Publications

2013
N Aharon, M Drewsen, and A Retzker. 12/6/2013. “General Scheme for the Construction of a Protected Qubit Subspace.” Physical Review Letters, 111, 23. Publisher's Version Abstract
We present a new robust decoupling scheme suitable for levels with either half-integer or integer angular momentum states. Through continuous dynamical decoupling techniques, we create a protected qubit subspace, utilizing a multistate qubit construction. Remarkably, the multistate system can also be composed of multiple substates within a single level. Our scheme can be realized with state-of-the-art experimental setups and thus has immediate applications for quantum information science. While the scheme is general and relevant for a multitude of solid-state and atomic systems, we analyze its performance for the case composed of trapped ions. Explicitly, we show how single qubit gates and an ensemble coupling to a cavity mode can be implemented efficiently. The scheme predicts a coherence time of ∼1  s, as compared to typically a few milliseconds for the bare states.
MB Plenio and A Retzker. 11/4/2013. “Ion Traps as a testbed of classical and quantum statistical mechanics.” Annalen Der Physik, 525, 10-11, Pp. A159-A162. Publisher's Version Abstract
The development of statistical mechanics over the last century represents a major advance in the Natural Sciences. It is capable of describing a wide range of phenomena including the properties of phase transitions by reducing the complexity of quantum-many-body systems to simple general principles rooted in statistical methods that hold true in macroscopic systems. These principles apply to a broad range of physical theories, encompassing phenomena that are for example governed by classical, relativistic or quantum physics. While many of these predictions have been confirmed experimentally, the exploration, under highly controlled conditions, of the statistical mechanics of mesoscopic systems and the theoretical prediction of their behavior does still represent a challenge for both theory and experiment. A new avenue towards the controlled exploration of the classical and quantum statistical mechanics of mesoscopic systems has opened up in recent years thanks to the remarkable achievements in ion trap physics, which is pursued mainly for the realization of quantum information processing and precision metrology, in controlling and manipulating ion crystals.
HL Partner, R Nigmatullin, T Burgermeister, K Pyka, J Keller, A Retzker, MB Plenio, and TE Mehlstaubler. 10/16/2013. “Dynamics of topological defects in ion Coulomb crystals.” New Journal of Physics, 15. Publisher's Version Abstract
We study experimentally and theoretically the properties of structural defects (kink solitons) in two-dimensional ion Coulomb crystals. We show how different types of kink solitons with different physical properties can be realized, and transformed from one type into another by varying the aspect ratio of the trap confinement. Further, we discuss how impurities in ion Coulomb crystals, such as mass defects, can modify the dynamics of kink creation and their stability. For both pure and impure crystals, the experimentally observed kink dynamics are analysed in detail and explained theoretically by numerical simulations and calculations of the Peierls–Nabarro potential. Finally, we demonstrate that static electric fields provide a handle to vary the influence of mass defects on kinks in a controlled way and allow for deterministic manipulation and creation of kinks.
D Shwa, RD Cohen, A Retzker, and N Katz. 8/7/2013. “Heralded generation of Bell states using atomic ensembles.” Physical Review a, 88, 6. Publisher's Version Abstract
Traversal of a symmetry-breaking phase transition at finite rates can lead to causally separated regions with incompatible symmetries and the formation of defects at their boundaries, which has a crucial role in quantum and statistical mechanics, cosmology and condensed matter physics. This mechanism is conjectured to follow universal scaling laws prescribed by the Kibble–Zurek mechanism. Here we determine the scaling law for defect formation in a crystal of 16 laser-cooled trapped ions, which are conducive to the precise control of structural phases and the detection of defects. The experiment reveals an exponential scaling of defect formation γβ, where γ is the rate of traversal of the critical point and β=2.68±0.06. This supports the prediction of β=8/3≈2.67 for finite inhomogeneous systems. Our result demonstrates that the scaling laws also apply in the mesoscopic regime and emphasizes the potential for further tests of non-equilibrium thermodynamics with ion crystals.
S Ulm, J Rossnagel, G Jacob, C Degunther, ST Dawkins, UG Poschinger, R Nigmatullin, A Retzker, MB Plenio, F Schmidt-Kaler, and K Singer. 8/7/2013. “Observation of the Kibble-Zurek scaling law for defect formation in ion crystals.” Nature Communications, 4. Publisher's Version Abstract
Traversal of a symmetry-breaking phase transition at finite rates can lead to causally separated regions with incompatible symmetries and the formation of defects at their boundaries, which has a crucial role in quantum and statistical mechanics, cosmology and condensed matter physics. This mechanism is conjectured to follow universal scaling laws prescribed by the Kibble–Zurek mechanism. Here we determine the scaling law for defect formation in a crystal of 16 laser-cooled trapped ions, which are conducive to the precise control of structural phases and the detection of defects. The experiment reveals an exponential scaling of defect formation γβ, where γ is the rate of traversal of the critical point and β=2.68±0.06. This supports the prediction of β=8/3≈2.67 for finite inhomogeneous systems. Our result demonstrates that the scaling laws also apply in the mesoscopic regime and emphasizes the potential for further tests of non-equilibrium thermodynamics with ion crystals.
K Pyka, J Keller, HL Partner, R Nigmatullin, T Burgermeister, DM Meier, K Kuhlmann, A Retzker, MB Plenio, WH Zurek, A del Campo, and TE Mehlstaubler. 8/7/2013. “Topological defect formation and spontaneous symmetry breaking in ion Coulomb crystals.” Nature Communications, 4. Publisher's Version Abstract
Symmetry breaking phase transitions play an important role in nature. When a system traverses such a transition at a finite rate, its causally disconnected regions choose the new broken symmetry state independently. Where such local choices are incompatible, topological defects can form. The Kibble–Zurek mechanism predicts the defect densities to follow a power law that scales with the rate of the transition. Owing to its ubiquitous nature, this theory finds application in a wide field of systems ranging from cosmology to condensed matter. Here we present the successful creation of defects in ion Coulomb crystals by a controlled quench of the confining potential, and observe an enhanced power law scaling in accordance with numerical simulations and recent predictions. This simple system with well-defined critical exponents opens up ways to investigate the physics of non-equilibrium dynamics from the classical to the quantum regime.
A Albrecht, A Retzker, F Jelezko, and MB Plenio. 8/6/2013. “Coupling of nitrogen vacancy centres in nanodiamonds by means of phonons.” New Journal of Physics, 15. Publisher's Version Abstract
Realizing controlled quantum dynamics via the magnetic interactions between colour centres in diamond remains a challenge despite recent demonstrations for nanometre separated pairs. Here we propose to use the intrinsic acoustical phonons in diamond as a data bus for accomplishing this task. We show that for nanodiamonds the electron–phonon coupling can take significant values that together with mode frequencies in the THz range can serve as a resource for conditional gate operations. Based on these results, we analyse how to use this phonon-induced interaction for constructing quantum gates among the electron-spin triplet ground states, introducing the phonon dependence via Raman transitions. Combined with decoupling pulses this offers the possibility for creating entangled states within nanodiamonds on the scale of several tens of nanometres, a promising prerequisite for quantum sensing applications.
P London, J Scheuer, JM Cai, I Schwarz, A Retzker, MB Plenio, M Katagiri, T Teraji, S Koizumi, J Isoya, R Fischer, LP McGuinness, B Naydenov, and F Jelezko. 8/5/2013. “Detecting and Polarizing Nuclear Spins with Double Resonance on a Single Electron Spin.” Physical Review Letters, 111, 6. Publisher's Version Abstract
We report the detection and polarization of nuclear spins in diamond at room temperature by using a single nitrogen-vacancy (NV) center. We use Hartmann-Hahn double resonance to coherently enhance the signal from a single nuclear spin while decoupling from the noisy spin bath, which otherwise limits the detection sensitivity. As a proof of principle, we (i) observe coherent oscillations between the NV center and a weakly coupled nuclear spin and (ii) demonstrate nuclear-bath cooling, which prolongs the coherence time of the NV sensor by more than a factor of 5. Our results provide a route to nanometer scale magnetic resonance imaging and novel quantum information processing protocols.
JM Cai, A Retzker, F Jelezko, and MB Plenio. 1/20/2013. “A large-scale quantum simulator on a diamond surface at room temperature.” Nature Physics, 9, 3, Pp. 168-173. Publisher's Version Abstract
Strongly correlated quantum many-body systems may exhibit exotic phases, such as spin liquids and supersolids. Although their numerical simulation becomes intractable for as few as 50 particles, quantum simulators offer a route to overcome this computational barrier. However, proposed realizations either require stringent conditions such as low temperature/ultra-high vacuum, or are extremely hard to scale. Here, we propose a new solid-state architecture for a scalable quantum simulator that consists of strongly interacting nuclear spins attached to the diamond surface. Initialization, control and read-out of this quantum simulator can be accomplished with nitrogen-vacancy centers implanted in diamond. The system can be engineered to simulate a wide variety of strongly correlated spin models. Owing to the superior coherence time of nuclear spins and nitrogen-vacancy centers in diamond, our proposal offers new opportunities towards large-scale quantum simulation at ambient conditions of temperature and pressure.
JM Cai, F Jelezko, MB Plenio, and A Retzker. 1/11/2013. “Diamond-based single-molecule magnetic resonance spectroscopy.” New Journal of Physics, 15. Publisher's Version Abstract
The detection of a nuclear spin in an individual molecule represents a key challenge in physics and biology whose solution has been pursued for many years. The small magnetic moment of a single nucleus and the unavoidable environmental noise present the key obstacles for its realization. In this paper, we demonstrate theoretically that a single nitrogen-vacancy center in diamond can be used to construct a nano-scale single-molecule spectrometer that is capable of detecting the position and spin state of a single nucleus and can determine the distance and alignment of a nuclear or electron spin pair. The proposed device would find applications in single-molecule spectroscopy in chemistry and biology, for example in determining the protein structure or in monitoring macromolecular motions, and can thus provide a tool to help unravel the microscopic mechanisms underlying bio-molecular function.
2012
H Kaufmann, S Ulm, G Jacob, U Poschinger, H Landa, A Retzker, MB Plenio, and F Schmidt-Kaler. 12/28/2012. “Precise Experimental Investigation of Eigenmodes in a Planar Ion Crystal.” Physical Review Letters, 109, 26. Publisher's Version Abstract
The accurate characterization of eigenmodes and eigenfrequencies of two-dimensional ion crystals provides the foundation for the use of such structures for quantum simulation purposes. We present a combined experimental and theoretical study of two-dimensional ion crystals. We demonstrate that standard pseudopotential theory accurately predicts the positions of the ions and the location of structural transitions between different crystal configurations. However, pseudopotential theory is insufficient to determine eigenfrequencies of the two-dimensional ion crystals accurately but shows significant deviations from the experimental data obtained from resolved sideband spectroscopy. Agreement at the level of 2.5×10−3 is found with the full time-dependent Coulomb theory using the Floquet-Lyapunov approach and the effect is understood from the dynamics of two-dimensional ion crystals in the Paul trap. The results represent initial steps towards an exploitation of these structures for quantum simulation schemes.
JM Cai, B Naydenov, R Pfeiffer, LP McGuinness, KD Jahnke, F Jelezko, MB Plenio, and A Retzker. 11/20/2012. “Robust dynamical decoupling with concatenated continuous driving.” New Journal of Physics, 14. Publisher's Version Abstract
The loss of coherence is one of the main obstacles for the implementation of quantum information processing. The efficiency of dynamical decoupling schemes, which have been introduced to address this problem, is limited itself by the fluctuations in the driving fields which will themselves introduce noise. We address this challenge by introducing the concept of concatenated continuous dynamical decoupling, which can overcome not only external magnetic noise but also noise due to fluctuations in driving fields. We show theoretically that this approach can achieve relaxation limited coherence times, and demonstrate experimentally that already the most basic implementation of this concept yields an order of magnitude improvement to the decoherence time for the electron spin of nitrogen vacancy centers in diamond. The proposed scheme can be applied to a wide variety of other physical systems, including trapped atoms and ions and quantum dots, and may be combined with other quantum technologies challenges such as quantum sensing and quantum information processing.
H Landa, M Drewsen, B Reznik, and A Retzker. 10/23/2012. “Classical and quantum modes of coupled Mathieu equations.” Journal of Physics a-Mathematical and Theoretical, 45, 45. Publisher's Version Abstract
We expand the solutions of linearly coupled Mathieu equations in terms of infinite-continued matrix inversions, and use it to find the modes which diagonalize the dynamical problem. This allows obtaining explicitly the (Floquet–Lyapunov) transformation to coordinates in which the motion is that of decoupled linear oscillators. We use this transformation to solve the Heisenberg equations of the corresponding quantum-mechanical problem, and find the quantum wavefunctions for stable oscillations, expressed in configuration space. The obtained transformation and quantum solutions can be applied to more general linear systems with periodic coefficients (coupled Hill equations, periodically driven parametric oscillators), and to nonlinear systems as a starting point for convenient perturbative treatment of the nonlinearity.
T Tufarelli, A Retzker, MB Plenio, and A Serafini. 9/26/2012. “Input-output Gaussian channels: theory and application.” New Journal of Physics, 14. Publisher's Version Abstract
Setting off from the classic input–output formalism, we develop a theoretical framework to characterize the Gaussian quantum channels relating the initial correlations of an open bosonic system to those of properly identified output modes. We then proceed to apply our formalism to the case of quantum harmonic oscillators, such as the motional degrees of freedom of trapped ions or nanomechanical oscillators, interacting with travelling electromagnetic modes through cavity fields and subject to external white noise. We thus determine the degree of squeezing that can be transferred from an intra-cavity oscillator to light and show that the intra-cavity squeezing can be transformed into distributed optical entanglement if one can access both output fields of a two-sided cavity.
A Bermudez, J Almeida, K Ott, H Kaufmann, S Ulm, U Poschinger, F Schmidt-Kaler, A Retzker, and MB Plenio. 9/25/2012. “Quantum magnetism of spin-ladder compounds with trapped-ion crystals.” New Journal of Physics, 14. Publisher's Version Abstract
The quest for experimental platforms that allow for the exploration, and even control, of the interplay of low dimensionality and frustration is a fundamental challenge in several fields of quantum many-body physics, such as quantum magnetism. Here, we propose the use of cold crystals of trapped ions to study a variety of frustrated quantum spin ladders. By optimizing the trap geometry, we show how to tailor the low dimensionality of the models by changing the number of legs of the ladders. Combined with a method for selectively hiding ions provided by laser addressing, it becomes possible to synthesize stripes of both triangular and Kagome lattices. Besides, the degree of frustration of the phonon-mediated spin interactions can be controlled by shaping the trap frequencies. We support our theoretical considerations by initial experiments with planar ion crystals, where a high and tunable anisotropy of the radial trap frequencies is demonstrated. We take into account an extensive list of possible error sources under typical experimental conditions, and describe explicit regimes that guarantee the validity of our scheme.
JM Cai, F Jelezko, N Katz, A Retzker, and MB Plenio. 9/17/2012. “Long-lived driven solid-state quantum memory.” New Journal of Physics, 14. Publisher's Version Abstract
We investigate the performance of inhomogeneously broadened spin ensembles as quantum memories under continuous dynamical decoupling. The role of the continuous driving field is twofold: firstly, it decouples individual spins from magnetic noise; secondly, and more importantly, it suppresses and reshapes the spectral inhomogeneity of spin ensembles. We show that a continuous driving field, which itself may also be inhomogeneous over the ensemble, can considerably enhance the decay of the tails of the inhomogeneous broadening distribution. This fact enables a spin-ensemble-based quantum memory to exploit the effect of cavity protection and achieve a much longer storage time. In particular, for a spin ensemble with a Lorentzian spectral distribution, our calculations demonstrate that continuous dynamical decoupling has the potential to improve its storage time by orders of magnitude for the state-of-the-art experimental parameters.
H Landa, M Drewsen, B Reznik, and A Retzker. 9/13/2012. “Modes of oscillation in radiofrequency Paul traps.” New Journal of Physics, 14. Publisher's Version Abstract
We examine the time-dependent dynamics of ion crystals in radiofrequency traps. The problem of stable trapping of general three-dimensional crystals is considered and the validity of the pseudopotential approximation is discussed. We analytically derive the micromotion amplitude of the ions, rigorously proving well-known experimental observations. We use a recently proposed method to find the modes that diagonalize the linearized time-dependent dynamical problem. This allows one to obtain explicitly the ('Floquet–Lyapunov') transformation to coordinates of decoupled linear oscillators. We demonstrate the utility of the method by analyzing the modes of a small 'peculiar' crystal in a linear Paul trap. The calculations can be readily generalized to multispecies ion crystals in general multipole traps, and time-dependent quantum wavefunctions of ion oscillations in such traps can be obtained.
S Machnes, J Cerrillo, M Aspelmeyer, W Wieczorek, MB Plenio, and A Retzker. 4/10/2012. “Pulsed Laser Cooling for Cavity Optomechanical Resonators.” Physical Review Letters, 108, 15. Publisher's Version Abstract
A pulsed cooling scheme for optomechanical systems is presented that is capable of cooling at much faster rates, shorter overall cooling times, and for a wider set of experimental scenarios than is possible by conventional methods. The proposed scheme can be implemented for both strongly and weakly coupled optomechanical systems in both weakly and highly dissipative cavities. We study analytically its underlying working mechanism, which is based on interferometric control of optomechanical interactions, and we demonstrate its efficiency with pulse sequences that are obtained by using methods from optimal control. The short time in which our scheme approaches the optomechanical ground state allows for a significant relaxation of current experimental constraints. Finally, the framework presented here can be used to create a rich variety of optomechanical interactions and hence offers a novel, readily available toolbox for fast optomechanical quantum control.
A Bermudez, PO Schmidt, MB Plenio, and A Retzker. 4/4/2012. “Robust trapped-ion quantum logic gates by continuous dynamical decoupling.” Physical Review a, 85, 4. Publisher's Version Abstract
We introduce a scheme that combines phonon-mediated quantum logic gates in trapped ions with the benefits of continuous dynamical decoupling. We demonstrate theoretically that a strong driving of the qubit decouples it from external magnetic-field noise, enhancing the fidelity of two-qubit quantum gates. Moreover, the scheme does not require ground-state cooling, and is inherently robust to undesired ac Stark shifts. The underlying mechanism can be extended to a variety of other systems where a strong driving protects the quantum coherence of the qubits without compromising the two-qubit couplings.
2011
A Bermudez, J Almeida, F Schmidt-Kaler, A Retzker, and MB Plenio. 11/11/2011. “Frustrated Quantum Spin Models with Cold Coulomb Crystals.” Physical Review Letters, 107, 20. Publisher's Version Abstract
We exploit the geometry of a zigzag cold-ion crystal in a linear trap to propose the quantum simulation of a paradigmatic model of long-ranged magnetic frustration. Such a quantum simulation would clarify the complex features of a rich phase diagram that presents ferromagnetic, dimerized-antiferromagnetic, paramagnetic, and floating phases, together with previously unnoticed features that are hard to assess by numerics. We analyze in detail its experimental feasibility, and provide supporting numerical evidence on the basis of realistic parameters in current ion-trap technology.