F. Kranzl, A. Lasek, M. K. Joshi, A. Kalev, R. Blatt, C. F. Roos, N. Yunger Halpern Experimental observation of thermalization with noncommuting charges,
Phys. Rev. X Quantum 4 20318 (2023-04-28),
http://dx.doi.org/10.1103/PRXQuantum.4.020318 doi:10.1103/PRXQuantum.4.020318 (ID: 720810)
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,
Phys. Rev. X Quantum 4 20317 (2023-04-28),
http://dx.doi.org/10.1103/PRXQuantum.4.020317 doi:10.1103/PRXQuantum.4.020317 (ID: 721039)
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.
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)
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)
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)
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)
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)
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)
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.
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)
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)
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)
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.
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)
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)
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)
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)
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)
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.
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)
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)
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)
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)
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. (local copy)
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)
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. (local copy)
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)
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. (local copy)
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)
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.
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),
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. (local copy)
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),
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),
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),
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),
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. (local copy)
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),
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),
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),
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),
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),
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),