations on the encoded qubits. One of the most resource efficient ways to implement logical operations is lattice surgery, where groups of physical qubits, arranged on lattices, can be merged and split to realize entangling gates and teleport logical information. Here, we report on the experimental realization of lattice surgery between two topologically encoded qubits in a 10qubit ion trap quantum information processor. In particular, we demonstrate entanglement between two logical qubits and we implement logical state teleportation.

A. Seshadri, M. Ringbauer, R. Blatt, T. Monz, S. Becker Versatile fidelity estimation with confidence,
(20211215),
arXiv:2112.07925 arXiv:2112.07925 (ID: 720738)
Toggle Abstract
As quantum devices become more complex and the requirements on these devices become more demanding, it is crucial to be able to verify the performance of such devices in a scalable and reliable fashion. A cornerstone task in this challenge is quantifying how close an experimentally prepared quantum state is to the desired one. Here we present a method to construct an estimator for the quantum state fidelity that is compatible with any measurement protocol. Our method provides a confidence interval on this estimator that is guaranteed to be nearly minimax optimal for the specified measurement protocol. For a wellchosen measurement scheme, our method is competitive in the number of measurement outcomes required for estimation. We demonstrate our method using simulations and experimental data from a trappedion quantum computer and compare the results to stateoftheart techniques. Our method can be easily extended to estimate the expectation value of any observable, such as entanglement witnesses.

L. Gerster, F. MartínezGarcía, P. Hrmo, M. van Mourik, B. Wilhelm, D. Vodola, M. Mueller, R. Blatt, P. Schindler, T. Monz Experimental Bayesian calibration of trapped ion entangling operations,
(20211202),
arXiv:2112.01411 arXiv:2112.01411 (ID: 720735)
Toggle Abstract
The performance of quantum gate operations is experimentally determined by how correct operational parameters can be determined and set, and how stable these parameters can be maintained. In addition, gates acting on different sets of qubits require unique sets of control parameters. Thus, an efficient multidimensional parameter estimation procedure is crucial to calibrate even medium sized quantum processors. Here, we develop and characterize an efficient calibration protocol to automatically estimate and adjust experimental parameters of the widely used MolmerSorensen entangling gate operation in a trapped ion quantum information processor. The protocol exploits Bayesian parameter estimation methods which includes a stopping criterion based on a desired gate infidelity. We experimentally demonstrate a median gate infidelity of 1.3(1)⋅10−3, requiring only 1200±500 experimental cycles, while completing the entire gate calibration procedure in less than one minute. This approach is applicable to other quantum information processor architectures with known or sufficiently characterized theoretical models.

L. Postler, S. Heußen, I. Pogorelov, M. Rispler, T. Feldker, M. Meth, C. Marciniak, R. Stricker, M. Ringbauer, R. Blatt, P. Schindler, M. Mueller, T. Monz Demonstration of faulttolerant universal quantum gate operations,
(20211124),
arXiv:2111.12654 arXiv:2111.12654 (ID: 720736)
Toggle Abstract
Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error correcting codes. When manipulating the logical quantum states, it is imperative that errors caused by imperfect operations do not spread uncontrollably through the quantum register. This requires that all operations on the quantum register obey a faulttolerant circuit design which, in general, increases the complexity of the implementation. Here, we demonstrate a faulttolerant universal set of gates on two logical qubits in a trappedion quantum computer. In particular, we make use of the recently introduced paradigm of flag fault tolerance, where the absence or presence of dangerous errors is heralded by usage of few ancillary 'flag' qubits. We perform a logical twoqubit CNOTgate between two instances of the seven qubit color code, and we also faulttolerantly prepare a logical magic state. We then realize a faulttolerant logical Tgate by injecting the magic state via teleportation from one logical qubit onto the other. We observe the hallmark feature of fault tolerance, a superior performance compared to a nonfaulttolerant implementation. In combination with recently demonstrated repeated quantum error correction cycles these results open the door to errorcorrected universal quantum computation.

M. Ringbauer, M. Meth, L. Postler, R. Stricker, R. Blatt, P. Schindler, T. Monz A universal qudit quantum processor with trapped ions,
(20210914),
arXiv:2109.06903 arXiv:2109.06903 (ID: 720737)
Toggle Abstract
Today's quantum computers operate with a binary encoding that is the quantum analog of classical bits. Yet, the underlying quantum hardware consists of information carriers that are not necessarily binary, but typically exhibit a rich multilevel structure, which is artificially restricted to two dimensions. A wide range of applications from quantum chemistry to quantum simulation, on the other hand, would benefit from access to higherdimensional Hilbert spaces, which conventional quantum computers can only emulate. Here we demonstrate a universal qudit quantum processor using trapped ions with a local Hilbert space dimension of up to 7. With a performance similar to qubit quantum processors, this approach enables native simulation of highdimensional quantum systems, as well as more efficient implementation of qubitbased algorithms.

M. van Mourik, P. Hrmo, L. Gerster, B. Wilhelm, R. Blatt, P. Schindler, T. Monz RFinduced heating dynamics of noncrystallized trapped ions ,
(20210422),
arXiv:2104.10623 arXiv:2104.10623 (ID: 720645)
Toggle Abstract
We investigate the energy dynamics of noncrystallized (melted) ions, confined in a Paul trap. The nonperiodic Coulomb interaction experienced by melted ions forms a medium for nonconservative energy transfer from the radiofrequency (rf) field to the ions, a process known as rf heating. We study rf heating by analyzing numerical simulations of noncrystallized ion motion in Paul trap potentials, in which the energy of the ions' secular motion changes at discrete intervals, corresponding to ionion collisions. The analysis of these collisions is used as a basis to derive a simplified model of rf heating energy dynamics, from which we conclude that the rf heating rate is predominantly dependent on the rf field strength. We confirm the predictability of the model experimentally: Two trapped 40Ca+ ions are deterministically driven to melt, and their fluorescence rate is used to infer the ions' energy. From simulation and experimental results, we generalize which experimental parameters are required for efficient recrystallization of melted trapped ions.

M. C. Bañuls, R. Blatt, J. Catani, A. Celi, J. I. Cirac, M. Dalmonte, L. Fallani, K. Jansen, M. Lewenstein, S. Montangero, C. A. Muschik, B. Reznik, E. Rico Ortega, L. Tagliacozzo, K. Van Acoleyen, F. Verstraete, U. Wiese, M. Wingate, J. Zakrzewski, P. Zo Simulating Lattice Gauge Theories within Quantum Technologies,
The European Physical Journal D 74 165 (20200804),
http://dx.doi.org/10.1140/epjd/e20201005718 doi:10.1140/epjd/e20201005718 (ID: 720395)
Toggle Abstract
Lattice gauge theories, which originated from particle physics in the context of Quantum Chromodynamics (QCD), provide an important intellectual stimulus to further develop quantum information technologies. While one longterm goal is the reliable quantum simulation of currently intractable aspects of QCD itself, lattice gauge theories also play an important role in condensed matter physics and in quantum information science. In this way, lattice gauge theories provide both motivation and a framework for interdisciplinary research towards the development of special purpose digital and analog quantum simulators, and ultimately of scalable universal quantum computers. In this manuscript, recent results and new tools from a quantum science approach to study lattice gauge theories are reviewed. Two new complementary approaches are discussed: first, tensor network methods are presented  a classical simulation approach  applied to the study of lattice gauge theories together with some results on Abelian and nonAbelian lattice gauge theories. Then, recent proposals for the implementation of lattice gauge theory quantum simulators in different quantum hardware are reported, e.g., trapped ions, Rydberg atoms, and superconducting circuits. Finally, the first proofofprinciple trapped ions experimental quantum simulations of the Schwinger model are reviewed.

E. Torrontegui, D. Heinrich, M. I. Hussain, R. Blatt, J. J. GarciaRipoll Ultrafast twoqubit ion gate using sequences of resonant pulses,
New J. Phys. 22 103024 (20200703),
103024 103024 (ID: 720513)
Toggle Abstract
We propose a new protocol to implement ultrafast twoqubit phase gates with trapped ions using spindependent kicks induced by resonant transitions. By only optimizing the allocation of the arrival times in a pulse train sequence the gate is implemented in times faster than the trapping oscillation period T<2*pi/ω. Such gates allow us to increase the number of gate operations that can be completed within the coherence time of the ionqubits favoring the development of scalable quantum computers.

M. K. Joshi, A. Fabre, C. Maier, T. Brydges, D. Kiesenhofer, H. Hainzer, R. Blatt, C. F. Roos Polarizationgradient cooling of 1D and 2D ion Coulomb crystals,
New J. Phys. 22 103013 (20200629),
http://dx.doi.org/10.1088/13672630/abb912 doi:10.1088/13672630/abb912 (ID: 720512)
Toggle Abstract
We present experiments on polarization gradient cooling of Ca+ multiion Coulomb crystals in a linear Paul trap. Polarization gradient cooling of the collective modes of motion whose eigenvectors have overlap with the symmetry axis of the trap is achieved by two counterpropagating laser beams with mutually orthogonal linear polarizations that are bluedetuned from the S1/2 to P1/2 transition. We demonstrate cooling of linear chains of up to 51 ions and 2Dcrystals in zigzag configuration with 22 ions. The cooling results are compared with numerical simulations and the predictions of a simple model of cooling in a moving polarization gradient.

P. Holz, S. Auchter , G. Stocker, M. Valentini, K. Lakhmanskiy, P. Stampfer, S. Sgouridis, E. Aschauer, Y. Colombe, R. Blatt, C. Rössler Twodimensional linear trap array for quantum information processing,
Advanced Quantum Technologies 3 2000031 (20200518),
http://dx.doi.org/10.1002/qute.202000031 doi:10.1002/qute.202000031 (ID: 720490)

A. Borne, T. E. Northup, R. Blatt, B. Dayan Efficient ionphoton qubit SWAP gate in realistic ion cavityQED systems without strong coupling,
Opt. Express 28 11839 (20200413),
http://dx.doi.org/10.1364/OE.376914 doi:10.1364/OE.376914 (ID: 720492)
Toggle Abstract
We present a scheme for deterministic ionphoton qubit exchange, namely a SWAP gate, based on realistic cavityQED systems with 171Yb+, 40Ca+ and 138Ba+ ions. The gate can also serve as a singlephoton quantum memory, in which an outgoing photon heralds the successful arrival of the incoming photonic qubit. Although strong coupling, namely having the singlephoton Rabi frequency be the fastest rate in the system, is often assumed essential, this gate (similarly to the DuanKimble Cphase gate) requires only Purcell enhancement, i.e. high singleatom cooperativity. Accordingly, it does not require small mode volume cavities, which are challenging to incorporate with ions due to the difficulty of trapping them close to dielectric surfaces. Instead, larger cavities, potentially more compatible with the trap apparatus, are sufficient, as long as their numerical aperture is high enough to maintain small mode area at the ion’s position. We define the optimal parameters for the gate’s operation and simulate the expected fidelities and efficiencies, demonstrating that efficient photonion qubit exchange, a valuable building block for scalable quantum computation, is practically attainable with current experimental capabilities.

F. Ong, K. Schüppert, P. Jobez, M. Teller, B. Ames, D. Fioretto, K. Friebe, M. Lee, Y. Colombe, R. Blatt, T. E. Northup Probing surface charge densities on optical fibers with a trapped ion,
New J. Phys. 22 63018 (20200330),
http://dx.doi.org/10.1088/13672630/ab8af9 doi:10.1088/13672630/ab8af9 (ID: 720489)

R. Stricker, D. Vodola, A. Erhard, L. Postler, M. Meth, M. Ringbauer, P. Schindler, T. Monz, M. Müller, R. Blatt Experimental deterministic correction of qubit loss,
Nature 585 207 (20200221),
http://dx.doi.org/10.1038/s4158602026670 doi:10.1038/s4158602026670 (ID: 720491)

M. van Mourik, E. A. Martínez, L. Gerster, P. Hrmo, T. Monz, P. Schindler, R. Blatt Coherent rotations of qubits within a multispecies iontrap quantum computer,
Phys. Rev. A 102 22611 (20200108),
http://dx.doi.org/10.1103/PhysRevA.102.022611 doi:10.1103/PhysRevA.102.022611 (ID: 720488)

M. K. Joshi, A. Elben, B. Vermersch, T. Brydges, C. Maier, P. Zoller, R. Blatt, C. F. Roos Quantum information scrambling in a trappedion quantum simulator with tunable range interactions,
Phys. Rev. Lett. 124 240505 (20200107),
http://dx.doi.org/10.1103/PhysRevLett.124.240505 doi:10.1103/PhysRevLett.124.240505 (ID: 720436)
Toggle Abstract
In ergodic manybody quantum systems, locally encoded quantum information becomes, in the course of time evolution, inaccessible to local measurements. This concept of "scrambling" is currently of intense research interest, entailing a deep understanding of manybody dynamics such as the processes of chaos and thermalization. Here, we present first experimental demonstrations of quantum information scrambling on a 10qubit trappedion quantum simulator representing a tunable longrange interacting spin system, by estimating outoftime ordered correlators (OTOCs) through randomized measurements. We also analyze the role of decoherence in our system by comparing our measurements to numerical simulations and by measuring Rényi entanglement entropies.

A. Elben, B. Vermersch, R. van Bijnen, C. Kokail, T. Brydges, C. Maier, M. K. Joshi, R. Blatt, C. F. Roos, P. Zoller CrossPlatform Verification of Intermediate Scale Quantum Devices,
Phys. Rev. Lett. 124 10504 (20200106),
http://dx.doi.org/10.1103/PhysRevLett.124.010504 doi:10.1103/PhysRevLett.124.010504 (ID: 720357)
Toggle Abstract
We describe a protocol for crossplatform verification of quantum simulators and quantum computers. We show how to measure directly the overlap Tr[ρ1ρ2] and the purities Tr[ρ21,2], and thus a (mixedstate) fidelity, of two quantum states ρ1 and ρ2 prepared in separate experimental platforms. We require only local measurements in randomized product bases, which are communicated classically. As a proofofprinciple, we present the measurement of experimenttheory fidelities for entangled 10qubit quantum states in a trapped ion quantum simulator.

A. Erhard, J. J. Wallman, L. Postler, M. Meth, R. Stricker, E. A. Martínez, P. Schindler, T. Monz, J. Emerson, R. Blatt Characterizing largescale quantum computers via cycle benchmarking,
Nat. Commun. 10 5347 (20191125),
(ID: 720497)
Toggle Abstract
Quantum computers promise to solve certain problems more efficiently than their digital counterparts. A major challenge towards practically useful quantum computing is characterizing and reducing the various errors that accumulate during an algorithm running on largescale processors. Current characterization techniques are unable to adequately account for the exponentially large set of potential errors, including crosstalk and other correlated noise sources. Here we develop cycle benchmarking, a rigorous and practically scalable protocol for characterizing local and global errors across multiqubit quantum processors. We experimentally demonstrate its practicality by quantifying such errors in nonentangling and entangling operations on an iontrap quantum computer with up to 10 qubits, and total process fidelities for multiqubit entangling gates ranging from 99.6(1)% for 2 qubits to 86(2)% for 10 qubits. Furthermore, cycle benchmarking data validates that the error rate per singlequbit gate and per twoqubit coupling does not increase with increasing system size.

Moonjoo Lee, Minjae Lee, S. Hong, K. Schüppert, Y. D. Kwon, T. Kim, Y. Colombe, T. E. Northup, D. D. Cho, R. Blatt MEMSbased design of a highfinesse fiber cavity integrated with an ion trap,
Phys. Rev. Applied 12 (20191023),
http://dx.doi.org/10.1103/PhysRevApplied.12.044052 doi:10.1103/PhysRevApplied.12.044052 (ID: 720498)
Toggle Abstract
We present a numerical study of a microelectromechanicalsystembased design of a fiber cavity integrated with an iontrap system. Each fiber mirror is supported by a microactuator that controls the mirror’s position in three dimensions. The mechanical stability is investigated by a feasibility analysis, which shows that the actuator offers stable support of the fiber. The actuators move the fibers’ positions continuously with a stroke of more than 10μm, with mechanical resonance frequencies on the order of kilohertz. A calculation of the trapping potential shows that a separation between the ion and the fiber consistent with strong ioncavity coupling is feasible. Our miniaturized ionphoton interface constitutes a viable approach to integrated hardware for quantum information.

G. Araneda, R. Walser, Y. Colombe, D. Higginbottom, J. Volz, R. Blatt, A. Rauschenbeutel "Wavelengthscale errors in optical localization due to spin–orbit coupling of light,
Nature Phys. 15 21 (20190820),
http://dx.doi.org/10.1038/s415670180301y doi:10.1038/s415670180301y (ID: 720501)
Toggle Abstract
The precise determination of the position of pointlike emitters and scatterers using farfield optical imaging techniques is of utmost importance for a wide range of applications in medicine, biology, astronomy, and physics. Although the optical wavelength sets a fundamental limit to the image resolution of unknown objects, the position of an individual emitter can in principle be estimated from the image with arbitrary precision. This is used, e.g., in stars' position determination and in optical superresolution microscopy. Furthermore, precise position determination is an experimental prerequisite for the manipulation and measurement of individual quantum systems, such as atoms, ions, and solid statebased quantum emitters. Here we demonstrate that spinorbit coupling of light in the emission of elliptically polarized emitters can lead to systematic, wavelengthscale errors in the estimate of the emitter's position. Imaging a single trapped atom as well as a single subwavelengthdiameter gold nanoparticle, we demonstrate a shift between the emitters' measured and actual positions which is comparable to the optical wavelength. Remarkably, for certain settings, the expected shift can become arbitrarily large. Beyond their relevance for optical imaging techniques, our findings apply to the localization of objects using any type of wave that carries orbital angular momentum relative to the emitter's position with a component orthogonal to the direction of observation.

D. Heinrich, M. Guggemos, M. GuevaraBertsch, M. I. Hussain, C. F. Roos, R. Blatt Ultrafast coherent excitation of a Ca+ ion,
New J. Phys. 21 83025 (20190701),
http://dx.doi.org/10.1088/13672630/ab2a7e doi:10.1088/13672630/ab2a7e (ID: 720108)
Toggle Abstract
Trapped ions are a wellstudied and promising system for the realization of a scalable quantum computer. Faster quantum gates would greatly improve the applicability of such a system and allow for greater flexibility in the number of calculation steps. In this paper we present a pulsed laser system, delivering picosecond pulses at a repetition rate of 5 GHz and resonant to the S1/2 to P3/2 transition in Ca+ for coherent population transfer to implement fast phase gate operations. The optical pulse train is derived from a modelocked, stabilized optical frequency comb and inherits its frequency stability. Using a single trapped ion, we implement three different techniques for measuring the ionlaser coupling strength and characterizing the pulse train emitted by the laser, and show how all requirements can be met for an implementation of a fast phase gate operation.

C. Kokail, C. Maier, R. van Bijnen, T. Brydges, M. K. Joshi, P. Jurcevic, C. A. Muschik, P. Silvi, R. Blatt, C. F. Roos, P. Zoller Selfverifying variational quantum simulation of lattice models,
Nature 569 360 (20190515),
http://dx.doi.org/10.1038/s4158601911774 doi:10.1038/s4158601911774 (ID: 720076)
Toggle Abstract
Hybrid classicalquantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum coprocessor, while benefitting from quantum resources. Here we present experiments demonstrating selfverifying, hybrid, variational quantum simulation of lattice models in condensed matter and highenergy physics. Contrary to analog quantum simulation, this approach forgoes the requirement of realising the targeted Hamiltonian directly in the laboratory, thus allowing the study of a wide variety of previously intractable target models. Here, we focus on the Lattice Schwinger model, a gauge theory of 1D quantum electrodynamics. Our quantum coprocessor is a programmable, trappedion analog quantum simulator with up to 20 qubits, capable of generating families of entangled trial states respecting symmetries of the target Hamiltonian. We determine ground states, energy gaps and, by measuring variances of the Schwinger Hamiltonian, we provide algorithmic error bars for energies, thus addressing the longstanding challenge of verifying quantum simulation.

M. Mamaev, R. Blatt, J. Ye, A. M. Rey Cluster State Generation with SpinOrbit Coupled Fermionic Atoms in Optical Lattices,
Phys. Rev. Lett. 122 160402 (20190427),
http://dx.doi.org/10.1103/PhysRevLett.122.160402 doi:10.1103/PhysRevLett.122.160402 (ID: 720107)
Toggle Abstract
Measurementbased quantum computation, an alternative paradigm for quantum information processing, uses simple measurements on qubits prepared in cluster states, a class of multiparty entangled states with useful properties. Here we propose and analyze a scheme that takes advantage of the interplay between spinorbit coupling and superexchange interactions, in the presence of a coherent drive, to deterministically generate macroscopic arrays of cluster states in fermionic alkaline earth atoms trapped in three dimensional (3D) optical lattices. The scheme dynamically generates cluster states without the need of engineered transport, and is robust in the presence of holes, a typical imperfection in cold atom Mott insulators. The protocol is of particular relevance for the new generation of 3D optical lattice clocks with coherence times >10 s, two orders of magnitude larger than the cluster state generation time. We propose the use of collective measurements and timereversal of the Hamiltonian to benchmark the underlying Ising model dynamics and the generated manybody correlations.

M. Guggemos, M. GuevaraBertsch, D. Heinrich, Ó. A. Herrera, Y. Colombe, R. Blatt, C. F. Roos Frequency measurement of the 1S0,F=5/2 to 3P1,F=7/2 transition of 27Al+ via quantum logic spectroscopy with 40Ca+,
New J. Phys. 21 103003 (20190425),
http://dx.doi.org/10.1088/13672630/ab447a doi:10.1088/13672630/ab447a (ID: 720264)
Toggle Abstract
We perform quantum logic spectroscopy with a 27Al+/40Ca+ mixed ion crystal in a linear Paul trap for a measurement of the (3s2)1S0 to (3s3p)3P1,F=7/2 intercombination transition in 27Al+. Towards this end, Ramsey spectroscopy is used for probing the transition in 27Al+ and the (4s2)S1/2 to (4s3d)D5/2 clock transition in 40Ca+ in interleaved measurements. By using the precisely measured frequency of the clock transition in 40Ca+ as a frequency reference, we determine the frequency of the intercombination line to be 1S0 to 3P1,F=7/2=1122 842 857 334 736(93) Hz and the Landé gfactor of the excited state to be g3P1,F=7/2=0.428132(2).

T. Brydges, A. Elben, P. Jurcevic, B. Vermersch, C. Maier, B. P. Lanyon, P. Zoller, R. Blatt, C. F. Roos Probing Renyi entanglement entropy via randomized measurements,
Science 364 260 (20190419),
http://dx.doi.org/10.1126/science.aau4963 doi:10.1126/science.aau4963 (ID: 720034)
Toggle Abstract
Entanglement is the key feature of manybody quantum systems, and the development of new tools to probe it in the laboratory is an outstanding challenge. Measuring the entropy of different partitions of a quantum system provides a way to probe its entanglement structure. Here, we present and experimentally demonstrate a new protocol for measuring entropy, based on statistical correlations between randomized measurements. Our experiments, carried out with a trappedion quantum simulator, prove the overall coherent character of the system dynamics and reveal the growth of entanglement between its parts  both in the absence and presence of disorder. Our protocol represents a universal tool for probing and characterizing engineered quantum systems in the laboratory, applicable to arbitrary quantum states of up to several tens of qubits.

M. Lee, K. Friebe, D. Fioretto, K. Schüppert, F. Ong, D. Plankensteiner, V. Torggler, H. Ritsch, R. Blatt, T. E. Northup IonBased Quantum Sensor for Optical Cavity Photon Numbers,
Phys. Rev. Lett. 122 153603 (20190419),
http://dx.doi.org/10.1103/PhysRevLett.122.153603 doi:10.1103/PhysRevLett.122.153603 (ID: 720499)
Toggle Abstract
We dispersively couple a single trapped ion to an optical cavity to extract information about the cavity photonnumber distribution in a nondestructive way. The photonnumberdependent ac Stark shift experienced by the ion is measured via Ramsey spectroscopy. We use these measurements first to obtain the ioncavity interaction strength. Next, we reconstruct the cavity photonnumber distribution for coherent states and for a state with mixed thermalcoherent statistics, finding overlaps above 99% with the calibrated states.

C. Maier, T. Brydges, P. Jurcevic, N. Trautmann, C. Hempel, B. P. Lanyon, P. Hauke, R. Blatt, C. F. Roos Environmentassisted quantum transport in a 10qubit network,
Phys. Rev. Lett. 122 50501 (20190208),
http://dx.doi.org/10.1103/PhysRevLett.122.050501 doi:10.1103/PhysRevLett.122.050501 (ID: 720065)
Toggle Abstract
The way in which energy is transported through an interacting system governs fundamental properties in many areas of physics, chemistry, and biology. Remarkably, environmental noise can enhance the transport, an effect known as environmentassisted quantum transport (ENAQT). In this paper, we study ENAQT in a network of coupled spins subject to engineered static disorder and temporally varying dephasing noise. The interacting spin network is realized in a chain of trapped atomic ions and energy transport is represented by the transfer of electronic excitation between ions. With increasing noise strength, we observe a crossover from coherent dynamics and Anderson localization to ENAQT and finally a suppression of transport due to the quantum Zeno effect. We found that in the regime where ENAQT is most effective the transport is mainly diffusive, displaying coherences only at very short times. Further, we show that dephasing characterized by nonMarkovian noise can maintain coherences longer than white noise dephasing, with a strong influence of the spectral structure on the transport effciency. Our approach represents a controlled and scalable way to investigate quantum transport in manybody networks under static disorder and dynamic noise.

K. Lakhmanskiy, P. Holz, D. Schärtl, B. Ames, R. Assouly, T. Monz, Y. Colombe, R. Blatt Observation of superconductivity and surface noise using a single trapped ion as a field probe,
Phys. Rev. A 99 23405 (20190204),
http://dx.doi.org/10.1103/PhysRevA.99.023405 doi:10.1103/PhysRevA.99.023405 (ID: 720500)
Toggle Abstract
Measuring and understanding electricfield noise from bulk material and surfaces is important for many areas of physics. In this work, we demonstrate the probing of electricfield noise from different sources with an ion, 225μm above the trap surface. We detect noise levels as small as SE=5.2(11)×10−16V2m−2Hz−1 at ωz=2π×1.51MHz and T=12K. Our setup incorporates a controllable noise source utilizing a hightemperature superconductor. This element allows us, first, to benchmark and validate the sensitivity of our probe. Second, it allows us to probe noninvasively the bulk properties of the superconductor, observing a superconducting transition with an ion. For temperatures below the transition, we use our setup to assess different surface noise processes. The measured surface noise shows a deviation from a power law in the frequency domain. However, the temperature scaling of the data is not in a good agreement with existing surface noise models. Our results open perspectives for models in surface science and pave the way to test them experimentally.

L. Postler, A. Rivas, P. Schindler, A. Erhardt, R. Stricker, D. Nigg, T. Monz, R. Blatt, M. Müller Experimental quantification of spatial correlations in quantum dynamics,
Quantum 2 90 (20180903),
http://dx.doi.org/10.22331/q2018090390 doi:10.22331/q2018090390 (ID: 720164)
Toggle Abstract
Correlations between different partitions of quantum systems play a central role in a variety of manybody quantum systems, and they have been studied exhaustively in experimental and theoretical research. Here, we investigate dynamical correlations in the time evolution of multiple parts of a composite quantum system. A rigorous measure to quantify correlations in quantum dynamics based on a full tomographic reconstruction of the quantum process has been introduced recently [Á. Rivas et al., New Journal of Physics, 17(6) 062001 (2015).]. In this work, we derive a lower bound for this correlation measure, which does not require full knowledge of the quantum dynamics. Furthermore we also extend the correlation measure to multipartite systems. We directly apply the developed methods to a trapped ion quantum information processor to experimentally characterize the correlations in quantum dynamics for two and fourqubit systems. The method proposed and demonstrated in this work is scalable, platformindependent and applicable to other composite quantum systems and quantum information processing architectures. We apply the method to estimate spatial correlations in environmental noise processes, which are crucial for the performance of quantum error correction procedures.

C. Hempel, C. Maier, J. Romero, J. McClean, T. Monz, H. Shen, P. Jurcevic, B. P. Lanyon, P. Love, R. Babbush, A. AspuruGuzik, R. Blatt, C. F. Roos Quantum chemistry calculations on a trappedion quantum simulator,
Phys. Rev. X 8 31022 (20180724),
http://dx.doi.org/10.1103/PhysRevX.8.031022 doi:10.1103/PhysRevX.8.031022 (ID: 720003)
Toggle Abstract
Quantumclassical hybrid algorithms are emerging as promising candidates for nearterm practical applications of quantum information processors in a wide variety of fields ranging from chemistry to physics and materials science. We report on the experimental implementation of such an algorithm to solve a quantum chemistry problem, using a digital quantum simulator based on trapped ions. Specifically, we implement the variational quantum eigensolver algorithm to calculate the molecular ground state energies of two simple molecules and experimentally demonstrate and compare different encoding methods using up to four qubits. Furthermore, we discuss the impact of measurement noise as well as mitigation strategies and indicate the potential for adaptive implementations focused on reaching chemical accuracy, which may serve as a crossplatform benchmark for multiqubit quantum simulators.

G. Araneda, D. Higginbottom, L. Slodicka, Y. Colombe, R. Blatt Interference of Single Photons Emitted by Entangled Atoms in Free Space,
Phys. Rev. Lett. 120 193603 (20180511),
http://dx.doi.org/10.1103/PhysRevLett.120.193603 doi:10.1103/PhysRevLett.120.193603 (ID: 720162)
Toggle Abstract
The generation and manipulation of entanglement between isolated particles has precipitated rapid progress in quantum information processing. Entanglement is also known to play an essential role in the optical properties of atomic ensembles, but fundamental effects in the controlled emission and absorption from small, welldefined numbers of entangled emitters in free space have remained unobserved. Here we present the control of the emission rate of a single photon from a pair of distant, entangled atoms into a freespace optical mode. Changing the length of the optical path connecting the atoms modulates the singlephoton emission rate in the selected mode with a visibility V=0.27±0.03 determined by the degree of entanglement shared between the atoms, corresponding directly to the concurrence Cρ=0.31±0.10 of the prepared state. This scheme, together with population measurements, provides a fully optical determination of the amount of entanglement. Furthermore, large sensitivity of the interference phase evolution points to applications of the presented scheme in highprecision gradient sensing.

N. Friis, O. Marty, C. Maier, C. Hempel, M. Holzapfel, P. Jurcevic, M. Plenio, M. Huber, C. F. Roos, R. Blatt, B. P. Lanyon Observation of Entangled States of a Fully Controlled 20Qubit System,
Phys. Rev. X 8 21012 (20180410),
http://dx.doi.org/10.1103/PhysRevX.8.021012 doi:10.1103/PhysRevX.8.021012 (ID: 720009)
Toggle Abstract
We generate and characterize entangled states of a register of 20 individually controlled qubits, where each qubit is encoded into the electronic state of a trapped atomic ion. Entanglement is generated amongst the qubits during the outofequilibrium dynamics of an Isingtype Hamiltonian, engineered via laser fields. Since the qubitqubit interactions decay with distance, entanglement is generated at early times predominantly between neighboring groups of qubits. We characterize entanglement between these groups by designing and applying witnesses for genuine multipartite entanglement. Our results show that, during the dynamical evolution, all neighboring qubit pairs, triplets, most quadruplets, and some quintuplets simultaneously develop genuine multipartite entanglement. Witnessing genuine multipartite entanglement in larger groups of qubits in our system remains an open challenge.

A. Bermudez, X. Xu, R. Nigmatullin, J. O’Gorman, V. Negnevitsky, P. Schindler, T. Monz, U. Poschinger, C. Hempel, J. Home, F. SchmidtKaler, M. Biercuk, R. Blatt, S. Benjamin, M. Müller Assessing the Progress of TrappedIon Processors Towards FaultTolerant Quantum Computation,
Phys. Rev. X 7 41061 (20171217),
http://dx.doi.org/10.1103/PhysRevX.7.041061 doi:10.1103/PhysRevX.7.041061 (ID: 719935)
Toggle Abstract
A quantitative assessment of the progress of small prototype quantum processors towards faulttolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the wellknown QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trappedion quantum processors and, more importantly, to guide the future hardware developments that will be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trappedion toolbox for QEC and a physically motivated error model that goes beyond standard simplifications in the QEC literature. We focus on laserbased quantum gates realized in twospecies trappedion crystals in highoptical aperture segmented traps. Our largescale numerical analysis shows that, with the foreseen technological improvements described here, this platform is a very promising candidate for faulttolerant quantum computation.

B. P. Lanyon, C. Maier, M. Holzapfel, T. Baumgratz, C. Hempel, P. Jurcevic, I. Dhand, A. S. Buyskik, A. J. Daley, M. Cramer, M. Plenio, R. Blatt, C. F. Roos Efficient tomography of a quantum manybody system,
Nature Phys. 13 1158 (20171205),
http://dx.doi.org/10.1038/nphys4244 doi:10.1038/nphys4244 (ID: 719716)
Toggle Abstract
Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes impractical as the effort required grows exponentially in the number of constituents. Developing more efficient techniques is particularly pressing as preciselycontrollable quantum systems that are well beyond the reach of QST are emerging in laboratories. Motivated by this, there is a considerable ongoing effort to develop new characterisation tools for quantum manybody systems. Here we demonstrate Matrix Product State (MPS) tomography, which is theoretically proven to allow the states of a broad class of quantum systems to be accurately estimated with an effort that increases efficiently with constituent number. We first prove that this broad class includes the outofequilbrium states produced by 1D systems with finiterange interactions, up to any fixed point in time. We then use the technique to reconstruct the dynamical state of a trappedion quantum simulator comprising up to 14 entangled spins (qubits): a size far beyond the reach of QST. Our results reveal the dynamical growth of entanglement and description complexity as correlations spread out during a quench: a necessary condition for future beyondclassical performance. MPS tomography should find widespread use to study large quantum manybody systems and to benchmark and verify quantum simulators and computers.

A. Bermudez, P. Schindler, T. Monz, R. Blatt, M. Müller Micromotionenabled improvement of quantum logic gates with trapped ions,
New J. Phys. 19 113038 (20171124),
http://dx.doi.org/10.1088/13672630/aa86eb doi:10.1088/13672630/aa86eb (ID: 719937)
Toggle Abstract
The micromotion of ion crystals confined in Paul traps is usually considered an inconvenient nuisance, and is thus typically minimized in highprecision experiments such as highfidelity quantum gates for quantum information processing (QIP). In this work, we introduce a particular scheme where this behavior can be reversed, making micromotion beneficial for QIP. We show that using laserdriven micromotion sidebands, it is possible to engineer statedependent dipole forces with a reduced effect of offresonant couplings to the carrier transition. This allows one, in a certain parameter regime, to devise entangling gate schemes based on geometric phase gates with both a higher speed and a lower error, which is attractive in light of current efforts towards faulttolerant QIP. We discuss the prospects of reaching the parameters required to observe this micromotionenabled improvement in experiments with current and future trap designs.

C. A. Muschik, M. Heyl, E. A. Martínez, T. Monz, P. Schindler, B. Vogell, M. Dalmonte, P. Hauke, R. Blatt, P. Zoller U(1) Wilson lattice gauge theories in digital quantum simulators,
New J. Phys. 19 103020 (20171020),
http://dx.doi.org/10.1088/13672630/aa89ab doi:10.1088/13672630/aa89ab (ID: 719936)
Toggle Abstract
Lattice gauge theories describe fundamental phenomena in nature, but calculating their realtime dynamics on classical computers is notoriously difficult. In a recent publication (Martinez et al 2016 Nature 534 516), we proposed and experimentally demonstrated a digital quantum simulation of the paradigmatic Schwinger model, a U(1)Wilson lattice gauge theory describing the interplay between fermionic matter and gauge bosons. Here, we provide a detailed theoretical analysis of the performance and the potential of this protocol. Our strategy is based on analytically integrating out the gauge bosons, which preserves exact gauge invariance but results in complicated longrange interactions between the matter fields. Trappedion platforms are naturally suited to implementing these interactions, allowing for an efficient quantum simulation of the model, with a number of gate operations that scales polynomially with system size. Employing numerical simulations, we illustrate that relevant phenomena can be observed in larger experimental systems, using as an example the production of particle–antiparticle pairs after a quantum quench. We investigate theoretically the robustness of the scheme towards generic error sources, and show that nearfuture experiments can reach regimes where finitesize effects are insignificant. We also discuss the challenges in quantum simulating the continuum limit of the theory. Using our scheme, fundamental phenomena of lattice gauge theories can be probed using a broad set of experimentally accessible observables, including the entanglement entropy and the vacuum persistence amplitude.

P. Jurcevic, H. Shen, P. Hauke, C. Maier, T. Brydges, C. Hempel, B. P. Lanyon, M. Heyl, R. Blatt, C. F. Roos Direct observation of dynamical quantum phase transitions in an interacting manybody system,
Phys. Rev. Lett. 119 80501 (20170821),
http://dx.doi.org/10.1103/PhysRevLett.119.080501 doi:10.1103/PhysRevLett.119.080501 (ID: 719714)
Toggle Abstract
Dynamical quantum phase transitions (DQPTs) extend the concept of phase transitions and thus universality
to the nonequilibrium regime. In this letter, we investigate DQPTs in a string of ions simulating interacting transversefield Ising models. We observe nonequilibrium dynamics induced by a quantum quench and show for strings of up to 10 ions the direct detection of DQPTs by measuring a quantity that becomes nonanalytic in time in the thermodynamic limit. Moreover, we provide a link between DQPTs and the dynamics of other relevant quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.
(local copy)

C. A. Riofrio, D. Gross, S. Flammia, T. Monz, D. Nigg, R. Blatt, J. Eisert Experimental quantum compressed sensing for a sevenqubit system,
Nat. Commun. 8 15305 (20170517),
http://dx.doi.org/10.1038/ncomms1530 doi:10.1038/ncomms1530 (ID: 719934)
Toggle Abstract
Wellcontrolled quantum devices with their increasing system size face a new roadblock hindering further development of quantum technologies. The effort of quantum tomography—the reconstruction of states and processes of a quantum device—scales unfavourably: stateoftheart systems can no longer be characterized. Quantum compressed sensing mitigates this problem by reconstructing states from incomplete data. Here we present an experimental implementation of compressed tomography of a sevenqubit system—a topological colour code prepared in a trapped ion architecture. We are in the highly incomplete—127 Pauli basis measurement settings—and highly noisy—100 repetitions each—regime. Originally, compressed sensing was advocated for states with few nonzero eigenvalues. We argue that lowrank estimates are appropriate in general since statistical noise enables reliable reconstruction of only the leading eigenvectors. The remaining eigenvectors behave consistently with a randommatrix model that carries no information about the true state.

E. A. Martínez, C. A. Muschik, P. Schindler, D. Nigg, A. Erhard, M. Heyl, P. Hauke, M. Dalmonte, T. Monz, P. Zoller, R. Blatt Realtime dynamics of lattice gauge theories with a fewqubit quantum computer,
Nature 534 519 (20160622),
http://dx.doi.org/10.1038/nature18318 doi:10.1038/nature18318 (ID: 719563)
Toggle Abstract
Gauge theories are fundamental to our understanding of interactions between the elementary constituents of matter as mediated by gauge bosons. However, computing the realtime dynamics in gauge theories is a notorious challenge for classical computational methods. In the spirit of Feynman's vision of a quantum simulator, this has recently stimulated theoretical effort to devise schemes for simulating such theories on engineered quantummechanical devices, with the difficulty that gauge invariance and the associated local conservation laws (Gauss laws) need to be implemented. Here we report the first experimental demonstration of a digital quantum simulation of a lattice gauge theory, by realising 1+1dimensional quantum electrodynamics (Schwinger model) on a fewqubit trappedion quantum computer. We are interested in the realtime evolution of the Schwinger mechanism, describing the instability of the bare vacuum due to quantum fluctuations, which manifests itself in the spontaneous creation of electronpositron pairs. To make efficient use of our quantum resources, we map the original problem to a spin model by eliminating the gauge fields in favour of exotic longrange interactions, which have a direct and efficient implementation on an ion trap architecture. We explore the Schwinger mechanism of particleantiparticle generation by monitoring the mass production and the vacuum persistence amplitude. Moreover, we track the realtime evolution of entanglement in the system, which illustrates how particle creation and entanglement generation are directly related. Our work represents a first step towards quantum simulating highenergy theories with atomic physics experiments, the longterm vision being the extension to realtime quantum simulations of nonAbelian lattice gauge theories.

M. F. Brandl, M. van Mourik, L. Postler, A. Nolf, K. Lakhmanskiy, R. R. Paiva, S. Möller, N. Daniilidis, H. Häffner, V. Kaushal, T. Ruster, C. Warschburger, H. Kaufmann, U. Poschinger, F. SchmidtKaler, P. Schindler, T. Monz, R. Blatt Cryogenic setup for trapped ion quantum computing,
Review of Scientific Instruments (Online) 87 113103 (20160621),
http://dx.doi.org/10.1063/1.4966970 doi:10.1063/1.4966970 (ID: 720506)

D. Higginbottom, L. Slodicka, G. Araneda, L. Lachman, S. N. Filippov, M. Hennrich, R. Blatt Pure single photons from a trapped atom source,
New J. Phys. 18 93038 (20160621),
http://dx.doi.org/10.1088/13672630/18/9/093038 doi:10.1088/13672630/18/9/093038 (ID: 720507)

E. A. Martínez, T. Monz, D. Nigg, P. Schindler, R. Blatt Compiling quantum algorithms for architectures with multiqubit gates,
New J. Phys. 18 63029 (20160621),
http://dx.doi.org/10.1088/13672630/18/6/063029 doi:10.1088/13672630/18/6/063029 (ID: 720509)

M. F. Brandl, P. Schindler, T. Monz, R. Blatt Cryogenic resonator design for trapped ion experiments in Paul traps,
Appl. Phys. B Las. Opt. 122 157 (20160621),
http://dx.doi.org/10.1007/s003400166430z doi:10.1007/s003400166430z (ID: 720510)

M. Müller, A. Rivas, E. A. Martínez, D. Nigg, P. Schindler, T. Monz, R. Blatt, M. A. MartinDelgado Iterative phase optimization of elementary quantum error correcting codes,
Phys. Rev. X 6 31030 (20160616),
(ID: 720508)

R. Lechner, C. Maier, C. Hempel, P. Jurcevic, B. P. Lanyon, T. Monz, M. Brownnutt, R. Blatt, C. F. Roos Electromagneticallyinducedtransparency groundstate cooling of long ion strings,
Phys. Rev. A 93 53401 (20160318),
http://dx.doi.org/10.1103/PhysRevA.93.053401 doi:10.1103/PhysRevA.93.053401 (ID: 719536)
Toggle Abstract
Electromagneticallyinducedtransparency (EIT) cooling is a groundstate cooling technique for trapped particles. EIT offers a broader cooling range in frequency space compared to more established methods. In this work, we experimentally investigate EIT cooling in strings of trapped atomic ions. In strings of up to 18 ions, we demonstrate simultaneous groundstate cooling of all radial modes in under 1 ms. This is a particularly important capability in view of emerging quantum simulation experiments with large numbers of trapped ions. Our analysis of the EIT cooling dynamics is based on a technique enabling singleshot measurements of phonon numbers, by rapid adiabatic passage on a vibrational sideband of a narrow transition.

D. Nigg, T. Monz, P. Schindler, E. A. Martínez, M. Hennrich, R. Blatt, M. F. Pusey, T. Rudolph, J. Barrett Can different quantum state vectors correspond to the same physical state? An experimental test,
New J. Phys. 18 13007 (20160304),
http://dx.doi.org/10.1088/13672630/18/1/013007 doi:10.1088/13672630/18/1/013007 (ID: 719518)
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A century after the development of quantum theory, the interpretation of a quantum state is still discussed. If a physicist claims to have produced a system with a particular quantum state vector, does this represent directly a physical property of the system, or is the state vector merely a summary of the physicist's information about the system? Assume that a state vector corresponds to a probability distribution over possible values of an unknown physical or 'ontic' state. Then, a recent nogo theorem shows that distinct state vectors with overlapping distributions lead to predictions different from quantum theory. We report an experimental test of these predictions using trapped ions. Within experimental error, the results confirm quantum theory. We analyse which kinds of models are ruled out.

M. Kumph, c. Henkel, P. Rabl, M. Brownnutt, R. Blatt Electricfield noise above a thin dielectric layer on metal electrodes,
New J. Phys. 18 23020 (20160304),
http://dx.doi.org/10.1088/13672630/18/2/023020 doi:10.1088/13672630/18/2/023020 (ID: 719519)
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The electricfield noise above a layered structure composed of a planar metal electrode covered by a thin dielectric is evaluated and it is found that the dielectric film considerably increases the noise level, in proportion to its thickness. Importantly, even a thin (mono) layer of a lowloss dielectric can enhance the noise level by several orders of magnitude compared to the noise above a bare metal. Close to this layered surface, the power spectral density of the electric field varies with the inverse fourth power of the distance to the surface, rather than with the inverse square, as it would above a bare metal surface. Furthermore, compared to a clean metal, where the noise spectrum does not vary with frequency (in the radiowave and microwave bands), the dielectric layer can generate electricfield noise which scales in inverse proportion to the frequency. For various realistic scenarios, the noise levels predicted from this model are comparable to those observed in trappedion experiments. Thus, these findings are of particular importance for the understanding and mitigation of unwanted heating and decoherence in miniaturized ion traps.

M. Kumph, P. Holz, K. Langer, M. R. Meraner, M. Niedermayr, M. Brownnutt, R. Blatt Operation of a planarelectrode iontrap array with adjustable RF electrodes,
New J. Phys. 18 23047 (20160304),
http://dx.doi.org/10.1088/13672630/18/2/023047 doi:10.1088/13672630/18/2/023047 (ID: 719520)
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One path to realizing systems of trapped atomic ions suitable for largescale quantum computing and simulation is to create a twodimensional (2D) array of ion traps. Interactions between nearestneighbouring ions could then be turned on and off by tuning the ions' relative positions and frequencies. We demonstrate and characterize the operation of a planarelectrode iontrap array. By driving the trap with a network of phaselocked radiofrequency resonators which provide independently variable voltage amplitudes we vary the position and motional frequency of a Ca+ ion in twodimensions within the trap array. Work on fabricating a miniaturised form of this 2D trap array is also described, which could ultimately provide a viable architecture for largescale quantum simulations.

T. Monz, D. Nigg, E. A. Martínez, M. F. Brandl, P. Schindler, R. Rines, S. Wang, I. L. Chuang, R. Blatt Realization of a scalable Shor algorithm,
Science 351 1070 (20160304),
http://dx.doi.org/10.1126/science.aad9480 doi:10.1126/science.aad9480 (ID: 719521)
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Certain algorithms for quantum computers are able to outperform their classical counterparts. In 1994, Peter Shor came up with a quantum algorithm that calculates the prime factors of a large number vastly more efficiently than a classical computer. For general scalability of such algorithms, hardware, quantum error correction, and the algorithmic realization itself need to be extensible. Here we present the realization of a scalable Shor algorithm, as proposed by Kitaev. We factor the number 15 by effectively employing and controlling seven qubits and four “cache qubits” and by implementing generalized arithmetic operations, known as modular multipliers. This algorithm has been realized scalably within an iontrap quantum computer and returns the correct factors with a confidence level exceeding 99%.

M. Brownnutt, M. Kumph, P. Rabl, R. Blatt Iontrap measurements of electricfield noise near surfaces,
Rev. Mod. Phys. 87 1419 (20151222),
http://dx.doi.org/10.1103/RevModPhys.87.1419 doi:10.1103/RevModPhys.87.1419 (ID: 719442)
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How can the electric noise in the vicinity of a metallic body be measured and understood? Trapped ions, known as unique tools for metrology and quantum information processing, also constitute very sensitive probes of this electric noise for distances from micrometers to millimeters. This paper presents various models for the origin of the electric noise, provides a critical review of the experimental findings, and summarizes the important questions that are still open in this active research area.
Electricfield noise near surfaces is a common problem in diverse areas of physics and a limiting factor for many precision measurements. There are multiple mechanisms by which such noise is generated, many of which are poorly understood. Lasercooled, trapped ions provide one of the most sensitive systems to probe electricfield noise at MHz frequencies and over a distance range 30−3000 μm from a surface. Over recent years numerous experiments have reported spectral densities of electricfield noise inferred from ion heatingrate measurements and several different theoretical explanations for the observed noise characteristics have been proposed. This paper provides an extensive summary and critical review of electricfield noise measurements in ion traps and compares these experimental findings with known and conjectured mechanisms for the origin of this noise. This reveals that the presence of multiple noise sources, as well as the different scalings added by geometrical considerations, complicates the interpretation of these results. It is thus the purpose of this review to assess which conclusions can be reasonably drawn from the existing data, and which important questions are still open. In so doing it provides a framework for future investigations of surfacenoise processes.

B. Casabone, K. Friebe, B. Brandstätter, K. Schüppert, R. Blatt, T. E. Northup Enhanced Quantum Interface with Collective IonCavity Coupling,
Phys. Rev. Lett. 114 023602 (20151001),
http://dx.doi.org/10.1103/PhysRevLett.114.023602 doi:10.1103/PhysRevLett.114.023602 (ID: 719349)
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We prepare a maximally entangled state of two ions and couple both ions to the mode of an optical cavity. The phase of the entangled state determines the collective interaction of the ions with the cavity mode, that is, whether the emission of a single photon into the cavity is suppressed or enhanced. By adjusting this phase, we tune the ioncavity system from sub to superradiance. We then encode a single qubit in the twoion superradiant state and show that this encoding enhances the transfer of quantum information onto a photon.

M. Guggemos, D. Heinrich, Ó. A. Herrera, R. Blatt, C. F. Roos Sympathetic cooling and detection of a hot trapped ion by a cold one,
New J. Phys. 17 103001 (20150729),
http://dx.doi.org/10.1088/13672630/17/10/103001 doi:10.1088/13672630/17/10/103001 (ID: 719305)
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We investigate the dynamics of an ion sympathetically cooled by another lasercooled ion or small ion crystal. To this end, we develop simple models of the cooling dynamics in the limit of weak Coulomb interactions. Experimentally, we create a twoion crystal of Ca+ and Al+ by photoionization of neutral atoms produced by laser ablation. We characterize the velocity distribution of the laserablated atoms crossing the trap by timeresolved fluorescence spectroscopy. We observe neutral atom velocities much higher than the ones of thermally heated samples and find as a consequence long sympathethic cooling times before crystallization occurs. Our key result is a new technique for detecting the loading of an initially hot ion with energy in the eV range by monitoring the motional state of a Dopplercooled ion already present in the trap. This technique not only detects the ion but also provides information about the dynamics of the sympathetic cooling process.

P. Jurcevic, P. Hauke, C. Maier, C. Hempel, B. P. Lanyon, R. Blatt, C. F. Roos Spectroscopy of interacting quasiparticles in trapped ions,
Phys. Rev. Lett. 115 100501 (20150511),
http://dx.doi.org/10.1103/PhysRevLett.115.100501 doi:10.1103/PhysRevLett.115.100501 (ID: 719241)
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The static and dynamic properties of manybody quantum systems are often well described by collective excitations, known as quasiparticles. Engineered quantum systems offer the opportunity to study such emergent phenomena in a precisely controlled and otherwise inaccessible way. We present a spectroscopic technique to study artificial quantum matter and use it for characterizing quasiparticles in a manybody system of trapped atomic ions. Our approach is to excite combinations of the system's fundamental quasiparticle eigenmodes, given by delocalised spin waves. By observing the dynamical response to superpositions of such eigenmodes, we extract the system dispersion relation, magnetic order, and even detect signatures of quasiparticle interactions. Our technique is not limited to trapped ions, and it is suitable for verifying quantum simulators by tuning them into regimes where the collective excitations have a simple form.

B. Brandstätter, A. McClung, K. Schüppert, B. Casabone, K. Friebe, A. Stute, P. O. Schmidt, C. Deutsch , J. Reichel, R. Blatt, T. E. Northup Integrated fibermirror ion trap for strong ioncavity coupling,
Review of Scientific Instruments (Print) 84 123104 (20131217),
http://dx.doi.org/10.1063/1.4838696 doi:10.1063/1.4838696 (ID: 718695)
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We present and characterize fiber mirrors and a miniaturized iontrap design developed to integrate a fiberbased FabryPerot cavity (FFPC) with a linear Paul trap for use in cavityQED experiments with trapped ions. Our fibermirror fabrication process not only enables the construction of FFPCs with small mode volumes, but also allows us to minimize the influence of the dielectric fiber mirrors on the trappedion pseudopotential. We discuss the effect of clipping losses for long FFPCs and the effect of angular and lateral displacements on the coupling efficiencies between cavity and fiber. Optical profilometry allows us to determine the radii of curvature and ellipticities of the fiber mirrors. From finesse measurements, we infer a singleatom cooperativity of up to 12 for FFPCs longer than 200 μm in length; comparison to cavities constructed with reference substrate mirrors produced in the same coating run indicates that our FFPCs have similar scattering losses. We characterize the birefringence of our fiber mirrors, finding that careful fibermirror selection enables us to construct FFPCs with degenerate polarization modes. As FFPCs are novel devices, we describe procedures developed for handling, aligning, and cleaning them. We discuss experiments to anneal fiber mirrors and explore the influence of the atmosphere under which annealing occurs on coating losses, finding that annealing under vacuum increases the losses for our reference substrate mirrors. Xray photoelectron spectroscopy measurements indicate that these losses may be attributable to oxygen depletion in the mirror coating. Special design considerations enable us to introduce a FFPC into a trapped ion setup. Our unique linear Paul trap design provides clearance for such a cavity and is miniaturized to shield trapped ions from the dielectric fiber mirrors. We numerically calculate the trap potential in the absence of fibers. In the experiment additional electrodes can be used to compensate distortions of the potential due to the fibers. Homebuilt fiber feedthroughs connect the FFPC to external optics, and an integrated nanopositioning system affords the possibility of retracting or realigning the cavity without breaking vacuum.

P. Schindler, D. Nigg, T. Monz, J. T. Barreiro, E. A. Martínez, S. Wang, S. Quint, M. F. Brandl, V. Nebendahl, C. F. Roos, M. Chwalla, M. Hennrich, R. Blatt A quantum information processor with trapped ions,
New J. Phys. 15 123012 (20131206),
http://dx.doi.org/10.1088/13672630/15/12/123012 doi:10.1088/13672630/15/12/123012 (ID: 718676)
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Quantum computers hold the promise to solve certain problems exponentially faster than their classical counterparts. Trapped atomic ions are among the physical systems in which building such a computing device seems viable. In this work we present a smallscale quantum information processor based on a string of 40Ca+ ions confined in a macroscopic linear Paul trap. We review our set of operations which includes noncoherent operations allowing us to realize arbitrary Markovian processes. In order to build a larger quantum information processor it is mandatory to reduce the error rate of the available operations which is only possible if the physics of the noise processes is well understood. We identify the dominant noise sources in our system and discuss their effects on different algorithms. Finally we demonstrate how our entire set of operations can be used to facilitate the implementation of algorithms by examples of the quantum Fourier transform and the quantum order finding algorithm.

B. P. Lanyon, P. Jurcevic, M. Zwerger, C. Hempel, E. A. Martínez, W. Dür, H. J. Briegel, R. Blatt, C. F. Roos Measurementbased quantum computation with trapped ions,
Phys. Rev. Lett. 111 210501 (20131119),
http://dx.doi.org/10.1103/PhysRevLett.111.210501 doi:10.1103/PhysRevLett.111.210501 (ID: 718582)
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Measurementbased quantum computation represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the oneway quantum computer, with the cluster state as its universal resource. Here we demonstrate the principles of measurementbased quantum computation using deterministically generated cluster states, in a system of trapped calcium ions. First we implement a universal set of operations for quantum computing. Second we demonstrate a family of measurementbased quantum error correction codes and show their improved performance as the code length is increased. The methods presented can be directly scaled up to generate graph states of several tens of qubits.

G. Hétet, L. Slodicka, N. Röck, R. Blatt Freespace readout and control of singleion dispersion using quantum interference,
Phys. Rev. A 88 041804(R) (20131024),
http://dx.doi.org/10.1103/PhysRevA.88.041804 doi:10.1103/PhysRevA.88.041804 (ID: 718623)
Toggle Abstract
We perform a freespace measurement and control of the refractive index of a single trapped ion in the presence of quantum interference effects. The single atom refractive index is characterized by the Faraday rotation of a laser field tightly focused onto a trapped and lasercooled barium ion. It is tuned using the internal ion state that is optically controlled via a V or a Λ scheme. Measurements of the phase shift associated with an electromagnetically induced transparency are then performed and the internal state on the qubit transition is readout with a detection fidelity of (98±1)%.

B. P. Lanyon, P. Jurcevic, C. Hempel, M. Gessner, V. Vedral, R. Blatt, C. F. Roos Experimental generation of quantum discord via noisy processes,
Phys. Rev. Lett. 111 100504 (20130906),
http://dx.doi.org/10.1103/PhysRevLett.111.100504 doi:10.1103/PhysRevLett.111.100504 (ID: 718585)
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Quantum systems in mixed states can be unentangled and yet still nonclassically correlated. These correlations can be quantified by the quantum discord and might provide a resource for quantum information processing tasks. By precisely controlling the interaction of two ionicqubits with their environment, we investigate the capability of noise to generate discord. Firstly we show that noise acting only one quantum system can generate discord between two. States generated in this way are restricted in terms of the rank of their correlation matrix. Secondly we show that classicallycorrelated noise processes are capable of generating a much broader range of discordant states, with correlation matrices of any rank. Our results show that noise processes, prevalent in many physical systems, can automatically generate nonclassical correlations and highlight fundamental differences between discord and entanglement.

J. T. Barreiro, J. Bancal, P. Schindler, D. Nigg, M. Hennrich, T. Monz, N. Gisin, R. Blatt Demonstration of genuine multipartite entanglement with deviceindependent witnesses,
Nature Phys. 9 562 (20130804),
http://dx.doi.org/10.1038/nphys2705 doi:10.1038/nphys2705 (ID: 718862)
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Entanglement in a quantum system can be demonstrated experimentally by performing the measurements prescribed by an appropriate entanglement witness. However, the unavoidable mismatch between the implementation of measurements in practical devices and their precise theoretical modelling generally results in the undesired possibility of falsepositive entanglement detection. Such scenarios can be avoided by using the recently developed deviceindependent entanglement witnesses (DIEWs) for genuine multipartite entanglement. Similarly to Bell inequalities, the only assumption of DIEWs is that consistent measurements are performed locally on each subsystem. No precise description of the measurement devices is required. Here we report an experimental test of DIEWs on up to six entangled 40Ca+ ions. We also demonstrate genuine multipartite quantum nonlocality between up to six parties with the detection loophole closed.

C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, C. F. Roos Entanglementenhanced detection of singlephoton scattering events,
Nature Photon. 7 633 (20130730),
http://dx.doi.org/10.1038/nphoton.2013.172 doi:10.1038/nphoton.2013.172 (ID: 718575)
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The ability to detect the interaction of light and matter at the singleparticle level is becoming increasingly important for many areas of science and technology. The absorption or emission of a photon on a narrow transition of a trapped ion can be detected with near unit probability, thereby enabling the realization of ultraprecise ion clocks and quantum information processing applications. Extending this sensitivity to broad transitions is challenging due to the difficulty of detecting the rapid photon scattering events in this case. Here, we demonstrate a technique to detect the scattering of a single photon on a broad optical transition with high sensitivity. Our approach is to use an entangled state to amplify the tiny momentum kick an ion receives upon scattering a photon. The method should find applications in spectroscopy of atomic and molecular ions and quantum information processing.

P. Schindler, M. Müller, D. Nigg, J. T. Barreiro, E. A. Martínez, M. Hennrich, T. Monz, S. Diehl, P. Zoller, R. Blatt Quantum simulation of opensystem dynamical maps with trapped ions,
Nature Phys. 9 367 (20130519),
http://dx.doi.org/10.1038/nphys2630 doi:10.1038/nphys2630 (ID: 718325)
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Dynamical maps describe general transformations of the state of a physical system, and their iteration can be interpreted as generating a discrete time evolution. Prime examples include classical nonlinear systems undergoing transitions to chaos. Quantum mechanical counterparts show intriguing phenomena such as dynamical localization on the single particle level. Here we extend the concept of dynamical maps to an opensystem, manyparticle context: We experimentally explore the stroboscopic dynamics of a complex manybody spin model by means of a universal quantum simulator using up to five ions. In particular, we generate longrange phase coherence of spin by an iteration of purely dissipative quantum maps. We also demonstrate the characteristics of competition between combined coherent and dissipative nonequilibrium evolution. This opens the door for studying manyparticle nonequilibrium physics and associated dynamical phase transitions with no immediate counterpart in equilibrium condensed matter systems. An error detection and reduction toolbox that facilitates the faithful quantum simulation of larger systems is developed as a first step in this direction.
(local copy)

P. Bushev, G. Hétet, L. Slodicka, D. Rotter, M. A. Wilson, F. SchmidtKaler, J. Eschner, R. Blatt Shotnoiselimited monitoring and phase locking of the motion of a single trapped ion,
Phys. Rev. Lett. 110 133602 (20130327),
http://dx.doi.org/10.1103/PhysRevLett.110.133602 doi:10.1103/PhysRevLett.110.133602 (ID: 718471)
Toggle Abstract
We perform a highresolution realtime readout of the motion of a single trapped and lasercooled Ba ion. By using an interferometric setup, we demonstrate a shotnoiselimited measurement of thermal oscillations with a resolution of 4 times the standard quantum limit.We apply the realtime monitoring for phase control of the ion motion through a feedback loop, suppressing the photon recoilinduced phase diffusion. Because of the spectral narrowing in the phaselocked mode, the coherent ion oscillation is measured with a resolution of about 0.3 times the standard quantum limit

A. Stute, B. Casabone, B. Brandstätter, K. Friebe, T. E. Northup, R. Blatt Quantumstate transfer from an ion to a photon,
Nature Photon. 7 222 (20130227),
http://dx.doi.org/10.1038/nphoton.2012.358 doi:10.1038/nphoton.2012.358 (ID: 718446)

L. Slodicka, G. Hétet, N. Röck, P. Schindler, M. Hennrich, R. Blatt Atomatom entanglement by singlephoton detection,
Phys. Rev. Lett. 110 083603 (20130222),
http://dx.doi.org/10.1103/PhysRevLett.110.083603 doi:10.1103/PhysRevLett.110.083603 (ID: 718441)

P. Schindler, T. Monz, D. Nigg, J. T. Barreiro, E. A. Martínez, M. F. Brandl, M. Chwalla, M. Hennrich, R. Blatt Undoing a quantum measurement,
Phys. Rev. Lett. 110 070403 (20130214),
http://dx.doi.org/10.1103/PhysRevLett.110.070403 doi:10.1103/PhysRevLett.110.070403 (ID: 718428)

D. Nigg, J. T. Barreiro, P. Schindler, M. Mohseni, T. Monz, M. Chwalla, M. Hennrich, R. Blatt Experimental Characterization of Quantum Dynamics Through ManyBody Interactions,
Phys. Rev. Lett. 110 040603 (20130206),
http://dx.doi.org/10.1103/PhysRevLett.110.060403 doi:10.1103/PhysRevLett.110.060403 (ID: 718422)

G. Hétet, L. Slodicka, M. Hennrich, R. Blatt Single atom as a mirror of an optical cavity,
Phys. Rev. Lett. 107 133002 (20110920),
http://dx.doi.org/10.1103/PhysRevLett.107.133002 doi:10.1103/PhysRevLett.107.133002 (ID: 717769)
Toggle Abstract
By tightly focussing a laser field onto a single cold ion trapped in front of a fardistant dielectric mirror, we could observe a quantum electrodynamic effect whereby the ion behaves as the optical mirror of a FabryP\'erot cavity. We show that the amplitude of the laser field is significantly altered due to a modification of the electromagnetic mode structure around the atom in a novel regime in which the laser intensity is already changed by the atom alone. e propose a direct application of this system as a quantum memory for single photons.

B. P. Lanyon, C. Hempel, D. Nigg, M. Müller, R. Gerritsma, F. Zähringer, P. Schindler, J. T. Barreiro, M. Rambach, G. Kirchmair, M. Hennrich, P. Zoller, R. Blatt, C. F. Roos Universal Digital Quantum Simulation with Trapped Ions,
Science 334 57 (20110901),
http://dx.doi.org/10.1126/science.1208001 doi:10.1126/science.1208001 (ID: 717768)
Toggle Abstract
A digital quantum simulator is an envisioned quantum device that can be programmed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions. Using sequences of up to 100 gates and 6 qubits, the fulltime dynamics of a range of spin systems are digitally simulated. Interactions beyond those naturally present in our simulator are accurately reproduced, and quantitative bounds are provided for the overall simulation quality. Our results demonstrate the key principles of digital quantum simulation and provide evidence that the level of control required for a fullscale device is within reach.
(local copy)

M. Kumph, M. Brownnutt, R. Blatt Twodimensional arrays of radiofrequency ion traps with addressable interactions,
New J. Phys. 13 073043 (20110825),
http://dx.doi.org/10.1088/13672630/13/7/073043 doi:10.1088/13672630/13/7/073043 (ID: 717756)
Toggle Abstract
We describe the advantages of twodimensional (2D), addressable arrays of spherical Paul traps. They would provide the ability to address and tailor the interaction strengths of trapped objects in 2D and could be a valuable new tool for quantum information processing. Simulations of trapping ions are compared to first tests utilizing printed circuit board trap arrays loaded with dust particles. Pairwise interactions in the array are addressed by means of an adjustable radiofrequency (RF) electrode shared between trapping sites. By attenuating this RF electrode potential, neighboring pairs of trapped objects have their interaction strength increased and are moved closer to one another. In the limit of the adjustable electrode being held at RF ground, the two formerly spherical traps are merged into one linear Paul trap.

R. Blatt Spin flips of a single proton,
Nature 475 298 (20110731),
http://dx.doi.org/10.1038/475298a doi:10.1038/475298a (ID: 717908)

P. Schindler, J. T. Barreiro, T. Monz, V. Nebendahl, D. Nigg, M. Chwalla, M. Hennrich, R. Blatt Experimental repetitive quantum error correction,
Science 332 1059 (20110527),
http://dx.doi.org/10.1126/science.1203329 doi:10.1126/science.1203329 (ID: 717685)

M. Harlander, R. Lechner, M. Brownnutt, R. Blatt, W. Hänsel Trappedion antennae for the transmission of quantum information,
Nature 471 203 (20110405),
http://dx.doi.org/10.1038/nature09800 doi:10.1038/nature09800 (ID: 717659)
Toggle Abstract
More than one hundred years ago Heinrich Hertz succeeded in transmitting signals over a few meters to a receiving antenna using an electromagnetic oscillator and thus proving the electromagnetic theory developed by James C. Maxwell[1]. Since then, technology has developed, and today a variety of oscillators is available at the quantum mechanical level. For quantized electromagnetic oscillations atoms in cavities can be used to couple electric fields[2, 3]. For mechanical oscillators realized, for example, with cantilevers[4, 5] or vibrational modes of trapped atoms[6] or ions[7, 8], a quantum mechanical link between two such oscillators has, to date, been demonstrated in very few cases and has only been achieved in indirect ways. Examples of this include the mechanical transport of atoms carrying the quantum information[9] or the use of spontaneously emitted photons[10]. In this work, direct coupling between the motional dipoles of separately trapped ions is achieved over a distance of 54 {\mu}m, using the dipoledipole interaction as a quantummechanical transmission line[11]. This interaction is small between single trapped ions, but the coupling is amplified by using additional trapped ions as antennae. With three ions in each well the interaction is increased by a factor of seven as compared to the singleion case. This enhancement facilitates bridging of larger distances and relaxes the constraints on the miniaturization of trap electrodes. This represents a new building block for quantum computation and also offers new opportunities to couple quantum systems of different natures.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, B. Coish, M. Harlander, W. Hänsel, M. Hennrich, R. Blatt 14qubit entanglement: creation and coherence,
Phys. Rev. Lett. 106 130506 (20110405),
http://dx.doi.org/10.1103/PhysRevLett.106.130506 doi:10.1103/PhysRevLett.106.130506 (ID: 717660)
Toggle Abstract
We report the creation of GreenbergerHorneZeilinger states with up to 14 qubits. By investigating the coherence of up to 8 ions over time, we observe a decay proportional to the square of the number of qubits. The observed decay agrees with a theoretical model which assumes a system affected by correlated, Gaussian phase noise. This model holds for the majority of current experimental systems developed towards quantum computation and quantum metrology.

J. T. Barreiro, M. Müller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C. F. Roos, P. Zoller, R. Blatt An opensystem quantum simulator with trapped ions,
Nature 470 491 (20110224),
http://dx.doi.org/10.1038/nature09801 doi:10.1038/nature09801 (ID: 717617)
Toggle Abstract
The control of quantum systems is of fundamental scientific interest and promises powerful applications and
technologies. Impressive progress has been achieved in isolating quantum systems from the environment and
coherently controlling their dynamics, as demonstrated by the creation and manipulation of entanglement in various
physical systems. However, for open quantum systems, engineering the dynamics of many particles by a controlled
coupling to an environment remains largely unexplored. Here we realize an experimental toolbox for simulating an open
quantum system with up to five quantum bits (qubits). Using a quantum computing architecture with trapped ions, we
combine multiqubit gates with optical pumping to implement coherent operations and dissipative processes. We
illustrate our ability to engineer the opensystem dynamics through the dissipative preparation of entangled states,
the simulation of coherent manybody spin interactions, and the quantum nondemolition measurement of multiqubit
observables. By adding controlled dissipation to coherent operations, this work offers novel prospects for opensystem
quantum simulation and computation.
(local copy)

R. Gerritsma, B. P. Lanyon, G. Kirchmair, F. Zähringer, C. Hempel, J. Casanova, J. J. GarcíaRipoll, E. Solano, R. Blatt, C. F. Roos Quantum simulation of the Klein paradox with trapped ions,
Phys. Rev. Lett. 106 060503 (20110211),
http://dx.doi.org/10.1103/PhysRevLett.106.060503 doi:10.1103/PhysRevLett.106.060503 (ID: 717611)
Toggle Abstract
We report on quantum simulations of relativistic scattering dynamics using trapped ions. The simulated state of a scattering particle is encoded in both the electronic and vibrational state of an ion, representing the discrete and continuous components of relativistic wave functions. Multiple laser fields and an auxiliary ion simulate the dynamics generated by the Dirac equation in the presence of a scattering potential. Measurement and reconstruction of the particle wave packet enables a framebyframe visualization of the scattering processes. By precisely engineering a range of external potentials we are able to simulate text book relativistic scattering experiments and study Klein tunneling in an analogue quantum simulator. We describe extensions to solve problems that are beyond current classical computing capabilities.

G. Hétet, L. Slodicka, A. Glätzle, M. Hennrich, R. Blatt QED with a spherical mirror,
Phys. Rev. A 063812 (20101209),
http://dx.doi.org/10.1103/PhysRevA.82.063812 doi:10.1103/PhysRevA.82.063812 (ID: 717398)
Toggle Abstract
We investigate the quantum electrodynamic (QED) properties of an atomic electron close to the focus of a spherical mirror. We first show that the spontaneous emission and excitedstate level shift of the atom can be fully suppressed with mirroratom distances of many wavelengths. A threedimensional theory predicts that the spectral density of vacuum fluctuations can indeed vanish within a volume λ3 around the atom, with the use of a fardistant mirror covering only half of the atomic emission solid angle. The modification of these QED atomic properties is also computed as a function of the mirror size, and large effects are found for only moderate numerical apertures. We also evaluate the longdistance groundstate energy shift (CasimirPolder shift) and find that it scales as (λ/R)2 at the focus of a hemispherical mirror of radius R, as opposed to the wellknown (λ/R)4 scaling law for an atom at a distance R from an infinite plane mirror. Our results are relevant for investigations of QED effects as well as freespace coupling to single atoms using highnumericalaperture lenses.
(local copy)

J. T. Barreiro, P. Schindler, O. Gühne, T. Monz, M. Chwalla, C. F. Roos, M. Hennrich, R. Blatt Experimental multiparticle entanglement dynamics induced by decoherence,
Nature Phys. 6 943 (20101202),
http://dx.doi.org/10.1038/nphys1781 doi:10.1038/nphys1781 (ID: 717355)
Toggle Abstract
Multiparticle entanglement leads to richer correlations than twoparticle entanglement and gives rise to striking contradictions with local realism1, inequivalent classes of entanglement2 and applications such as oneway or topological quantum computing3, 4. When exposed to decohering or dissipative environments, multiparticle entanglement yields subtle dynamical features and access to new classes of states and applications. Here, using a string of trapped ions, we experimentally characterize the dynamics of entanglement of a multiparticle state under the influence of decoherence. By embedding an entangled state of four qubits in a decohering environment (through spontaneous decay), we observe a rich dynamics crossing distinctive domains: Bellinequality violation, entanglement superactivation, bound entanglement and full separability. We also develop new theoretical tools for characterizing entanglement in quantum states. Recent quantumcomputing, stateengineering and simulation paradigms driven by dissipative or decohering environments5, 6, 7 can benefit from the environment engineering techniques demonstrated here.

M. Harlander, M. Brownnutt, R. Blatt Trappedion probing of lightinduced charging effects on dielectrics,
12 093035 (20101006),
http://dx.doi.org/10.1088/13672630/12/9/093035 doi:10.1088/13672630/12/9/093035 (ID: 717314)
Toggle Abstract
We use a string of confined 40Ca+ ions to measure perturbations to a trapping potential which are caused by the lightinduced charging of an antireflectioncoated window and of insulating patches on the iontrap electrodes. The electric fields induced at the ions' position are characterized as a function of distance to the dielectric and as a function of the incident optical power and wavelength. The measurement of the ionstring position is sensitive to as few as 40 elementary charges per \sqrt{\rm Hz} on the dielectric at distances of the order of millimetres, and perturbations are observed for illuminations with light of wavelengths as large as 729 nm. This has important implications for the future of miniaturized iontrap experiments, notably with regard to the choice of electrode material and the optics that must be integrated in the vicinity of the ion. The method presented here can be readily applied to the investigation of charging effects beyond the context of iontrap experiments.

T. Monz, P. Schindler, J. T. Barreiro, M. Chwalla, D. Nigg, B. Coish, M. Harlander, W. Hänsel, M. Hennrich, R. Blatt Electromagnetically Induced Transparency from a Single Atom in Free Space,
Phys. Rev. Lett. 105 153604 (20101006),
http://dx.doi.org/10.1103/PhysRevLett.105.153604 doi:10.1103/PhysRevLett.105.153604 (ID: 717316)
Toggle Abstract
In this Letter, we report an absorption spectroscopy experiment and the observation of electromagnetically
induced transparency from a single trapped atom. We focus a weak and narrow band Gaussian light
beam onto an optically cooled 138Baþ ion using a high numerical aperture lens. Extinction of this beam is
observed with measured values of up to 1.35%.We demonstrate electromagnetically induced transparency
of the ion by tuning a strong control beam over a twophoton resonance in a threelevel Lambdatype system.
The probe beam extinction is inhibited by more than 75% due to population trapping.

F. Dubin, C. Russo, H. Barros, A. Stute, C. Becher, P. O. Schmidt, R. Blatt Quantum to classical transition in a singleion laser,
Nature Phys. 6 350 (20100329),
http://dx.doi.org/10.1038/NPHYS1627 doi:10.1038/NPHYS1627 (ID: 717177)

A. Glätzle, K. Hammerer, A. J. Daley, R. Blatt, P. Zoller A single trapped atom in front of an oscillating mirror,
Opt. Com. 283 765 (20100315),
http://dx.doi.org/10.1016/j.optcom.2009.10.063 doi:10.1016/j.optcom.2009.10.063 (ID: 717009)
Toggle Abstract
We investigate the Wigner–Weisskopf decay of a twolevel atom in front of an oscillating mirror. This work builds on and extends previous theoretical and experimental studies of the effects of a static mirror on spontaneous decay and resonance fluorescence. The spontaneously emitted field is inherently nonstationary due to the timedependent boundary conditions and in order to study its spectral distribution we employ the operational definition of the spectrum of nonstationary light due to the seminal work by Eberly and Wódkiewicz. We find a rich dependence of this spectrum as well as of the effective decay rates and level shifts on the mirror–atom distance and on the amplitude and frequency of the mirror’s oscillations. The results presented here provide the basis for future studies of more complex setups, where the motion of the atom and/or the mirror are included as quantum degrees of freedom.
(local copy)

F. Zähringer, G. Kirchmair, R. Gerritsma, E. Solano, R. Blatt, C. F. Roos Realization of a Quantum Walk with One and Two Trapped Ions,
Phys. Rev. Lett. 104 100503 (20100309),
http://dx.doi.org/10.1103/PhysRevLett.104.100503 doi:10.1103/PhysRevLett.104.100503 (ID: 717148)

R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C. F. Roos Quantum simulation of the Dirac equation,
Nature 463 71 (20100107),
http://dx.doi.org/10.1038/nature08688 doi:10.1038/nature08688 (ID: 716977)

P. Zoller, T. Beth, D. Binosi, R. Blatt, H. J. Briegel, D. Bruss, T. Calarco, J. I. Cirac, D. Deutsch, J. Eisert, A. Ekert, C. Fabre, N. Gisin, P. Grangiere, M. Grassl, S. Haroche, A. Imamoglu, A. Karlson, J. Kempe, L. Louwenhofen, S. Kröll, G. Leuchs, M. Quantum information processing and communication,
Eur. Phys. J. D 36/2 203  228 (20051101),
http://dx.doi.org/10.1140/epjd/e2005002511 doi:10.1140/epjd/e2005002511 (ID: 375863)
Toggle Abstract
We present an excerpt of the document “Quantum Information Processing and Communication: Strategic report on current status, visions and goals for research in Europe”, which has been recently published in electronic form at the website of FET (the Future and Emerging Technologies Unit of the Directorate General Information Society of the European Commission, http://www.cordis.lu/ist/fet/qipcsr.htm). This document has been elaborated, following a former suggestion by FET, by a committee of QIPC scientists to provide input towards the European Commission for the preparation of the Seventh Framework Program. Besides being a document addressed to policy makers and funding agencies (both at the European and national level), the document contains a detailed scientific assessment of the stateoftheart, main research goals, challenges, strengths, weaknesses, visions and perspectives of all the most relevant QIPC subfields, that we report here. Dedicated to the memory of Prof. Th. Beth, one of the pioneers of QIPC, whose contributions have had a significant scientific impact on the development as well as on the visibility of a field that he enthusiastically helped to shape since its early days.

L. Tian, R. Blatt, P. Zoller Scalable ion trap quantum computing without moving ions,
Eur. Phys. J. D 32 201208 (2005),
http://dx.doi.org/10.1140/epjd/e2004001725 doi:10.1140/epjd/e2004001725 (ID: 308239)
Toggle Abstract
A hybrid quantum computing scheme is studied where the hybrid qubit is made of an ion trap qubit serving as the information storage and a solidstate charge qubit serving as the quantum processor, connected by a superconducting cavity. In this paper, we extend our previous work [1] and study the decoherence, coupling and scalability of the hybrid system. We present our calculations of the decoherence of the coupled ioncharge system due to the charge fluctuations in the solidstate system and the dissipation of the superconducting cavity under laser radiation. A gate scheme that exploits rapid state flips of the charge qubit to reduce decoherence by the charge noise is designed. We also study a superconducting switch that is inserted between the cavity and the charge qubit and provides tunable coupling between the qubits. The scalability of the hybrid scheme is discussed together with several potential experimental obstacles in realizing this scheme.

H. Häffner, W. Hänsel, C. Roos, J. Benhelm, D. ChekalKar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, R. Blatt Scalable multiparticle entanglement of trapped ions,
Nature 438 646 (2005),
http://dx.doi.org/10.1038/nature04279 doi:10.1038/nature04279 (ID: 314190)
Toggle Abstract
The generation, manipulation and fundamental understanding of entanglement lies at the very heart of quantum mechanics. Entangled particles are noninteracting but are described by a common wavefunction; consequently, individual particles are not independent of each other and their quantum properties are inextricably interwoven. The intriguing features of entanglement become particularly evident if the particles can be individually controlled and physically separated. However, both the experimental realization and characterization of entanglement become exceedingly difficult for systems with many particles. The main difficulty is to manipulate and detect the quantum state of individual particles as well as to control the interaction between them. So far, entanglement of four ions or five photons has been demonstrated experimentally. The creation of scalable multiparticle entanglement demands a nonexponential scaling of resources with particle number. Among the various kinds of entangled states, the 'W state' plays an important role as its entanglement is maximally persistent and robust even under particle loss. Such states are central as a resource in quantum information processing and multiparty quantum communication. Here we report the scalable and deterministic generation of four, five, six, seven and eightparticle entangled states of the W type with trapped ions. We obtain the maximum possible information on these states by performing full characterization via state tomography, using individual control and detection of the ions. A detailed analysis proves that the entanglement is genuine. The availability of such multiparticle entangled states, together with full information in the form of their density matrices, creates a testbed for theoretical studies of multiparticle entanglement. Independently, 'Greenberger–Horne–Zeilinger' entangled states with up to six ions have been created and analysed in Boulder.

H. Häffner, F. SchmidtKaler, W. Hänsel, C. Roos, T. Körber, M. Chwalla, J. Benhelm, U. D. Rapol, C. Becher, R. Blatt Robust Entanglement,
81 151 (2005),
(ID: 314806)
Toggle Abstract
It is common belief among physicists that entangled states of quantum
systems lose their coherence rather quickly. The reason is that any interaction with
the environment which distinguishes between the entangled subsystems collapses
the quantum state. Here we investigate entangled states of two trapped Ca+ ions
and observe robust entanglement lasting for more than 20 s.
(local copy)

A. Kreuter, C. Becher, G. Lancaster, A. B. Mundt, C. Russo, H. Häffner, C. Roos, W. Hänsel, F. SchmidtKaler, R. Blatt, M. Safronova New experimental and theoretical approach to the 3d ²Dlevel lifetimes of ⁴⁰Ca⁺,
Phys. Rev. A 71 032504 (2005),
(ID: 314807)
(local copy)

R. Blatt Ionen in Reih und Glied,
Physik Journal 4, Nr. 11 37 (2005),
(ID: 327389)
Toggle Abstract
Ist eine Münze gezinkt oder nicht, d. h. weist
sie Kopf und Zahl auf oder stimmen beide Seiten
überein? Ein einfacher Quantenalgorithmus
erlaubt es, diese Frage mit nur einem Blick auf
die Münze statt zweien zu beantworten. Der
„Rechner“, auf dem dieser Algorithmus ausgeführt
wird, besteht nicht aus Transistoren, sondern
aus kalten, eingesperrten Ionen.
(local copy)

L. Tian, P. Rabl, R. Blatt, P. Zoller Interfacing QuantumOptical and SolidState Qubits,
Phys. Rev. Lett. 92 247902 (2004),
http://dx.doi.org/10.1103/PhysRevLett.92.247902 doi:10.1103/PhysRevLett.92.247902 (ID: 314633)
Toggle Abstract
We present a generic model of coupling quantumoptical and solidstate qubits, and the corresponding transfer protocols. The example discussed is a trapped ion coupled to a charge qubit (e.g., Cooper pair box). To enhance the coupling and to achieve compatibility between the different experimental setups we introduce a superconducting cavity as the connecting element.

C. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. Lancaster, C. Becher, F. SchmidtKaler, R. Blatt Control and Measurment of ThreeQubit Entangled States,
Science 304 1478 (2004),
(ID: 342102)
Toggle Abstract
We report the deterministic creation of maximally entangled threequbit
states—specifically the GreenbergerHorneZeilinger (GHZ ) state and the
W state—with a trappedion quantum computer.We read out one of the
qubits selectively and show how GHZ andWstates are affected by this local
measurement.Additionally, we demonstrate conditional operations controlled
by the results from reading out one qubit.Tripartite entanglement
is deterministically transformed into bipartite entanglement by local operations
only.These operations are the measurement of one qubit of a GHZ
state in a rotated basis and, conditioned on this measurement result, the
application of singlequbit rotations.
(local copy)

C. Roos, G. Lancaster, M. Riebe, H. Häffner, W. Hänsel, S. Gulde, C. Becher, J. Eschner, F. SchmidtKaler, R. Blatt Bell States of Atoms with Ultralong Lifetimes and Their Tomographic State Analysis,
Phys. Rev. Lett. 92 220402 (2004),
(ID: 342103)
Toggle Abstract
Arbitrary atomic Bell states with two trapped ions are generated in a deterministic and preprogrammed way. The resulting entanglement is quantitatively analyzed using various measures of entanglement. For this, we reconstruct the density matrix using single qubit rotations and subsequent measurements with nearunity detection efficiency. This procedure represents the basic building block for future process tomography of quantum computations. As a first application, the temporal decay of entanglement is investigated in detail.We observe ultralong lifetimes for the Bell states, close to the fundamental limit set by the spontaneous emission from the metastable upper qubit level and longer than all reported values by 3 orders of magnitude.

S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, H. Häffner, F. SchmidtKaler, R. Blatt Quantized ACStark shifts and their use for multiparticle entanglement and quantum gates,
65 587 (2004),
(ID: 342104)

A. Kreuter, C. Becher, G. Lancaster, A. B. Mundt, C. Russo, H. Häffner, C. Roos, J. Eschner, F. SchmidtKaler, R. Blatt Spontaneous Emission Lifetime of a Single Trapped Ca+ Ion in a High Finesse Cavity,
Phys. Rev. Lett. 92 203002 (2004),
(ID: 342120)

C. Maurer, C. Becher, C. Russo, J. Eschner, R. Blatt A singlephoton source based on a single Ca+ ion,
New J. Phys. 6 94 (2004),
(ID: 343914)
Toggle Abstract
We propose a deterministic source of single photons based on the
vacuumstimulated Raman transition of a single Ca+ ion trapped inside a high
finesse cavity. Assuming realistic experimental parameters, the efficiency of
photon emission into the cavity mode reaches 95%.
(local copy)

P. Bushev, M. A. Wilson, J. Eschner, C. Raab, F. SchmidtKaler, C. Becher, R. Blatt Forces between a Single Atom and Its Distant Mirror Image,
Phys. Rev. Lett. 92 223602 (2004),
(ID: 343934)
Toggle Abstract
An excitedstate atom whose emitted light is backreflected by a distant mirror can experience
trapping forces, because the presence of the mirror modifies both the electromagnetic vacuum field and
the atom’s own radiation reaction field.We demonstrate this mechanical action using a single trapped
barium ion. We observe the trapping conditions to be notably altered when the distant mirror is
translated across an optical wavelength. The welllocalized barium ion enables the spatial dependence
of the forces to be measured explicitly. The experiment has implications for quantum information
processing and may be regarded as the most elementary optical tweezers.

R. Blatt, H. Häffner, C. Roos, C. Becher, F. SchmidtKaler Ion Trap Quantum Computing with Ca+ Ions,
Quant. Inf. Proc. 3 15 (2004),
(ID: 513993)

M. Riebe, H. Häffner, C. Roos, W. Hänsel, J. Benhelm, G. Lancaster, T. Körber, C. Becher, F. SchmidtKaler, D. James, R. Blatt Deterministic quantum teleportation with atoms,
Nature 429 734 (2004),
(ID: 520666)
Toggle Abstract
Teleportation of a quantum state encompasses the complete
transfer of information from one particle to another. The complete
specification of the quantum state of a system generally
requires an infinite amount of information, even for simple twolevel
systems (qubits). Moreover, the principles of quantum
mechanics dictate that any measurement on a system immediately
alters its state, while yielding at most one bit of information.
The transfer of a state from one system to another (by performing
measurements on the first and operations on the second) might
therefore appear impossible. However, it has been shown1 that
the entangling properties of quantum mechanics, in combination
with classical communication, allow quantumstate teleportation
to be performed. Teleportation using pairs of
entangled photons has been demonstrated2–6, but such techniques
are probabilistic, requiring postselection of measured
photons. Here, we report deterministic quantumstate teleportation
between a pair of trapped calcium ions. Following closely the
original proposal1, we create a highly entangled pair of ions and
perform a complete Bellstate measurement involving one ion
from this pair and a third source ion. State reconstruction
conditioned on this measurement is then performed on the
other half of the entangled pair. The measured fidelity is 75%,
demonstrating unequivocally the quantum nature of the process.
(local copy)

F. SchmidtKaler, H. Häffner, S. Gulde, M. Riebe, G. Lancaster, T. Deuschle, C. Becher, W. Hänsel, J. Eschner, C. Roos, R. Blatt How to realize a universal quantum gate with trapped ions,
Appl. Phys. B Las. Opt. 77 789 (2003),
http://dx.doi.org/10.1007/s0034000313469 doi:10.1007/s0034000313469 (ID: 342105)
Toggle Abstract
We report the realization of an elementary quantum
processor based on a linear crystal of trapped ions. Each
ion serves as a quantum bit (qubit) to store the quantum information
in long lived electronic states.We present the realization
of singlequbit and of universal twoqubit logic gates. The twoqubit
operation relies on the coupling of the ions through their
collective quantized motion. A detailed description of the setup
and the methods is included.

G. Lancaster, H. Häffner, M. A. Wilson, C. Becher, J. Eschner, F. SchmidtKaler, R. Blatt Doppler cooling a single Ca+ ion with a violet extendedcavity diode laser,
Appl. Phys. B Las. Opt. 76 805 (2003),
(ID: 342107)
Toggle Abstract
We present a scheme for employing a violet
extendedcavity diode laser in experiments with single, trapped
ions. For this the gratingstabilised laser is spatially and spectrally
filtered and referenced to a Fabry–P´erot cavity. We measure
an upper limit to the line width by observing a 305kHz
FWHM beat note with the second harmonic of a titanium sapphire
laser. The laser is subsequently used to optically cool
a single 40Ca+ ion close to the Doppler limit.

H. Häffner, S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. SchmidtKaler, R. Blatt Precision measurement and compensation of optical Stark shifts for an iontrap quantum processor,
Phys. Rev. Lett. 90 143602 (2003),
(ID: 342109)

F. SchmidtKaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, R. Blatt Realization of the CiracZoller controlledNOT quantum gate,
Nature 422 408 (2003),
(ID: 342111)
Toggle Abstract
Quantum computers have the potential to perform certain
computational tasks more efficiently than their classical counterparts.
The Cirac–Zoller proposal1 for a scalable quantum computer
is based on a string of trapped ions whose electronic states
represent the quantum bits of information (or qubits). In this
scheme, quantum logical gates involving any subset of ions are
realized by coupling the ions through their collective quantized
motion. The main experimental step towards realizing the
scheme is to implement the controlledNOT (CNOT) gate operation
between two individual ions. The CNOT quantum logical
gate corresponds to the XOR gate operation of classical logic that
flips the state of a target bit conditioned on the state of a control
bit. Here we implement a CNOT quantum gate according to the
Cirac–Zoller proposal1. In our experiment, two 40Ca1 ions are
held in a linear Paul trap and are individually addressed using
focused laser beams2; the qubits3 are represented by superpositions
of two longlived electronic states. Our work relies onrecently developed
precise control of atomic phases4 and the
application of composite pulse sequences adapted from nuclear
magnetic resonance techniques5,6.

S. Gulde, M. Riebe, G. Lancaster, C. Becher, J. Eschner, H. Häffner, F. SchmidtKaler, I. L. Chuang, R. Blatt Implementing the DeutschJozsa algorithm on an iontrap quantum computer,
Nature 421 4850 (2003),
(ID: 342116)
Toggle Abstract
Determining classically whether a coin is fair (head on one side,
tail on the other) or fake (heads or tails on both sides) requires an
examination of each side. However, the analogous quantum
procedure (the Deutsch–Jozsa algorithm1,2) requires just one
examination step. The Deutsch–Jozsa algorithm has been realized
experimentally using bulk nuclear magnetic resonance
techniques3,4, employing nuclear spins as quantum bits (qubits).
In contrast, the ion trap processor utilises5 motional and electronic
quantum states of individual atoms as qubits, and in
principle is easier to scale to many qubits. Experimental advances
in the latter area include the realization of a twoqubit quantum
gate6, the entanglement of four ions7, quantum state engineering8
and entanglementenhanced phase estimation9. Here we exploit
techniques10,11 developed for nuclear magnetic resonance to
implement the Deutsch–Jozsa algorithm on an iontrap quantum
processor, using as qubits the electronic and motional states of a
single calcium ion. Our ionbased implementation of a full
quantum algorithm serves to demonstrate experimental procedures
with the quality and precision required for complex
computations, confirming the potential of trapped ions for
quantum computation.

F. SchmidtKaler, S. Gulde, M. Riebe, T. Deuschle, A. Kreuter, G. Lancaster, C. Becher, J. Eschner, H. Häffner, R. Blatt Coherence of qubits based on single Ca+ ions,
J. Phys. B: At. Mol. Opt. Phys. 36 623636 (2003),
(ID: 342123)

M. A. Wilson, P. Bushev, J. Eschner, F. SchmidtKaler, C. Becher, R. Blatt, U. Dorner Vacuumfield level shifts in a single trapped ion mediated by a single distant mirror,
Phys. Rev. Lett. 91 213602 (2003),
(ID: 343935)
Toggle Abstract
A distant mirror leads to a vacuuminduced level shift in a laserexcited atom. This effect has been
measured with a single mirror 25 cm away from a single, trapped barium ion. This dispersive action is
the counterpart to the mirror’s dissipative effect, which has been shown earlier to effect a change in the
ion’s spontaneous decay [J. Eschner et al., Nature (London) 413, 495 (2001)]. The experimental data are
well described by eightlevel optical Bloch equations which are amended to take into account the
presence of the mirror according to the model in U. Dorner and P. Zoller, Phys. Rev. A 66, 023816
(2002). Observed deviations from simple dispersive behavior are attributed to multilevel effects.

J. Eschner, G. Morigi, F. SchmidtKaler, R. Blatt Laser cooling of trapped ions,
J. Opt. Soc. Am. B 20 1003 (2003),
(ID: 343940)
Toggle Abstract
Trapped and lasercooled ions are increasingly used for a variety of modern highprecision experiments, for
frequency standard applications, and for quantum information processing. Therefore laser cooling of trapped
ions is reviewed, the current state of the art is reported, and several new cooling techniques are outlined. The
principles of ion trapping and the basic concepts of laser cooling for trapped atoms are introduced. The underlying
physical mechanisms are presented, and basic experiments are briefly sketched. Particular attention
is paid to recent progress by elucidating several milestone experiments. In addition, a number of special
cooling techniques pertaining to trapped ions are reviewed; open questions and future research lines are indicated.

D. Leibfried, R. Blatt, C. Monroe, D. Wineland Quantum dynamics of single trapped ions,
Rev. Mod. Phys. 75 281 (2003),
(ID: 343943)
Toggle Abstract
Single trapped ions represent elementary quantum systems that are well isolated from the
environment. They can be brought nearly to rest by laser cooling, and both their internal electronic states and external motion can be coupled to and manipulated by light fields. This makes them ideally suited for quantumoptical and quantumdynamical studies under wellcontrolled conditions. Theoretical and experimental work on these topics is reviewed in the paper, with a focus on ions trapped in radiofrequency (Paul) traps.

A. B. Mundt, A. Kreuter, C. Russo, C. Becher, D. Leibfried, J. Eschner, F. SchmidtKaler, R. Blatt Coherent coupling of a single Ca+ ion to a highfinesse optical cavity,
Appl. Phys. B Las. Opt. 76 117124 (2003),
(ID: 343950)
Toggle Abstract
We demonstrate coherent coupling of the quadrupole
S1/2 ↔ D5/2 optical transition of a single trapped 40Ca+
ion to the standing wave field of a highfinesse cavity. The
dependence of the coupling on temporal dynamics and spatial
variations of the intracavity field is investigated in detail.
By precisely controlling the position of the ion in the cavity
standing wave field and by selectively exciting vibrational statechanging
transitions the ion’s quantized vibration in the trap
is deterministically coupled to the cavity mode. We confirm
coherent interaction of ion and cavity field by exciting Rabi
oscillations with short resonant laser pulses injected into the
cavity, which is frequencystabilized to the atomic transition.

S. Gulde, H. Häffner, M. Riebe, G. Lancaster, C. Becher, J. Eschner, F. SchmidtKaler, I. L. Chuang, R. Blatt Quantum information Processing with Trapped Ca+ ions,
Phil. Trans. R. Soc. Lond. A 361 112 (2003),
(ID: 619585)

J. Eschner, C. Raab, A. B. Mundt, A. Kreuter, C. Becher, F. SchmidtKaler, R. Blatt Single trapped ions interacting with low und highfinesse optical cavities,
Fortschr. Phys. 51 359368 (2003),
(ID: 619586)

J. Eschner, C. Raab, F. SchmidtKaler, R. Blatt Light interference from single atoms and their mirror images,
Nature 413 495498 (2001),
(ID: 343953)
Toggle Abstract
A single atom emitting single photons is a fundamental source of
light. But the characteristics of this light depend strongly on the
environment of the atom1,2. For example, if an atom is placed
between two mirrors, both the total rate and the spectral composition
of the spontaneous emission can be modi®ed. Such effects
have been observed using various systems: molecules deposited on
mirrors3, dye molecules in an optical cavity4, an atom beam
traversing a twomirror optical resonator5±8, single atoms traversing
a microwave cavity9±11 and a single trapped electron12. A
related and equally fundamental phenomenon is the optical
interaction between two atoms of the same kind when their
separation is comparable to their emission wavelength. In this
situation, light emitted by one atom may be reabsorbed by the
other, leading to cooperative processes in the emission13,14. Here
we observe these phenomena with high visibility by using one or
two single atom(s), a collimating lens and a mirror, and by
recording the individual photons scattered by the atom(s). Our
experiments highlight the intimate connection between oneatom
and twoatom effects, and allow their continuous observation
using the same apparatus.

S. Gulde, D. Rotter, P. Barton, F. SchmidtKaler, R. Blatt, W. Hogervorst Simple and efficient photoionization loading of ions for precision iontrapping experiments,
Appl. Phys. B Las. Opt. 73 861863 (2001),
(ID: 343955)
Toggle Abstract
We report a simple and efficient method to load a Paul trap with Ca+ ions.
A beam of neutral atomic calcium is ionized in a twostep photoionization process
using uvdiode lasers near 423 nm and 390 nm. Photoionization of a calcium beam
for loading a Paul trap has first been demonstrated by Kjærgaard et al. The advantages
of ourmethod are the use of cheap and easily handled diodelaser systems and the large
cross section for field ionization when exciting highlying Rydberg states. Finally, we
discuss the advantages of photoionization for ion generation compared to loading by
electron bombardment

R. Blatt Delicate information,
Nature 412 773 (2001),
(ID: 343960)

F. SchmidtKaler, J. Eschner, G. Morigi, C. Roos, D. Leibfried, A. B. Mundt, R. Blatt Laser cooling with electromagnetically induced transparency: Application to trapped samples of ions or neutral atoms,
Appl. Phys. B Las. Opt. 73 807 (2001),
(ID: 343962)
Toggle Abstract
A novel method of groundstate laser cooling of
trapped atoms utilizes the absorption profile of a three (or
multi) level system that is tailored by a quantum interference.
With cooling rates comparable to conventional sideband cooling,
lower final temperatures may be achieved. The method was
experimentally implemented to cool a single Ca+ ion to its
vibrational ground state. Since a broad band of vibrational frequencies
can be cooled simultaneously, the technique will be
particularly useful for the cooling of larger ion strings, thereby
being of great practical importance for initializing a quantum
register based on trapped ions.We also discuss its application to
different level schemes and for groundstate cooling of neutral
atoms trapped by a fardetuned standing wave laser field.

H. Rohde, S. Gulde, C. Roos, P. Barton, D. Leibfried, J. Eschner, F. SchmidtKaler, R. Blatt Sympathetic ground state cooling and coherent manipulation with twoioncrystals,
J. Opt. B: Quantum Semiclass. Opt. 3 34 (2001),
(ID: 469819)

C. Roos, D. Leibfried, A. B. Mundt, F. SchmidtKaler, J. Eschner, R. Blatt Experimental demonstration of ground state laser cooling with electromagnetically induced transparency,
Phys. Rev. Lett. 85 5547 (2000),
(ID: 344232)
Toggle Abstract
A laser cooling method for trapped atoms is described which achieves ground state cooling by exploiting
quantum interference in a driven Lshaped arrangement of atomic levels. The scheme is technically
simpler than existing methods of sideband cooling, yet it can be significantly more efficient, in particular
when several motional modes are involved, and it does not impose restrictions on the transition linewidth.
We study the full quantum mechanical model of the cooling process for one motional degree of freedom
and show that a rate equation provides a good approximation.

H. Rohde, S. Gulde, C. Roos, P. Barton, D. Leibfried, J. Eschner, F. SchmidtKaler, R. Blatt Sympathetic ground state cooling and coherent manipulation with twoioncrystals,
J. Opt. B: Quantum Semiclass. Opt. 3 S3 (2000),
(ID: 344234)
Toggle Abstract
We have cooled a twoion crystal to the groundstate of its collective modes
of motion. Laser cooling, more specifically resolved sideband cooling, is
performed sympathetically by illuminating only one of the two 40Ca+ ions in
the crystal. The heating rates of the motional modes of the crystal in our
linear trap have been measured, and we found them considerably smaller
than those previously reported by Turchette et al (2000 Phys.Rev.A 61
063418) in the case of trapped 9Be+ ions. After the ground state is prepared,
coherent quantum state manipulation of the atomic population can be
performed. Up to 12 Rabi oscillations are observed, showing that many
coherent manipulations can be achieved. Coherent excitation of each ion
individually and ground state cooling are important tools for the realization
of quantum information processing in ion traps.

R. Blatt Pushbutton entanglement,
Nature 404 231 (2000),
(ID: 344235)
Toggle Abstract
Quantum mechanics allows matter to be prepared in a strangely correlated
way called entanglement. In future, large numbers of entangled particles may
be put to work in quantum computers and precise quantum measurements.

A. Steane, C. Roos, D. Stevens, A. B. Mundt, D. Leibfried, F. SchmidtKaler, R. Blatt Speed of ion trap quantum information processors,
Phys. Rev. A 62 042305 (2000),
(ID: 344236)
Toggle Abstract
We investigate theoretically the speed limit of quantum gate operations for ion trap quantum information processors. The proposed methods use laser pulses for quantum gates that entangle the electronic and vibrational degrees of freedom of the trapped ions. Two of these methods are studied in detail and for both of them the speed is limited by a combination of the recoil frequency of the relevant electronic transition, and the
vibrational frequency in the trap. We have experimentally studied the gate operations below and above this
speed limit. In the latter case, the fidelity is reduced, in agreement with our theoretical findings.

C. Raab, J. Eschner, J. Bolle, H. Oberst, F. SchmidtKaler, R. Blatt Motional sidebands and direct measurement of the cooling rate in the resonance fluorescence of a single trapped ion,
Phys. Rev. Lett. 85 538 (2000),
(ID: 344237)
Toggle Abstract
Resonance fluorescence of a single trapped ion is spectrally analyzed using a heterodyne technique.
Motional sidebands due to the oscillation of the ion in the harmonic trap potential are observed in the
fluorescence spectrum. From the width of the sidebands the cooling rate is obtained and found to be in
agreement with the theoretical prediction.

H. Nägerl, C. Roos, D. Leibfried, H. Rohde, G. Thalhammer, J. Eschner, F. SchmidtKaler, R. Blatt Investigating a qubit candidate: Spectroscopy on the S1/2 to D5/2 transition of a trapped calcium ion in a linear Paul trap,
Phys. Rev. A 61 023405 (2000),
(ID: 344239)
Toggle Abstract
A single 40Ca1 ion is confined in a linear Paul trap and Dopplercooled on the S1/2 to P1/2 dipole transition.
Then the narrow quadrupole S1/2 to D5/2 transition at 729 nm is probed. The observed spectrum is interpreted
in terms of the Zeeman substructure superimposed with oscillation sidebands due to the harmonic motion in the
trap. The height of the motional sidebands provides a sensitive method to determine the ion’s temperature and
thus allows us to test subDoppler laser cooling schemes needed for quantum state preparation and quantum
computation. We also observe the dynamics induced by Rabi oscillations on a carrier transition and interpret it
in terms of the thermal state which is reached after Doppler cooling.

F. SchmidtKaler, C. Roos, H. Nägerl, H. Rohde, S. Gulde, A. B. Mundt, M. Lederbauer, G. Thalhammer, T. Zeiger, P. Barton, L. Hornekaer, G. Reymond, D. Leibfried, J. Eschner, R. Blatt Ground state cooling, quantum state engineering, and study of decoherence in Paul traps,
J. Mod. Opt. 47 2573 (2000),
(ID: 469818)

H. Nägerl, C. Roos, H. Rohde, D. Leibfried, J. Eschner, F. SchmidtKaler, R. Blatt Addressing and cooling of single ions in Paul traps,
Fortschr. Phys. 48 623 (2000),
(ID: 619587)

J. I. Cirac, R. Blatt, A. S. Parkins, P. Zoller Spectrum of resonance fluorescence from a single trapped ion,
Phys. Rev. A 48 2169–2181 (19930903),
http://dx.doi.org/10.1103/PhysRevA.48.2169 doi:10.1103/PhysRevA.48.2169 (ID: 375421)
Toggle Abstract
The spectrum of resonance fluorescence of a single trapped and lasercooled ion is studied theoretically. The quantum motion of the trapped particle manifests itself in the form of narrow motional sidebands in the fluorescence spectrum. For our calculations it is assumed that the ion is confined to dimensions much smaller than the optical wavelength (LambDicke limit) and the approach is valid for multilevel systems, general trapping potentials, and for both travelingwave and standingwave configurations. The motional sidebands in the spectrum have asymmetric amplitudes and this asymmetry is shown to depend on the ion energy, the detector position, and the choice of standing or travelingwave laser excitation.
©1993 The American Physical Society

J. I. Cirac, R. Blatt, A. S. Parkins, P. Zoller Laser cooling of trapped ions with polarization gradients,
Phys. Rev. A 48 1434–1445 (19930802),
http://dx.doi.org/10.1103/PhysRevA.48.1434 doi:10.1103/PhysRevA.48.1434 (ID: 375420)
Toggle Abstract
Laser cooling of a single trapped ion with Zeeman substructure below the Doppler limit is considered theoretically. The laser field consists of two counterpropagating beams linearly polarized in different directions, and the internal atomic transition is Jg=1/2→Je=3/2. The ion is assumed to be localized to spatial dimensions smaller than the optical wavelength (LambDicke limit) and placed at a specific position with respect to the laser beams. Under the assumption that the rate for optical pumping between the atomic ground states defines the smallest time constant in the system, analytic expressions for the final energy and the cooling rates are derived, with both a semiclassical and a full quantum treatment. The results show that laser cooling of a trapped ion using polarization gradients leads to very low energies. These energies are insensitive to the precise localization of the ion with respect to the lasers, the angle between the direction of the polarizations of the laser beams, and the detuning of the cooling laser.
©1993 The American Physical Society

J. I. Cirac, A. S. Parkins, R. Blatt, P. Zoller Cooling of a trapped ion coupled strongly to a quantized cavity mode,
Opt. Com. 97 353359 (19930401),
http://dx.doi.org/10.1016/00304018(93)90502V doi:10.1016/00304018(93)90502V (ID: 375419)
Toggle Abstract
The interaction of a trapped twolevel ion, confined in a harmonic potential, with a quantized cavity mode of the radiation field is studied theoretically. The ion is considered to be spatially localized on the scale of the optical wavelength (LambDicke limit), and the ioncavitymode coupling is assumed to be larger than or comparable to the spontaneous emission and cavitymode loss rates. With broadband thermal light driving the cavity mode, we show that the cooling rates and final temperatures of the trappedion motion reflect the JaynesCummings energy spectrum of the stronglycoupled ioncavity system.
1 Present address: Departamento de Fisica Aplicada, Facultad de Ciencias, Paseo Universidad 4, 13071 Ciudad Real, Spain.
2 Permanent address: I. Institut für Laserphysik, Jungiusstr. 9, W2000 Hamburg 36, Germany.

J. I. Cirac, R. Blatt, A. S. Parkins, P. Zoller Preparation of Fock states by observation of quantum jumps in an ion trap,
Phys. Rev. Lett. 70 762–765 (19930206),
http://dx.doi.org/10.1103/PhysRevLett.70.762 doi:10.1103/PhysRevLett.70.762 (ID: 375422)
Toggle Abstract
We propose a technique for the preparation of Fock states of a harmonic oscillator strongly coupled to a single twolevel atomic transition based on the observation of quantum jumps. Examples are taken from the fields of cavity QED and ion trapping, where photon number states and number states of the quantized atomic motion may be prepared, respectively.
©1993 The American Physical Society

J. I. Cirac, A. S. Parkins, R. Blatt, P. Zoller ‘‘Dark’’ squeezed states of the motion of a trapped ion,
Phys. Rev. Lett. 70 556–559 (19930201),
http://dx.doi.org/10.1103/PhysRevLett.70.556 doi:10.1103/PhysRevLett.70.556 (ID: 375418)
Toggle Abstract
We propose a scheme for preparing coherent squeezed states of motion in an ion trap based on the multichromatic excitation of a trapped ion by standing and travelingwave light fields. The squeezed state is produced when the beat frequency between two standingwave light fields is equal to twice the trap frequency, and is indicated by a ‘‘dark resonance’’ in the fluorescence emitted by the ion.
©1993 The American Physical Society

V. Enders, P. Courteille, R. Huesmann, L. S. Ma, W. Neuhauser, R. Blatt, P. E. Toschek MicrowaveOptical Double Resonance on a Single LaserCooled 171Yb+ Ion,
24 325 (1993),
(ID: 619599)

J. Walz, I. Siemers, M. Schubert, W. Neuhauser, R. Blatt Motional Stability of a Nonlinear Parametric Oscillator: Ion Storage in the RF Octupole Trap,
21 183 (1993),
(ID: 619622)

L. S. Ma, P. Courteille, G. Ritter, W. Neuhauser, R. Blatt ModulationTransfer Spectroscopy in Te2 at 467 nm,
57 159 (1993),
(ID: 619690)