
M. K. Joshi, C. Kokail, R. van Bijnen, F. Kranzl, T. Zache, R. Blatt, C. F. Roos, P. Zoller Exploring LargeScale Entanglement in Quantum Simulation,
Nature 624 539 (20231129),
http://dx.doi.org/10.1038/s41586023067680 doi:10.1038/s41586023067680 (ID: 721080)
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Entanglement is a distinguishing feature of quantum manybody 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 51ion programmable quantum simulator and perform sampleefficient `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 spatiallyvarying temperature profile as a signature of entanglement. Our results also show the transition from area to volumelaw 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 wideranging applicability to revealing and understanding entanglement in manybody 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 longrange, anisotropic Heisenberg model,
Phys. Rev. X 13 03101712 (20230811),
http://dx.doi.org/10.1103/PhysRevX.13.031017 doi:10.1103/PhysRevX.13.031017 (ID: 720909)
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Over the recent years coherent, timeperiodic modulation has been established as a versatile tool for realizing novel Hamiltonians. Using this approach, known as Floquet engineering, we experimentally realize a longranged, anisotropic Heisenberg model with tunable interactions in a trapped ion quantum simulator. We demonstrate that the spectrum of the model contains not only single magnon excitations but also composite magnon bound states. For the longrange interactions with the experimentally realized powerlaw exponent, the group velocity of magnons is unbounded. Nonetheless, for sufficiently strong interactions we observe bound states of these unconventional magnons which possess a nondiverging group velocity. By measuring the configurational mutual information between two disjoint intervals, we demonstrate the implications of the bound state formation on the entanglement dynamics of the system. Our observations provide key insights into the peculiar role of composite excitations in the nonequilibrium dynamics of quantum manybody systems.

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 (20230614),
http://dx.doi.org/10.1103/PRXQuantum.4.040346 doi:10.1103/PRXQuantum.4.040346 (ID: 721085)
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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 groundstate cooled crystal is interrogated for thermometry, complex manybody 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 (20230428),
http://dx.doi.org/10.1103/PRXQuantum.4.020318 doi:10.1103/PRXQuantum.4.020318 (ID: 720810)
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Quantum simulators have recently enabled experimental observations of the internal thermalization of quantum manybody systems. Often, the global energy and particle number are conserved and the system is prepared with a welldefined 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 trappedion 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 welldefined nontrivial values simultaneously. We simulate a Heisenberg evolution using laserinduced 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 nonAbelian thermal state. This work bridges quantum manybody 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 twodimensional Coulomb crystals of more than 100 ions in a monolithic radiofrequency trap,
PRX Quantum 4 20317 (20230428),
http://dx.doi.org/10.1103/PRXQuantum.4.020317 doi:10.1103/PRXQuantum.4.020317 (ID: 721039)
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Linear strings of trapped atomic ions held in radiofrequency (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 twodimensional spin models with singleparticle 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 outofplane 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 longrange entangling interactions.

J. Franke, S. M. Muleady, C. R. Kaubrügger, F. Kranzl, R. Blatt, A. M. Rey, M. K. Joshi, C. F. Roos Quantumenhanced sensing on optical transitions through finiterange interactions,
Nature 621 740 (20230327),
http://dx.doi.org/10.1038/s4158602306472z doi:10.1038/s4158602306472z (ID: 721072)
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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 statedependent interactions that decay as a powerlaw function of the ion separation. We show our sensor can be made to behave as a oneaxistwisting (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 spinwave 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 nonGaussian states in the form of atomic multiheaded cat states in the Qdistribution. 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 Ramseytype interferometer, where we reduce the measurement uncertainty by −3.2±0.5 dB below the standard quantum limit for N = 51 ions.

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

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

A. Elben, B. Vermersch, C. F. Roos, P. Zoller Statistical correlations between locally randomized measurements: a toolbox for probing entanglement in manybody quantum states,
Phys. Rev. A 99 52323 (20190515),
http://dx.doi.org/10.1103/PhysRevA.99.052323 doi:10.1103/PhysRevA.99.052323 (ID: 720100)
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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 trappedion 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. GuevaraBertsch, D. Heinrich, Ó. A. Herrera, Y. Colombe, R. Blatt, C. F. Roos Frequency measurement of the 1S0,F=5/2 to 3P1,F=7/2 transition of 27Al+ via quantum logic spectroscopy with 40Ca+,
New J. Phys. 21 103003 (20190425),
http://dx.doi.org/10.1088/13672630/ab447a doi:10.1088/13672630/ab447a (ID: 720264)
Toggle Abstract
We perform quantum logic spectroscopy with a 27Al+/40Ca+ mixed ion crystal in a linear Paul trap for a measurement of the (3s2)1S0 to (3s3p)3P1,F=7/2 intercombination transition in 27Al+. Towards this end, Ramsey spectroscopy is used for probing the transition in 27Al+ and the (4s2)S1/2 to (4s3d)D5/2 clock transition in 40Ca+ in interleaved measurements. By using the precisely measured frequency of the clock transition in 40Ca+ as a frequency reference, we determine the frequency of the intercombination line to be 1S0 to 3P1,F=7/2=1122 842 857 334 736(93) Hz and the Landé gfactor of the excited state to be g3P1,F=7/2=0.428132(2).

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

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

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

M. Hettrich, T. Ruster, H. Kaufmann, C. F. Roos, C. T. Schmiegelow, F. SchmidtKaler, U. Poschinger Measurement of dipole matrix elements with a single trapped ion,
Phys. Rev. Lett. 115 143003 (20150512),
http://dx.doi.org/10.1103/PhysRevLett.115.143003 doi:10.1103/PhysRevLett.115.143003 (ID: 719242)
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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 offresonant lightion 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 (20150511),
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 manybody quantum systems are often well described by collective excitations, known as quasiparticles. Engineered quantum systems offer the opportunity to study such emergent phenomena in a precisely controlled and otherwise inaccessible way. We present a spectroscopic technique to study artificial quantum matter and use it for characterizing quasiparticles in a manybody system of trapped atomic ions. Our approach is to excite combinations of the system's fundamental quasiparticle eigenmodes, given by delocalised spin waves. By observing the dynamical response to superpositions of such eigenmodes, we extract the system dispersion relation, magnetic order, and even detect signatures of quasiparticle interactions. Our technique is not limited to trapped ions, and it is suitable for verifying quantum simulators by tuning them into regimes where the collective excitations have a simple form.

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

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

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

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

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 (20130530),
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 nonequilibrium coherent dynamics after a quantum quench in such systems, identifying qualitatively different behavior as the exponent of algebraically decaying spinspin interactions in a transverse Ising chain is varied. Computing the buildup 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. Counterintuitively, the growth of bipartite entanglement for longrange 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 largescale 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. GarcíaRipoll, E. Solano Quantum simulation of quantum field theories in trapped ions,
Phys. Rev. Lett. 107 260501 (20111219),
http://dx.doi.org/10.1103/PhysRevLett.107.260501 doi:10.1103/PhysRevLett.107.260501 (ID: 717840)
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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. GarcíaRipoll, E. Solano Quantum simulation of the Majorana equation and unphysical operations,
Phys. Rev. X 1 021018 (20111212),
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 nonHamiltonian 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. GarcíaRipoll, E. Solano Relativistic quantum mechanics with trapped ions,
New J. Phys. 13 095003 (20110911),
http://dx.doi.org/10.1088/13672630/13/9/095003 doi:10.1088/13672630/13/9/095003 (ID: 717766)
Toggle Abstract
We consider the quantum simulation of relativistic quantum
mechanics, as described by the Dirac equation and classical potentials, in trappedion 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 (20110901),
http://dx.doi.org/10.1126/science.1208001 doi:10.1126/science.1208001 (ID: 717768)
Toggle Abstract
A digital quantum simulator is an envisioned quantum device that can be programmed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions. Using sequences of up to 100 gates and 6 qubits, the fulltime dynamics of a range of spin systems are digitally simulated. Interactions beyond those naturally present in our simulator are accurately reproduced, and quantitative bounds are provided for the overall simulation quality. Our results demonstrate the key principles of digital quantum simulation and provide evidence that the level of control required for a fullscale device is within reach.
(local copy)

M. Müller, K. Hammerer, Y. Zhou, C. F. Roos, P. Zoller Simulating open quantum systems: from manybody interactions to stabilizer pumping,
New J. Phys. 13 085007 (20110810),
http://dx.doi.org/10.1088/13672630/13/8/085007 doi:10.1088/13672630/13/8/085007 (ID: 717750)
Toggle Abstract
In a recent experiment, Barreiro et al (2011 Nature 470 486) demonstrated the fundamental building blocks of an opensystem quantum simulator with trapped ions. Using up to five ions, dynamics were realized by sequences that combined single and multiqubit entangling gate operations with optical pumping. This enabled the implementation of both coherent manybody 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 fourqubit states, the simulation of coherent fourbody spin interactions and the quantum nondemolition measurement of a multiqubit stabilizer operator. In this paper, we present the theoretical framework of this gatebased ('digital') simulation approach for opensystem 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 stateoftheart linear iontrap 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 twodimensional iontrap 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 opensystem quantum simulator with trapped ions,
Nature 470 491 (20110224),
http://dx.doi.org/10.1038/nature09801 doi:10.1038/nature09801 (ID: 717617)
Toggle Abstract
The control of quantum systems is of fundamental scientific interest and promises powerful applications and
technologies. Impressive progress has been achieved in isolating quantum systems from the environment and
coherently controlling their dynamics, as demonstrated by the creation and manipulation of entanglement in various
physical systems. However, for open quantum systems, engineering the dynamics of many particles by a controlled
coupling to an environment remains largely unexplored. Here we realize an experimental toolbox for simulating an open
quantum system with up to five quantum bits (qubits). Using a quantum computing architecture with trapped ions, we
combine multiqubit gates with optical pumping to implement coherent operations and dissipative processes. We
illustrate our ability to engineer the opensystem dynamics through the dissipative preparation of entangled states,
the simulation of coherent manybody spin interactions, and the quantum nondemolition measurement of multiqubit
observables. By adding controlled dissipation to coherent operations, this work offers novel prospects for opensystem
quantum simulation and computation.
(local copy)

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

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

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

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

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

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

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

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

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

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

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

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