Publications Christian F. ROOS

2024

Articles

• L. K. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese, C. F. Roos, M. K. Joshi Observing the quantum Mpemba effect in quantum simulations, PRL 133 10402 (2024-07-01), http://dx.doi.org/10.1103/PhysRevLett.133.010402 doi:10.1103/PhysRevLett.133.010402 (ID: 721174) Toggle Abstract
  The non-equilibrium physics of many-body quantum systems harbors various unconventional phenomena. In this study, we experimentally investigate one of the most puzzling of these phenomena— the quantum Mpemba effect, where a tilted ferromagnet restores its symmetry more rapidly when it is farther from the symmetric state compared to when it is closer. We present the first experimental evidence of the occurrence of this effect in a trapped-ion quantum simulator. The symmetry breaking and restoration are monitored through entanglement asymmetry, probed via randomized measurements, and post-processed using the classical shadows technique. Our findings are further substantiated by measuring the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, offering direct evidence of subsystem thermalization.
• H. Hainzer, D. Kiesenhofer, T. Ollikainen, M. Bock, F. Kranzl, M. K. Joshi, G. Yoeli, R. Blatt, T. Gefen, C. F. Roos Correlation Spectroscopy with Multiqubit-Enhanced Phase Estimation, Phys. Rev. X 14 24 (2024-02-29), URL (ID: 721249) Toggle Abstract
  Ramsey interferometry is a widely used tool for precisely measuring transition frequencies between two energy levels of a quantum system, with applications in time keeping, precision spectroscopy, quantum optics, and quantum information. Often, the coherence time of the quantum system surpasses the one of the oscillator probing the system, thereby limiting the interrogation time and associated spectral resolution. Correlation spectroscopy overcomes this limitation by probing two quantum systems with the same noisy oscillator for a measurement of their transition frequency difference; this technique has enabled very precise comparisons of atomic clocks. Here, we extend correlation spectroscopy to the case of multiple quantum systems undergoing strong correlated dephasing. We model Ramsey correlation spectroscopy with N particles as a multiparameter phase estimation problem and demonstrate that multiparticle correlations can assist in reducing the measurement uncertainties even in the absence of entanglement. We derive precision limits and optimal sensing techniques for this problem and compare the performance of probe states and measurement with and without entanglement. Using one- and two-dimensional ion Coulomb crystals with up to 91 qubits, we experimentally demonstrate the advantage of measuring multiparticle correlations for reducing phase uncertainties and apply correlation spectroscopy to measure ion-ion distances, transition frequency shifts, laser-ion detunings, and path-length fluctuations. Our method can be straightforwardly implemented in experimental setups with globally coherent qubit control and qubit-resolved single-shot readout and is, thus, applicable to other physical systems such as neutral atoms in tweezer arrays.

Preprints

• M. K. Joshi, M. Guevara-Bertsch, F. Kranzl, R. Blatt, C. F. Roos Characterization of ion-trap-induced ac-magnetic fields, (2024-05-30), arXiv:2405.18883 arXiv:2405.18883 (ID: 721258) Toggle Abstract
  The oscillating magnetic field produced by unbalanced currents in radio-frequency ion traps induces transition frequency shifts and sideband transitions that can be harmful to precision spectroscopy experiments. Here, we describe a methodology, based on two-photon spectroscopy, for determining both the strength and direction of rf-induced magnetic fields without modifying any DC magnetic bias field or changing any trap RF power. The technique is readily applicable to any trapped-ion experiment featuring narrow linewidth transitions.
• M. Mallweger, M. Guevara-Bertsch, B. T. Torosov, R. Thomm, N. Kuk, H. Parke, C. F. Roos, G. Higgins, M. Hennrich, N. V. Vitanov Motional state analysis of a trapped ion by ultra-narrowband composite pulses, (2024-02-15), arXiv:2402.10041 arXiv:2402.10041 (ID: 721243) Toggle Abstract
  In this work, we present a method for measuring the motional state of a two-level system coupled to a harmonic oscillator. Our technique uses ultra-narrowband composite pulses on the blue sideband transition to scan through the populations of the different motional states. Our approach does not assume any previous knowledge of the motional state distribution and is easily implemented. It is applicable both inside and outside of the Lamb-Dicke regime. For higher phonon numbers especially, the composite pulse sequence can be used as a filter for measuring phonon number ranges. We demonstrate this measurement technique using a single trapped ion and show good detection results with the numerically evaluated pulse sequence.

2023

Articles

• M. K. Joshi, C. Kokail, R. van Bijnen, F. Kranzl, T. Zache, R. Blatt, C. F. Roos, P. Zoller Exploring Large-Scale Entanglement in Quantum Simulation, Nature 624 539 (2023-11-29), http://dx.doi.org/10.1038/s41586-023-06768-0 doi:10.1038/s41586-023-06768-0 (ID: 721080) Toggle Abstract
  Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science. Here we perform experimental investigations of entanglement based on the entanglement Hamiltonian, as an effective description of the reduced density operator for large subsystems. We prepare ground and excited states of a 1D XXZ Heisenberg chain on a 51-ion programmable quantum simulator and perform sample-efficient `learning' of the entanglement Hamiltonian for subsystems of up to 20 lattice sites. Our experiments provide compelling evidence for a local structure of the entanglement Hamiltonian. This observation marks the first instance of confirming the fundamental predictions of quantum field theory by Bisognano and Wichmann, adapted to lattice models that represent correlated quantum matter. The reduced state takes the form of a Gibbs ensemble, with a spatially-varying temperature profile as a signature of entanglement. Our results also show the transition from area to volume-law scaling of Von Neumann entanglement entropies from ground to excited states. As we venture towards achieving quantum advantage, we anticipate that our findings and methods have wide-ranging applicability to revealing and understanding entanglement in many-body problems with local interactions including higher spatial dimensions.
• F. Kranzl, S. Birnkammer, M. K. Joshi, A. Bastianello, R. Blatt, M. Knap, C. F. Roos Observation of magnon bound states in the long-range, anisotropic Heisenberg model, Phys. Rev. X 13 031017-12 (2023-08-11), http://dx.doi.org/10.1103/PhysRevX.13.031017 doi:10.1103/PhysRevX.13.031017 (ID: 720909) Toggle Abstract
  Over the recent years coherent, time-periodic modulation has been established as a versatile tool for realizing novel Hamiltonians. Using this approach, known as Floquet engineering, we experimentally realize a long-ranged, 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 long-range interactions with the experimentally realized power-law exponent, the group velocity of magnons is unbounded. Nonetheless, for sufficiently strong interactions we observe bound states of these unconventional magnons which possess a non-diverging 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 non-equilibrium dynamics of quantum many-body systems.
• I. Vybornyi, L. Dreissen, D. Kiesenhofer, H. Hainzer, M. Bock, T. Ollikainen, D. Vadlejch, C. F. Roos, T. E. Mehlstäubler, K. Hammerer Sideband thermometry of ion crystals, PRX Quantum 4 40346 (2023-06-14), http://dx.doi.org/10.1103/PRXQuantum.4.040346 doi:10.1103/PRXQuantum.4.040346 (ID: 721085) Toggle Abstract
  Coulomb crystals of cold trapped ions are a leading platform for the realisation of quantum processors and quantum simulations and, in quantum metrology, for the construction of optical atomic clocks and for fundamental tests of the Standard Model. For these applications, it is not only essential to cool the ion crystal in all its degrees of freedom down to the quantum ground state, but also to be able to determine its temperature with a high accuracy. However, when a large ground-state cooled crystal is interrogated for thermometry, complex many-body interactions take place, making it challenging to accurately estimate the temperature with established techniques. In this work we present a new thermometry method tailored for ion crystals. The method is applicable to all normal modes of motion and does not suffer from a computational bottleneck when applied to large ion crystals. We test the temperature estimate with two experiments, namely with a 1D linear chain of 4 ions and a 2D crystal of 19 ions and verify the results, where possible, using other methods. The results show that the new method is an accurate and efficient tool for thermometry of ion crystals.
• F. Kranzl, A. Lasek, M. K. Joshi, A. Kalev, R. Blatt, C. F. Roos, N. Yunger Halpern Experimental observation of thermalization with noncommuting charges, PRX Quantum 4 20318 (2023-04-28), http://dx.doi.org/10.1103/PRXQuantum.4.020318 doi:10.1103/PRXQuantum.4.020318 (ID: 720810) Toggle Abstract
  Quantum simulators have recently enabled experimental observations of the internal thermalization of quantum many-body systems. Often, the global energy and particle number are conserved and the system is prepared with a well-defined particle number—in a microcanonical subspace. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information. Until now, this subfield has remained theoretical. We initiate the experimental testing of its predictions, with a trapped-ion simulator. We prepare 6–21 spins in an approximate microcanonical subspace, a generalization of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have well-defined nontrivial values simultaneously. We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations. The noncommuting charges are the three spin components. We find that small subsystems equilibrate to near a recently predicted non-Abelian thermal state. This work bridges quantum many-body simulators to the quantum thermodynamics of noncommuting charges, the predictions of which can now be tested.
• D. Kiesenhofer, H. Hainzer, A. Zhdanov, P. Holz, M. Bock, T. Ollikainen, C. F. Roos Controlling two-dimensional Coulomb crystals of more than 100 ions in a monolithic radio-frequency trap, PRX Quantum 4 20317 (2023-04-28), http://dx.doi.org/10.1103/PRXQuantum.4.020317 doi:10.1103/PRXQuantum.4.020317 (ID: 721039) Toggle Abstract
  Linear strings of trapped atomic ions held in radio-frequency (rf) traps constitute one of the leading platforms for quantum simulation experiments, allowing the investigation of interacting quantum matter. However, linear ion strings have drawbacks, such as the difficulty of scaling beyond approximately 50 particles as well as the inability to naturally implement spin models with more than one spatial dimension. Here we present experiments with planar Coulomb crystals of up to 105 40Ca+ ions in a novel monolithic rf trap, laying the groundwork for quantum simulations of two-dimensional spin models with single-particle control. We characterize the trapping potential by analysis of crystal images and compare the observed crystal configurations with numerical simulations. We further demonstrate stable confinement of large crystals, free of structural configuration changes, and find that rf heating of the crystal is not an obstacle for future quantum simulation experiments. Finally, we prepare the out-of-plane motional modes of planar crystals consisting of up to 105 ions close to their ground state by electromagnetically induced transparency cooling, an important prerequisite for implementing long-range entangling interactions.
• J. Franke, S. M. Muleady, C. R. Kaubrügger, F. Kranzl, R. Blatt, A. M. Rey, M. K. Joshi, C. F. Roos Quantum-enhanced sensing on optical transitions through finite-range interactions, Nature 621 740 (2023-03-27), http://dx.doi.org/10.1038/s41586-023-06472-z doi:10.1038/s41586-023-06472-z (ID: 721072) Toggle Abstract
  The control over quantum states in atomic systems has led to the most precise optical atomic clocks to date. Their sensitivity is currently bounded by the standard quantum limit, a fundamental floor set by quantum mechanics for uncorrelated particles, which can nevertheless be overcome when operated with entangled particles. Yet demonstrating a quantum advantage in real world sensors is extremely challenging and remains to be achieved aside from two remarkable examples, LIGO and more recently HAYSTAC. Here we illustrate a pathway for harnessing scalable entanglement in an optical transition using 1D chains of up to 51 ions with state-dependent interactions that decay as a power-law function of the ion separation. We show our sensor can be made to behave as a one-axis-twisting (OAT) model, an iconic fully connected model known to generate scalable squeezing. The collective nature of the state manifests itself in the preservation of the total transverse magnetization, the reduced growth of finite momentum spin-wave excitations, the generation of spin squeezing comparable to OAT (a Wineland parameter of −3.9±0.3 dB for only N = 12 ions) and the development of non-Gaussian states in the form of atomic multi-headed cat states in the Q-distribution. The simplicity of our protocol enables scalability to large arrays with minimal overhead, opening the door to advances in timekeeping as well as new methods for preserving coherence in quantum simulation and computation. We demonstrate this in a Ramsey-type interferometer, where we reduce the measurement uncertainty by −3.2±0.5 dB below the standard quantum limit for N = 51 ions.

Preprint

• M. I. Hussain, M. Guevara-Bertsch, E. Torrontegui, J. García-Ripoll, R. Blatt, C. F. Roos Single-ion optical autocorrelator, (2023-12-07), arXiv:2312.03679 arXiv:2312.03679 (ID: 721153) Toggle Abstract
  Well isolated quantum systems are exquisite sensors of electromagnetic fields. In this work, we use a single trapped ion for characterizing chirped ultraviolet (UV) picosecond laser pulses. The frequency swept pulses resonantly drive a strong dipole transition via rapid adiabatic passage, resulting in near deterministic population exchange caused by absorption or stimulated emission of photons. When subjecting an ion to counterpropagating pulse pairs, we observe the loss and revival of atomic coherence as a function of the pulse pair spatial overlap enabling quantification of the temporal pulse broadening caused by a frequency chirp in shaped UV pulses with a very low peak power. We find good agreement between measured and applied chirp. The ultrafast population exchange imparts an impulsive force where the estimated change in the mean phonon numbers of 0.5 is measured for two pairs of pulses. The resonant ultrafast kicks could be applied to matter wave interferometry experiments and present a step towards ultrafast entanglement operations in trapped ions.

2022

Articles

• 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 (2022-05-18), http://dx.doi.org/10.1103/PhysRevA.105.052426 doi:10.1103/PhysRevA.105.052426 (ID: 720726) Toggle Abstract
  Scaling a trapped-ion based quantum simulator to a large number of ions creates a fully-controllable 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 high-fidelity coherent control of a quantum system extending over hundreds of micrometers. In this paper, we describe a setup for carrying out many-ion quantum simulations including single-ion coherent control that we use for demonstrating entanglement in 50-ion strings. Furthermore, we present a set of experimental techniques probing ion-qubits by Ramsey and Carr-Purcell-Meiboom-Gill (CPMG) pulse sequences that enable detection (and compensation) of power-line-synchronous magnetic-field 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 long-range quantum magnet, Science 376 720 (2022-05-02), http://dx.doi.org/10.1126/science.abk2400 doi:10.1126/science.abk2400 (ID: 720666) Toggle Abstract
  Identifying universal properties of non-equilibrium 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 long-range interacting spin chain. By measuring space-time 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 non-equilibrium states of quantum matter.

Preprint

• 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 multi-qubit-enhanced phase estimation, (2022-03-25), arXiv:2203.12656 arXiv:2203.12656 (ID: 720825) Toggle Abstract
  Precision spectroscopy on trapped-ion crystals subject to correlated dephasing can reveal a multitude of information in the absence of any single-particle coherences. We use correlation spectroscopy for measuring ion-ion distances and transition frequency shifts in one- and two-dimensional ion crystals by analyzing multi-particle correlations of up to N=91 qubits, each of which is encoded in a single ion. Additionally we carry out single-shot measurements of the laser-ion detuning and of path-length fluctuations. We show that the information contained in N-particle correlations reduces the measurement uncertainty as compared to the case where only two-particle correlations are analyzed. We derive quantum precision limits for this problem. While for a pair of qubits entanglement can reduce the measurement uncertainty, entanglement-free correlation spectroscopy becomes asymptotically optimal in the limit of N→∞ when the measurement goal is the determination of all phase differences between the qubits.

2021

Article

• M. I. Hussain, D. Heinrich, M. Guevara-Bertsch, E. Torrontegui, J. J. Garcia-Ripoll, C. F. Roos, R. Blatt Ultraviolet Laser Pulses with Multigigahertz Repetition Rate and Multiwatt Average Power for Fast Trapped-Ion Entanglement Operations, Phys. Rev. Applied 15 24054 (2021-02-23), http://dx.doi.org/10.1103/PhysRevApplied.15.024054 doi:10.1103/PhysRevApplied.15.024054 (ID: 720517) Toggle Abstract
  The conventional approach to perform two-qubit 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 off-the-shelf. For this, we have engineered an ultrafast entangling gate source based on a frequency comb. The laser generates bursts of several hundred mode-locked pulses with pulse energy ∼800 pJ at 5 GHz repetition rate at 393.3 nm and complies with all requirements for implementing a fast two-qubit 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).

2020

Articles

• M. K. Joshi, A. Fabre, C. Maier, T. Brydges, D. Kiesenhofer, H. Hainzer, R. Blatt, C. F. Roos Polarization-gradient cooling of 1D and 2D ion Coulomb crystals, New J. Phys. 22 103013 (2020-06-29), http://dx.doi.org/10.1088/1367-2630/abb912 doi:10.1088/1367-2630/abb912 (ID: 720512) Toggle Abstract
  We present experiments on polarization gradient cooling of Ca+ multi-ion 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 counter-propagating laser beams with mutually orthogonal linear polarizations that are blue-detuned from the S1/2 to P1/2 transition. We demonstrate cooling of linear chains of up to 51 ions and 2D-crystals in zig-zag 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.
• M. K. Joshi, A. Elben, B. Vermersch, T. Brydges, C. Maier, P. Zoller, R. Blatt, C. F. Roos Quantum information scrambling in a trapped-ion quantum simulator with tunable range interactions, Phys. Rev. Lett. 124 240505 (2020-01-07), http://dx.doi.org/10.1103/PhysRevLett.124.240505 doi:10.1103/PhysRevLett.124.240505 (ID: 720436) Toggle Abstract
  In ergodic many-body 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 many-body dynamics such as the processes of chaos and thermalization. Here, we present first experimental demonstrations of quantum information scrambling on a 10-qubit trapped-ion quantum simulator representing a tunable long-range interacting spin system, by estimating out-of-time 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 Cross-Platform Verification of Intermediate Scale Quantum Devices, Phys. Rev. Lett. 124 10504 (2020-01-06), http://dx.doi.org/10.1103/PhysRevLett.124.010504 doi:10.1103/PhysRevLett.124.010504 (ID: 720357) Toggle Abstract
  We describe a protocol for cross-platform 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 (mixed-state) 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 proof-of-principle, we present the measurement of experiment-theory fidelities for entangled 10-qubit quantum states in a trapped ion quantum simulator.

2019

Articles

• D. Heinrich, M. Guggemos, M. Guevara-Bertsch, M. I. Hussain, C. F. Roos, R. Blatt Ultrafast coherent excitation of a Ca+ ion, New J. Phys. 21 83025 (2019-07-01), http://dx.doi.org/10.1088/1367-2630/ab2a7e doi:10.1088/1367-2630/ab2a7e (ID: 720108) Toggle Abstract
  Trapped ions are a well-studied 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 mode-locked, stabilized optical frequency comb and inherits its frequency stability. Using a single trapped ion, we implement three different techniques for measuring the ion-laser 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 Self-verifying variational quantum simulation of lattice models, Nature 569 360 (2019-05-15), http://dx.doi.org/10.1038/s41586-019-1177-4 doi:10.1038/s41586-019-1177-4 (ID: 720076) Toggle Abstract
  Hybrid classical-quantum algorithms aim at variationally solving optimisation problems, using a feedback loop between a classical computer and a quantum co-processor, while benefitting from quantum resources. Here we present experiments demonstrating self-verifying, hybrid, variational quantum simulation of lattice models in condensed matter and high-energy 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 co-processor is a programmable, trapped-ion 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 long-standing challenge of verifying quantum simulation.
• A. Elben, B. Vermersch, C. F. Roos, P. Zoller Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in many-body quantum states, Phys. Rev. A 99 52323 (2019-05-15), http://dx.doi.org/10.1103/PhysRevA.99.052323 doi:10.1103/PhysRevA.99.052323 (ID: 720100) Toggle Abstract
  We develop a general theoretical framework for measurement protocols employing statistical correlations of randomized measurements. We focus on locally randomized measurements implemented with local random unitaries in quantum lattice models. In particular, we discuss the theoretical details underlying the recent measurement of the second Rényi entropy of highly mixed quantum states consisting of up to 10 qubits in a trapped-ion quantum simulator [Brydges et al., arXiv:1806.05747]. We generalize the protocol to access the overlap of quantum states, prepared sequentially in an experiment. Furthermore, we discuss proposals for quantum state tomography based on randomized measurements within our framework and the respective scaling of statistical errors with system size.
• M. Guggemos, M. Guevara-Bertsch, 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 (2019-04-25), http://dx.doi.org/10.1088/1367-2630/ab447a doi:10.1088/1367-2630/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 g-factor 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 (2019-04-19), http://dx.doi.org/10.1126/science.aau4963 doi:10.1126/science.aau4963 (ID: 720034) Toggle Abstract
  Entanglement is the key feature of many-body 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 trapped-ion 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.
• C. Maier, T. Brydges, P. Jurcevic, N. Trautmann, C. Hempel, B. P. Lanyon, P. Hauke, R. Blatt, C. F. Roos Environment-assisted quantum transport in a 10-qubit network, Phys. Rev. Lett. 122 50501 (2019-02-08), 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 environment-assisted 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 non-Markovian 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 many-body networks under static disorder and dynamic noise.

2018

Articles

• C. Hempel, C. Maier, J. Romero, J. McClean, T. Monz, H. Shen, P. Jurcevic, B. P. Lanyon, P. Love, R. Babbush, A. Aspuru-Guzik, R. Blatt, C. F. Roos Quantum chemistry calculations on a trapped-ion quantum simulator, Phys. Rev. X 8 31022 (2018-07-24), http://dx.doi.org/10.1103/PhysRevX.8.031022 doi:10.1103/PhysRevX.8.031022 (ID: 720003) Toggle Abstract
  Quantum-classical hybrid algorithms are emerging as promising candidates for near-term 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 cross-platform benchmark for multi-qubit quantum simulators.
• 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 20-Qubit System, Phys. Rev. X 8 21012 (2018-04-10), 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 out-of-equilibrium dynamics of an Ising-type Hamiltonian, engineered via laser fields. Since the qubit-qubit 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.

2017

Articles

• 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 many-body system, Nature Phys. 13 1158 (2017-12-05), 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 precisely-controllable 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 many-body 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 out-of-equilbrium states produced by 1D systems with finite-range interactions, up to any fixed point in time. We then use the technique to reconstruct the dynamical state of a trapped-ion 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 beyond-classical performance. MPS tomography should find widespread use to study large quantum many-body systems and to benchmark and verify quantum simulators and computers.
• 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 many-body system, Phys. Rev. Lett. 119 80501 (2017-08-21), 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 non-equilibrium regime. In this letter, we investigate DQPTs in a string of ions simulating interacting transverse-field Ising models. We observe non-equilibrium 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 non-analytic 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.
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• C. F. Roos, A. Alberti, D. Meschede, P. Hauke, H. Häffner Revealing quantum statistics with a pair of distant atoms, Phys. Rev. Lett. 119 160401 (2017-06-15), http://dx.doi.org/10.1103/PhysRevLett.119.160401 doi:10.1103/PhysRevLett.119.160401 (ID: 719812) Toggle Abstract
  Quantum statistics have a profound impact on the properties of systems composed of identical particles. In this Letter, we demonstrate that the quantum statistics of a pair of identical massive particles can be probed by a direct measurement of the exchange symmetry of their wave function even in conditions where the particles always remain spatially well separated and thus the exchange contribution to their interaction energy is negligible. We present two protocols revealing the bosonic or fermionic nature of a pair of particles and discuss possible implementations with a pair of trapped atoms or ions.

2016

Article

• R. Lechner, C. Maier, C. Hempel, P. Jurcevic, B. P. Lanyon, T. Monz, M. Brownnutt, R. Blatt, C. F. Roos Electromagnetically-induced-transparency ground-state cooling of long ion strings, Phys. Rev. A 93 53401 (2016-03-18), http://dx.doi.org/10.1103/PhysRevA.93.053401 doi:10.1103/PhysRevA.93.053401 (ID: 719536) Toggle Abstract
  Electromagnetically-induced-transparency (EIT) cooling is a ground-state 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 ground-state 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 single-shot measurements of phonon numbers, by rapid adiabatic passage on a vibrational sideband of a narrow transition.

2015

Articles

• 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 (2015-07-29), http://dx.doi.org/10.1088/1367-2630/17/10/103001 doi:10.1088/1367-2630/17/10/103001 (ID: 719305) Toggle Abstract
  We investigate the dynamics of an ion sympathetically cooled by another laser-cooled 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 two-ion crystal of Ca+ and Al+ by photo-ionization of neutral atoms produced by laser ablation. We characterize the velocity distribution of the laser-ablated atoms crossing the trap by time-resolved 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 Doppler-cooled 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.
• M. Hettrich, T. Ruster, H. Kaufmann, C. F. Roos, C. T. Schmiegelow, F. Schmidt-Kaler, U. Poschinger Measurement of dipole matrix elements with a single trapped ion, Phys. Rev. Lett. 115 143003 (2015-05-12), http://dx.doi.org/10.1103/PhysRevLett.115.143003 doi:10.1103/PhysRevLett.115.143003 (ID: 719242) Toggle Abstract
  We demonstrate a new method for the direct measurement of atomic dipole transition matrix elements based on techniques developed for quantum information purposes. The scheme consists of measuring dispersive and absorptive off-resonant light-ion interactions and is applicable to many atomic species. We determine the dipole matrix element pertaining to the Ca II H line, i.e. the 4 2S1/2 - 4 2P1/2 transition of 40Ca+, for which we find the value 2.893(8) ea_0. Moreover, the method allows us to deduce the lifetime of the 4 2P1/2 state to be 6.90(5) ns, which is in agreement with predictions from recent theoretical calculations and resolves a longstanding discrepancy between calculated values and experimental results.
• 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 (2015-05-11), http://dx.doi.org/10.1103/PhysRevLett.115.100501 doi:10.1103/PhysRevLett.115.100501 (ID: 719241) Toggle Abstract
  The static and dynamic properties of many-body 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 many-body 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.

2014

Articles

• P. Jurcevic, B. P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, C. F. Roos Quasiparticle engineering and entanglement propagation in a quantum many-body system, Nature 511 202 (2014-07-10), http://dx.doi.org/10.1038/nature13461 doi:10.1038/nature13461 (ID: 718717) Toggle Abstract
  The key to explaining a wide range of quantum phenomena is understanding how entanglement propagates around many-body systems. Furthermore, the controlled distribution of entanglement is of fundamental importance for quantum communication and computation. In many situations, quasiparticles are the carriers of information around a quantum system and are expected to distribute entanglement in a fashion determined by the system interactions. Here we report on the observation of magnon quasiparticle dynamics in a one-dimensional many-body quantum system of trapped ions representing an Ising spin model. Using the ability to tune the effective interaction range, and to prepare and measure the quantum state at the individual particle level, we observe new quasiparticle phenomena. For the first time, we reveal the entanglement distributed by quasiparticles around a many-body system. Second, for long-range interactions we observe the divergence of quasiparticle velocity and breakdown of the light-cone picture that is valid for short-range interactions. Our results will allow experimental studies of a wide range of phenomena, such as quantum transport, thermalisation, localisation and entanglement growth, and represent a first step towards a new quantum-optical regime with on-demand quasiparticles with tunable non-linear interactions.
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• B. P. Lanyon, M. Zwerger, P. Jurcevic, C. Hempel, W. Dür, H. J. Briegel, R. Blatt, C. F. Roos Experimental Violation of Multipartite Bell Inequalities with Trapped Ions, Phys. Rev. Lett. 112 100403 (2014-03-13), http://dx.doi.org/10.1103/PhysRevLett.112.100403 doi:10.1103/PhysRevLett.112.100403 (ID: 718697) Toggle Abstract
  We report on the experimental violation of multipartite Bell inequalities by entangled states of trapped ions. First, we consider resource states for measurement-based quantum computation of between 3 and 7 ions and show that all strongly violate a Bell-type inequality for graph states, where the criterion for violation is a sufficiently high fidelity. Second, we analyze Greenberger-Horne-Zeilinger states of up to 14 ions generated in a previous experiment using stronger Mermin-Klyshko inequalities, and show that in this case the violation of local realism increases exponentially with system size. These experiments represent a violation of multipartite Bell-type inequalities of deterministically prepared entangled states. In addition, the detection loophole is closed.

2013

Articles

• 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 (2013-12-06), http://dx.doi.org/10.1088/1367-2630/15/12/123012 doi:10.1088/1367-2630/15/12/123012 (ID: 718676) Toggle Abstract
  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 small-scale 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 non-coherent 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 Measurement-based quantum computation with trapped ions, Phys. Rev. Lett. 111 210501 (2013-11-19), http://dx.doi.org/10.1103/PhysRevLett.111.210501 doi:10.1103/PhysRevLett.111.210501 (ID: 718582) Toggle Abstract
  Measurement-based 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 one-way quantum computer, with the cluster state as its universal resource. Here we demonstrate the principles of measurement-based 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 measurement-based 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.
• 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 (2013-09-06), http://dx.doi.org/10.1103/PhysRevLett.111.100504 doi:10.1103/PhysRevLett.111.100504 (ID: 718585) Toggle Abstract
  Quantum systems in mixed states can be unentangled and yet still non-classically 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 ionic-qubits 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 classically-correlated 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 non-classical correlations and highlight fundamental differences between discord and entanglement.
• C. Hempel, B. P. Lanyon, P. Jurcevic, R. Gerritsma, R. Blatt, C. F. Roos Entanglement-enhanced detection of single-photon scattering events, Nature Photon. 7 633 (2013-07-30), http://dx.doi.org/10.1038/nphoton.2013.172 doi:10.1038/nphoton.2013.172 (ID: 718575) Toggle Abstract
  The ability to detect the interaction of light and matter at the single-particle 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 ultra-precise 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.
• J. Schachenmayer, B. P. Lanyon, C. F. Roos, A. J. Daley Entanglement growth in quench dynamics with variable range interactions, Phys. Rev. X 3 031015 (2013-05-30), http://dx.doi.org/10.1103/PhysRevX.3.031015 doi:10.1103/PhysRevX.3.031015 (ID: 718525) Toggle Abstract
  Studying entanglement growth in quantum dynamics provides both insight into the underlying microscopic processes, and information about the complexity of the quantum states, which is related to the efficiency of simulations on classical computers. Recently, experiments with trapped ions, polar molecules, and Rydberg excitations have provided new opportunities to observe dynamics with long range interactions. We explore non-equilibrium coherent dynamics after a quantum quench in such systems, identifying qualitatively different behavior as the exponent of algebraically decaying spin-spin interactions in a transverse Ising chain is varied. Computing the build-up of bipartite entanglement as well as mutual information between distant spins, we identify linear growth of entanglement entropy corresponding to propagation of quasiparticles for shorter range interactions, with the maximum rate of growth occurring when the Hamiltonian parameters match those for the quantum phase transition. Counter-intuitively, the growth of bipartite entanglement for long-range interactions is only logarithmic for most regimes, i.e., substantially slower than for shorter range interactions. Experiments with trapped ions allow for the realization of this system with tunable interaction range, and we show that the different phenomena are robust for finite systems sizes and in the presence of noise. These results can act as a direct guide for the generation of large-scale entanglement in such experiments, towards a regime where the entanglement growth can render existing classical simulations inefficient.

2012

Articles

• C. F. Roos Viewpoint: Moving traps offer fast delivery of cold ions, Physics 5 94 (2012-08-21), http://dx.doi.org/10.1103/Physics.5.94 doi:10.1103/Physics.5.94 (ID: 718180)
• J. Casanova, C. E. Lopez, J. J. García-Ripoll, C. F. Roos, E. Solano Quantum tomography in position and momentum space, Eur. Phys. J. D 66 222 (2012-08-01), http://dx.doi.org/10.1140/epjd/e2012-30016-6 doi:10.1140/epjd/e2012-30016-6 (ID: 718184)
• C. F. Roos News and Views: Simulating magnetism, Nature 484 461 (2012-04-25), http://dx.doi.org/10.1038/484461a doi:10.1038/484461a (ID: 718064)
• R. Blatt, C. F. Roos Quantum simulations with trapped ions, Nature Phys. 8 277 (2012-04-03), http://dx.doi.org/10.1038/NPHYS2252 doi:10.1038/NPHYS2252 (ID: 718042)

2011

Articles

• J. Casanova, L. Lamata, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. García-Ripoll, E. Solano Quantum simulation of quantum field theories in trapped ions, Phys. Rev. Lett. 107 260501 (2011-12-19), http://dx.doi.org/10.1103/PhysRevLett.107.260501 doi:10.1103/PhysRevLett.107.260501 (ID: 717840) Toggle Abstract
  We propose the quantum simulation of fermion and antifermion field modes interacting via a bosonic field mode, and present a possible implementation with two trapped ions. This quantum platform allows for the scalable add up of bosonic and fermionic modes, and represents an avenue towards quantum simulations of quantum field theories in perturbative and nonperturbative regimes.
• J. Casanova, C. Sabin, J. Leon, I. L. Egusquiza, R. Gerritsma, C. F. Roos, J. J. García-Ripoll, E. Solano Quantum simulation of the Majorana equation and unphysical operations, Phys. Rev. X 1 021018 (2011-12-12), http://dx.doi.org/10.1103/PhysRevX.1.021018 doi:10.1103/PhysRevX.1.021018 (ID: 717833) Toggle Abstract
  We design a quantum simulator for the Majorana equation, a non-Hamiltonian relativistic wave equation that might describe neutrinos and other exotic particles beyond the standard model. Driven by the need of the simulation, we devise a general method for implementing a number of mathematical operations that are unphysical, including charge conjugation, complex conjugation, and time reversal. Furthermore, we describe how to realize the general method in a system of trapped ions. The work opens a new front in quantum simulations.
• L. Lamata, J. Casanova, R. Gerritsma, C. F. Roos, J. J. García-Ripoll, E. Solano Relativistic quantum mechanics with trapped ions, New J. Phys. 13 095003 (2011-09-11), http://dx.doi.org/10.1088/1367-2630/13/9/095003 doi:10.1088/1367-2630/13/9/095003 (ID: 717766) Toggle Abstract
  We consider the quantum simulation of relativistic quantum mechanics, as described by the Dirac equation and classical potentials, in trapped-ion systems. We concentrate on three problems of growing complexity. Firstly, we study the bidimensional relativistic scattering of single Dirac particles by a linear potential. Secondly, we explore the case of a Dirac particle in a magnetic field and its topological properties. Finally, we analyze the problem of two Dirac particles that are coupled by a controllable and confining potential. The latter interaction may be useful to study important phenomena such as the confinement and asymptotic freedom of quarks.
• 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 (2011-09-01), 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 full-time 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 full-scale device is within reach.
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• M. Müller, K. Hammerer, Y. Zhou, C. F. Roos, P. Zoller Simulating open quantum systems: from many-body interactions to stabilizer pumping, New J. Phys. 13 085007 (2011-08-10), http://dx.doi.org/10.1088/1367-2630/13/8/085007 doi:10.1088/1367-2630/13/8/085007 (ID: 717750) Toggle Abstract
  In a recent experiment, Barreiro et al (2011 Nature 470 486) demonstrated the fundamental building blocks of an open-system quantum simulator with trapped ions. Using up to five ions, dynamics were realized by sequences that combined single- and multi-qubit entangling gate operations with optical pumping. This enabled the implementation of both coherent many-body dynamics and dissipative processes by controlling the coupling of the system to an artificial, suitably tailored environment. This engineering was illustrated by the dissipative preparation of entangled two- and four-qubit states, the simulation of coherent four-body spin interactions and the quantum non-demolition measurement of a multi-qubit stabilizer operator. In this paper, we present the theoretical framework of this gate-based ('digital') simulation approach for open-system dynamics with trapped ions. In addition, we discuss how within this simulation approach, minimal instances of spin models of interest in the context of topological quantum computing and condensed matter physics can be realized in state-of-the-art linear ion-trap quantum computing architectures. We outline concrete simulation schemes for Kitaev's toric code Hamiltonian and a recently suggested color code model. The presented simulation protocols can be adapted to scalable and two-dimensional ion-trap architectures, which are currently under development.
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• J. T. Barreiro, M. Müller, P. Schindler, D. Nigg, T. Monz, M. Chwalla, M. Hennrich, C. F. Roos, P. Zoller, R. Blatt An open-system quantum simulator with trapped ions, Nature 470 491 (2011-02-24), 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 multi-qubit gates with optical pumping to implement coherent operations and dissipative processes. We illustrate our ability to engineer the open-system dynamics through the dissipative preparation of entangled states, the simulation of coherent many-body spin interactions, and the quantum non-demolition measurement of multi-qubit observables. By adding controlled dissipation to coherent operations, this work offers novel prospects for open-system quantum simulation and computation.
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• R. Gerritsma, B. P. Lanyon, G. Kirchmair, F. Zähringer, C. Hempel, J. Casanova, J. J. García-Ripoll, E. Solano, R. Blatt, C. F. Roos Quantum simulation of the Klein paradox with trapped ions, Phys. Rev. Lett. 106 060503 (2011-02-11), 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 frame-by-frame 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.

Proceeding

• C. F. Roos, R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt Quantum simulation of relativistic quantum physics with trapped ions, 22nd International Conference on Atomic Physics (Cairns, Australia, 2010-07-25) J. Phys. Conf. Ser. 264 012020 (2011-01-27), http://dx.doi.org/10.1088/1742-6596/264/1/012020 doi:10.1088/1742-6596/264/1/012020 (ID: 717471)

2010

Articles

• 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 (2010-12-02), http://dx.doi.org/10.1038/nphys1781 doi:10.1038/nphys1781 (ID: 717355) Toggle Abstract
  Multiparticle entanglement leads to richer correlations than two-particle entanglement and gives rise to striking contradictions with local realism1, inequivalent classes of entanglement2 and applications such as one-way 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: Bell-inequality violation, entanglement superactivation, bound entanglement and full separability. We also develop new theoretical tools for characterizing entanglement in quantum states. Recent quantum-computing, state-engineering and simulation paradigms driven by dissipative or decohering environments5, 6, 7 can benefit from the environment engineering techniques demonstrated here.
• J. Casanova, J. J. García-Ripoll, R. Gerritsma, C. F. Roos, E. Solano Klein tunneling and Dirac potentials in trapped ions, Phys. Rev. A 82 020101(R) (2010-10-01), http://dx.doi.org/10.1103/PhysRevA.82.020101 doi:10.1103/PhysRevA.82.020101 (ID: 717386)
• J. Casanova, G. Romero, I. Lizuain, J. C. Retamal, C. F. Roos, J. G. Muga, E. Solano Short-time-interaction quantum measurement through an incoherent mediator, Phys. Rev. A 81 062126 (2010-06-25), http://dx.doi.org/10.1103/PhysRevA.81.062126 doi:10.1103/PhysRevA.81.062126 (ID: 717259)
• 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 (2010-03-09), http://dx.doi.org/10.1103/PhysRevLett.104.100503 doi:10.1103/PhysRevLett.104.100503 (ID: 717148)
• O. Gühne, M. Kleinmann, A. Cabello, J. Larson, G. Kirchmair, F. Zähringer, R. Gerritsma, C. F. Roos Compatibility and noncontextuality for sequential measurements, Phys. Rev. A 81 022121 (2010-02-26), http://dx.doi.org/10.1103/PhysRevA.81.022121 doi:10.1103/PhysRevA.81.022121 (ID: 717143)
• R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C. F. Roos Quantum simulation of the Dirac equation, Nature 463 71 (2010-01-07), http://dx.doi.org/10.1038/nature08688 doi:10.1038/nature08688 (ID: 716977)

2009

Articles

• T. Monz, K. Kim, A. Villar, P. Schindler, M. Chwalla, M. Riebe, C. F. Roos, H. Häffner, W. Hänsel, M. Hennrich, R. Blatt Realization of universal ion-trap quantum computation with decoherence-free qubits, Phys. Rev. Lett. 103 200503 (2009-11-13), http://dx.doi.org/10.1103/PhysRevLett.103.200503 doi:10.1103/PhysRevLett.103.200503 (ID: 716801)
• X. R. Nie, C. Roos, D. James Theory of cross phase modulation for the vibrational modes of trapped ions, DFG - Physik, Math. u. Geowissen. 373 422 (2009), http://dx.doi.org/10.1016/j.physleta.2008.11.045 doi:10.1016/j.physleta.2008.11.045 (ID: 646595)
• M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. Villar, W. Hänsel, C. Roos, R. Blatt, M. Abgrall, G. Santarelli, G. D. Rovera, P. Laurent Absolute frequency measurement of the 40Ca+ 4s 2S1/2 - 3d 2D5/2 clock transition, Phys. Rev. Lett. 102 023002 (2009), http://dx.doi.org/10.1103/PhysRevLett.102.023002 doi:10.1103/PhysRevLett.102.023002 (ID: 650530)
• V. Nebendahl, H. Häffner, C. Roos Optimal control of entangling operations for trapped-ion quantum computing, Phys. Rev. A 79 012312 (2009), http://dx.doi.org/10.1103/PhysRevA.79.012312 doi:10.1103/PhysRevA.79.012312 (ID: 650641)
• G. Kirchmair, J. Benhelm, F. Zähringer, R. Gerritsma, C. Roos, R. Blatt Deterministic entanglement of ions in thermal states of motion, 11 023002 (2009), http://dx.doi.org/10.1088/1367-2630/11/2/023002 doi:10.1088/1367-2630/11/2/023002 (ID: 655090)
• G. Kirchmair, J. Benhelm, F. Zähringer, R. Gerritsma, C. Roos, R. Blatt High-fidelity entanglement of 43Ca+ hyperfine clock states, Phys. Rev. A 79 020304 (2009), http://dx.doi.org/10.1103/PhysRevA.79.020304 doi:10.1103/PhysRevA.79.020304 (ID: 657856)
• G. Kirchmair, F. Zähringer, R. Gerritsma, M. Kleinmann, O. Gühne, A. Cabello, R. Blatt, C. Roos State-independent experimental test of quantum contextuality, Nature 460 494 (2009), http://dx.doi.org/10.1038/nature08172 doi:10.1038/nature08172 (ID: 695207) Toggle Abstract
  The question of whether quantum phenomena can be explained by classical models with hidden variables is the subject of a long-lasting debate. In 1964, Bell showed that certain types of classical models cannot explain the quantum mechanical predictions for specific states of distant particles, and some types of hidden variable models have been experimentally ruled out. An intuitive feature of classical models is non-contextuality: the property that any measurement has a value independent of other compatible measurements being carried out at the same time. However, a theorem derived by Kochen, Specker and Bell shows that non-contextuality is in conflict with quantum mechanics. The conflict resides in the structure of the theory and is independent of the properties of special states. It has been debated whether the Kochen–Specker theorem could be experimentally tested at all. First tests of quantum contextuality have been proposed only recently, and undertaken with photons and neutrons. But these tests required the generation of special quantum states and left various loopholes open. Here we perform an experiment with trapped ions that demonstrates a state-independent conflict with non-contextuality. The experiment is not subject to the detection loophole and we show that, despite imperfections and possible measurement disturbances, our results cannot be explained in non-contextual terms.

Proceedings

• M. Chwalla, J. Benhelm, K. Kim, G. Kirchmair, T. Monz, M. Riebe, P. Schindler, A. Villar, W. Hänsel, C. F. Roos, R. Blatt, M. Abgrall, G. Santarelli, D. Rovera, P. Laurent Absolute frequency measurement of the 40Ca+ S1/2-D5/2 clock transition, Proceedings of the 7th symposium on frequency standards and metrology 7th symposium on frequency standards and metrology (Pacific Grove, 2008-10-05) 108 (2009-10-28), (ID: 716779)
• J. Benhelm, G. Kirchmair, R. Gerritsma, F. Zähringer, T. Monz, P. Schindler, M. Chwalla, W. Hänsel, M. Hennrich, C. F. Roos, R. Blatt Ca+ quantum bits for quantum information processing, Physica Scripta T137 014008 (2009-05-25), (ID: 716979)

2008

Articles

• C. Roos Ion trap quantum gates with amplitude-modulated laser beams, 10 013002 (2008), http://dx.doi.org/10.1088/1367-2630/10/1/013002 doi:10.1088/1367-2630/10/1/013002 (ID: 551545)
• C. Roos Dynamics of entanglement, Nature Phys. 4 97 (2008), http://dx.doi.org/10.1038/nphys847 doi:10.1038/nphys847 (ID: 557615)
• J. Benhelm, G. Kirchmair, C. Roos, R. Blatt Towards fault-tolerant quantum computing with trapped ions, Nature Phys. 4 463 (2008), http://dx.doi.org/10.1038/nphys961 doi:10.1038/nphys961 (ID: 578533)
• C. Roos, T. Monz, K. Kim, M. Riebe, H. Häffner, D. James, R. Blatt Nonlinear coupling of continuous variables at the single quantum level, Phys. Rev. A 77 040302(R) (2008), http://dx.doi.org/10.1103/PhysRevA.77.040302 doi:10.1103/PhysRevA.77.040302 (ID: 579025)
• K. Kim, C. Roos, L. Aolita, H. Häffner, V. Nebendahl, R. Blatt Geometric phase gate on an optical transition for ion trap quantum computation, Phys. Rev. A 77 050303(R) (2008), http://dx.doi.org/10.1103/PhysRevA.77.050303 doi:10.1103/PhysRevA.77.050303 (ID: 583053)
• J. Benhelm, G. Kirchmair, C. Roos, R. Blatt Experimental quantum information processing with 43Ca+ ions, Phys. Rev. A 77 062306 (2008), http://dx.doi.org/10.1103/PhysRevA.77.062306 doi:10.1103/PhysRevA.77.062306 (ID: 595124)
• R. Gerritsma, G. Kirchmair, F. Zähringer, J. Benhelm, R. Blatt, C. Roos Precision measurement of the branching fractions of the 4p 2P3/2 decay of Ca II, Eur. Phys. J. D 50 13 (2008), http://dx.doi.org/10.1140/epjd/e2008-00196-9 doi:10.1140/epjd/e2008-00196-9 (ID: 621123)
• H. Häffner, C. Roos, R. Blatt Quantum computing with trapped ions, Physics Reports 469 155-203 (2008), http://dx.doi.org/10.1016/j.physrep.2008.09.003 doi:10.1016/j.physrep.2008.09.003 (ID: 630261)

Proceeding

• C. Roos, M. Chwalla, T. Monz, P. Schindler, K. Kim, M. Riebe, R. Blatt Quantum information processing and Ramsey spectroscopy with trapped ions, Laser Spectroscopy: Proceedings of the XVIII International Conference (ICOLS) (Telluride, USA, 2007-06-24) 53 (2008), (ID: 594009)

2007

Articles

• C. Wunderlich, T. Hannemann, T. Körber, H. Häffner, C. Roos, W. Hänsel, R. Blatt, F. Schmidt-Kaler Robust state preparation of a single trapped ion by adiabatic passage, J. Mod. Opt. 1541 (2007), http://dx.doi.org/10.1080/09500340600741082 doi:10.1080/09500340600741082 (ID: 434966) (local copy)
• J. Benhelm, G. Kirchmair, U. D. Rapol, T. Körber, C. Roos, R. Blatt Measurement of the hyperfine structure of the S1/2-D5/2 transition in 43Ca+, Phys. Rev. A 75 032506 (2007), http://dx.doi.org/10.1103/PhysRevA.75.032506 doi:10.1103/PhysRevA.75.032506 (ID: 461034) (local copy)
• M. Riebe, M. Chwalla, J. Benhelm, H. Häffner, W. Hänsel, C. Roos, R. Blatt Quantum teleportation with atoms: quantum process tomography, 9 211 (2007), (ID: 499882) Toggle Abstract
  The performance of a quantum teleportation algorithm implemented on an ion trap quantum computer is investigated. First the algorithm is analysed in terms of the teleportation fidelity of six input states evenly distributed over the Bloch sphere. Furthermore, a quantum process tomography of the teleportation algorithm is carried out which provides almost complete knowledge about the algorithm.
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• L. Aolita, K. Kim, J. Benhelm, C. Roos, H. Häffner High-fidelity ion-trap quantum computing with hyperfine clock states, Phys. Rev. A 76 040303(R) (2007), URL (ID: 532174)
• M. Chwalla, K. Kim, T. Monz, P. Schindler, M. Riebe, C. Roos, R. Blatt Precision spectroscopy with two correlated atoms, 89 483 (2007), (ID: 545098)

2006

Articles

• C. Roos, M. Chwalla, K. Kim, M. Riebe, R. Blatt Designer atoms for quantum metrology, Nature 443 319 (2006), http://dx.doi.org/10.1038/nature05101 doi:10.1038/nature05101 (ID: 390237) (local copy)
• J. Korbicz, O. Gühne, M. Lewenstein, H. Häffner, C. Roos, R. Blatt Generalized spin-queezing inequalities in N-qubit systems, Phys. Rev. A 74 052319 (2006), http://dx.doi.org/10.1103/PhysRevA.74.052319 doi:10.1103/PhysRevA.74.052319 (ID: 420124) Toggle Abstract
  We present detailed derivations, various improvements and application to concrete experimental data of spin squeezing inequalities formulated recently by some of us [Phys. Rev. Lett. 95, 120502 (2005)]. These inequalities generalize the concept of the spin squeezing parameter, and provide necessary and sufficient conditions for genuine 2-, or 3- qubit entanglement for symmetric states, and sufficient entanglement condition for general $N$-qubit states. We apply our method to theoretical study of Dicke states, and, in particular, to W-states of N qubits. Then, we analyze the recently experimentally generated 7- and 8-ion W-states [Nature 438, 643 (2005)]. We also present some novel details concerning this experiment. Finally, we improve criteria for detection of genuine tripartite entanglement based on entanglement witnesses.
• M. Riebe, K. Kim, P. Schindler, T. Monz, P. O. Schmidt, T. Körber, W. Hänsel, H. Häffner, C. Roos, R. Blatt Process tomography of ion trap quantum gates, Phys. Rev. Lett. 97 220407 (2006), http://dx.doi.org/10.1103/PhysRevLett.97.220407 doi:10.1103/PhysRevLett.97.220407 (ID: 423123) (local copy)

Proceedings

• H. Häffner, M. Riebe, F. Schmidt-Kaler, W. Hänsel, C. Roos, M. Chwalla, J. Benhelm, T. Körber, G. Lancaster, C. Becher, D. James, R. Blatt Controlling three atomic qubits, Physical Realizations of Quantum Computing 108 (2006), (ID: 361308) Toggle Abstract
  We present a series of experiments where up to three ions held in a Paul trap are entangled, a given number of ions is selectively read out while conditional single-quantum-bit (qubit) operations are performed coherently on the remaining ion(s). Using these techniques, we demonstrate also a state transfer of a quantum bit from one ion to another one using two measurements and entanglement between an auxiliary ion and the target ion -- also known as teleportation.
• H. Häffner, F. Schmidt-Kaler, W. Hänsel, C. Roos, P. O. Schmidt, M. Riebe, M. Chwalla, D. Chek-al-Kar, J. Benhelm, U. D. Rapol, T. Körber, C. Becher, R. Blatt Long lived entangled states, Foundations of Quantum Mechanics in the Light of New Technology ISQM-Tokyo (Tokyo, Japan, 2005-08-22) 33 (2006), (ID: 375560) Toggle Abstract
  We investigate entangled states of two trapped Calcium-40 ions. By encoding the quantum information in the Zeeman-manifold of the ground state, we observe entangled states lasting for more than 20 seconds.
• C. Roos, M. Chwalla, K. Kim, M. Riebe, R. Blatt Precision spectroscopy with entangled states: Measurement of electric quadrupole moments, Atomic physics 20 (Innsbruck, Austria, 2006-07-16) 111-118 (2006), (ID: 420335)

2005

Articles

• H. Häffner, W. Hänsel, C. Roos, J. Benhelm, D. Chek-al-Kar, M. Chwalla, T. Körber, U. D. Rapol, M. Riebe, P. O. Schmidt, C. Becher, O. Gühne, W. Dür, R. Blatt Scalable multi-particle 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 non-interacting 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 non-exponential 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 eight-particle 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 test-bed 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. Schmidt-Kaler, 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 sub-systems collapses the quantum state. Here we investigate entangled states of two trapped Ca+ ions and observe robust entanglement lasting for more than 20 s.
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• A. Kreuter, C. Becher, G. Lancaster, A. B. Mundt, C. Russo, H. Häffner, C. Roos, W. Hänsel, F. Schmidt-Kaler, R. Blatt, M. Safronova New experimental and theoretical approach to the 3d ²D-level lifetimes of ⁴⁰Ca⁺, Phys. Rev. A 71 032504 (2005), (ID: 314807) (local copy)

Proceedings

• H. Häffner, M. Riebe, F. Schmidt-Kaler, W. Hänsel, C. Roos, M. Chwalla, J. Benhelm, T. Körber, C. Becher, D. James, R. Blatt Teleportation with Atoms, Atomic Physics (Rio De Janeiro) 19 341-349 (2005), (ID: 314808) Toggle Abstract
  The teleportation of an atomic state accomplishes the complete transfer of information from one particle to another, employing the non-local properties of quantum mechanics. Recently, two groups have achieved the deterministic teleportation of a quantum state between a pair of trapped ions. Following closely the original proposal of Bennett et al.[1], a highly entangled pair of ions is created, a complete Bell-state projective measurement involving the source ion and one of the entangled pair is carried out, and state reconstruction conditioned on this measurement is performed on the other half of the entangled pair.
• C. Becher, J. Benhelm, D. Chek-al-Kar, M. Chwalla, W. Dür, O. Gühne, H. Häffner, W. Hänsel, T. Körber, A. Kreuter, G. Lancaster, T. Monz, E. Phillips, U. D. Rapol, M. Riebe, C. Roos, C. Russo, F. Schmidt-Kaler, R. Blatt Entanglement of trapped ions, Laser Spectroscopy ICOLS XVII 392 (2005), (ID: 327393) Toggle Abstract
  Entanglement, its generation, manipulation, measurement and fundamental understanding is at the very heart of quantum mechanics. We here report on the creation and characterization of entangled states of up to 8 trapped ions, the investigation of long-lived two-ion Bell-states and on experiments towards entangling ions and photons.

2004

Articles

• C. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. Lancaster, C. Becher, F. Schmidt-Kaler, R. Blatt Control and Measurment of Three-Qubit Entangled States, Science 304 1478 (2004), (ID: 342102) Toggle Abstract
  We report the deterministic creation of maximally entangled three-qubit states—specifically the Greenberger-Horne-Zeilinger (GHZ ) state and the W state—with a trapped-ion 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 single-qubit rotations.
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• C. Roos, G. Lancaster, M. Riebe, H. Häffner, W. Hänsel, S. Gulde, C. Becher, J. Eschner, F. Schmidt-Kaler, 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 near-unity 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.
• A. Kreuter, C. Becher, G. Lancaster, A. B. Mundt, C. Russo, H. Häffner, C. Roos, J. Eschner, F. Schmidt-Kaler, R. Blatt Spontaneous Emission Lifetime of a Single Trapped Ca+ Ion in a High Finesse Cavity, Phys. Rev. Lett. 92 203002 (2004), (ID: 342120)
• R. Blatt, H. Häffner, C. Roos, C. Becher, F. Schmidt-Kaler Ion Trap Quantum Computing with Ca+ Ions, Quant. Inf. Proc. 3 1-5 (2004), (ID: 513993)
• M. Riebe, H. Häffner, C. Roos, W. Hänsel, J. Benhelm, G. Lancaster, T. Körber, C. Becher, F. Schmidt-Kaler, 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 quantum-state teleportation to be performed. Teleportation using pairs of entangled photons has been demonstrated2–6, but such techniques are probabilistic, requiring post-selection of measured photons. Here, we report deterministic quantum-state 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 Bell-state 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.
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2003

Articles

• F. Schmidt-Kaler, 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/s00340-003-1346-9 doi:10.1007/s00340-003-1346-9 (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 single-qubit and of universal two-qubit 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.
• F. Schmidt-Kaler, H. Häffner, M. Riebe, S. Gulde, G. Lancaster, T. Deuschle, C. Becher, C. Roos, J. Eschner, R. Blatt Realization of the Cirac-Zoller controlled-NOT 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 controlled-NOT (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 long-lived 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.
• C. Roos, P. Cren, D. Guery-Odelin, J. Dalibard Continuous loading of a non-dissipative atom trap, 61 187 (2003), (ID: 469814)
• C. Roos, P. Cren, T. Lahaye, J. Dalibard, D. Guery-Odelin Injection of a cold atomic beam into a magnetic guide, Laser Phys. 13 605 (2003), (ID: 469815)
• T. Lahaye, P. Cren, C. Roos, D. Guery-Odelin Propagation of guided atoms, Comm. Nonlin. Sci. Num. 8 315 (2003), (ID: 469816)

2002

Article

• P. Cren, C. Roos, A. Aclan, J. Dalibard, D. Guery-Odelin Loading of a cold atomic beam into a magnetic guide, Eur. Phys. J. D 20 107 (2002), (ID: 469813)

Proceedings

• F. Schmidt-Kaler, J. Eschner, R. Blatt, D. Leibfried, C. Roos, G. Morigi Laser Cooling of trapped ions, Laser Physics at the limit 243-260 (2002), (ID: 628430)
• C. Roos, D. Leibfried, F. Schmidt-Kaler, J. Eschner, R. Blatt Sideband cooling and state manipulation: Application in precision spectroscopy, Proc. 6th Symp. Frequency Standards and Metrology 376-384 (2002), (ID: 628432)

2001

Articles

• F. Schmidt-Kaler, 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 ground-state 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 ground-state cooling of neutral atoms trapped by a far-detuned standing wave laser field.
• H. Rohde, S. Gulde, C. Roos, P. Barton, D. Leibfried, J. Eschner, F. Schmidt-Kaler, R. Blatt Sympathetic ground state cooling and coherent manipulation with two-ion-crystals, J. Opt. B: Quantum Semiclass. Opt. 3 34 (2001), (ID: 469819)

Proceedings

• D. Leibfried, C. Roos, P. Barton, H. Rohde, S. Gulde, A. B. Mundt, F. Schmidt-Kaler, J. Eschner, R. Blatt Towards quantum information with trapped Calcium ions, Quantum Communication, Computing and Measurement 3 179 (2001), (ID: 628450)
• D. Leibfried, C. Roos, P. Barton, H. Rohde, S. Gulde, A. B. Mundt, G. Reymond, M. Lederbauer, F. Schmidt-Kaler, J. Eschner, R. Blatt Experiments towards quantum information with trapped Calcium ions, Atomic Physics (Proceedings of the ICAP 2000) 17 130 (2001), (ID: 628457)

2000

Articles

• C. Roos, D. Leibfried, A. B. Mundt, F. Schmidt-Kaler, 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 L-shaped 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. Schmidt-Kaler, R. Blatt Sympathetic ground state cooling and coherent manipulation with two-ion-crystals, J. Opt. B: Quantum Semiclass. Opt. 3 S3 (2000), (ID: 344234) Toggle Abstract
  We have cooled a two-ion crystal to the ground-state 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.
• A. Steane, C. Roos, D. Stevens, A. B. Mundt, D. Leibfried, F. Schmidt-Kaler, 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.
• H. Nägerl, C. Roos, D. Leibfried, H. Rohde, G. Thalhammer, J. Eschner, F. Schmidt-Kaler, 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 Doppler-cooled 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 sub-Doppler 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. Schmidt-Kaler, 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. Schmidt-Kaler, R. Blatt Addressing and cooling of single ions in Paul traps, Fortschr. Phys. 48 623 (2000), (ID: 619587)

1999

Article

• C. Roos, T. Zeiger, H. Rohde, H. Nägerl, J. Eschner, D. Leibfried, F. Schmidt-Kaler, R. Blatt Quantum state engineering on an optical transition and decoherence in a Paul trap, Phys. Rev. Lett. 83 4713 (1999), (ID: 344238)

Proceedings

• F. Schmidt-Kaler, C. Roos, H. Nägerl, H. Rohde, S. Gulde, A. B. Mundt, T. Zeiger, G. Reymond, G. Thalhammer, D. Leibfried, J. Eschner, R. Blatt Single ions in Paul traps, Laser Spectroscopy XIV 246 (1999), (ID: 628460)
• H. Nägerl, C. Roos, H. Rohde, D. Leibfried, J. Eschner, F. Schmidt-Kaler, R. Blatt Single Ions in Paul traps, Decoherence: Theoretical, Experimental and Conceptual Problems (1999), (ID: 628462)

1997

Article

• C. Roos, A. Zippelius, P. M. Goldbart Random networks of crosslinked manifolds, J. Phys. A: Math. Gen. 30 1967 (1997), (ID: 469817)