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Quantum technologies

Dieter Meschede's research group
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Publications - Quantum walks

2017

  • C. Robens, S. Brakhane, W. Alt, D. Meschede, J. Zopes and A. Alberti
    Fast, high-precision optical polarization synthesizer for ultracold-atom experiments, arXiv:1608.02410, (2017)arXivBibTeXPDF
    ABSTRACT »

    We present a novel approach to precisely synthesize arbitrary polarization states of light with a high modulation bandwidth. Our approach consists in superimposing two laser light fields with the same wavelength, but with opposite circular polarizations, where the phase and amplitude of each light field are individually controlled. We find that the polarization-synthesized beam reaches a degree of polarization of 99.99%, which is mainly limited by static spatial variations of the polarization state over the beam profile. We also find that the depolarization caused by temporal fluctuations of the polarization state is about two orders of magnitude smaller. In a recent work, Robens et al. [Phys. Rev. Lett. 118, 065302 (2017)] demonstrated an application of the polarization synthesizer to create two independently controllable optical lattices, which trap atoms depending on their internal spin state. We here use ultracold atoms in polarization-synthesized optical lattices to give an independent, in-situ demonstration of the performance of the polarization synthesizer.

  • A. Alberti and S. Wimberger
    Quantum walk of a Bose-Einstein condensate in the Brillouin zone, Phys. Rev. A 96, 023620 (2017)arXivBibTeXPDF
    ABSTRACT »
    We propose a realistic scheme to implement discrete-time quantum walks in the Brillouin zone (i.e., in quasimomentum space) with a spinor Bose-Einstein condensate. Relying on a static optical lattice to suppress tunneling in real space, the condensate is  displaced in quasimomentum space in discrete steps conditioned upon the internal state of the atoms, while short pulses periodically couple the internal states. We show that tunable twisted boundary conditions can be implemented in a fully natural way by exploiting the periodicity of the Brillouin zone. The proposed setup does not suffer from off-resonant scattering of photons and could allow a robust implementation of quantum walks with  several tens of steps at least.  In addition, onsite atom-atom interactions can be used to simulate interactions with infinitely long range in the Brillouin zone.
  • C. Robens, J. Zopes, W. Alt, S. Brakhane, D. Meschede and A. Alberti
    Low-entropy states of neutral atoms in polarization-synthesized optical lattices, Phys. Rev. Lett. 118, 065302 (2017)arXivBibTeXPDF
    ABSTRACT »

    We create low-entropy states of neutral atoms by utilizing a conceptually new optical-lattice technique that relies on a high-precision, high-bandwidth synthesis of light polarization. Polarization-synthesized optical lattices provide two fully controllable optical lattice potentials, each of them confining only atoms in either one of the two long-lived hyperfine states. By employing one lattice as the storage register and the other one as the shift register, we provide a proof of concept using four atoms that selected regions of the periodic potential can be filled with one particle per site. We expect that our results can be scaled up to thousands of atoms by employing an atom-sorting algorithm with logarithmic complexity, which is enabled by polarization-synthesized optical lattices. Vibrational entropy is subsequently removed by sideband cooling methods. Our results pave the way for a bottom-up approach to creating ultralow-entropy states of a many-body system.

  • C. Robens, S. Brakhane, W. Alt, F. Kleißler, D. Meschede, G. Moon, G. Ramola and A. Alberti
    High numerical aperture (NA = 0.92) objective lens for imaging and addressing of cold atoms, Opt. Lett. 42, 1043 (2017)arXivBibTeXPDF
    ABSTRACT »

    We have designed, built, and characterized a high- resolution objective lens that is compatible with an ultra-high vacuum environment. The lens system ex- ploits the principle of the Weierstrass-sphere solid immersion lens to reach a numerical aperture (NA) of 0.92. Tailored to the requirements of optical lattice experiments, the objective lens features a relatively long working distance of 150 μm. Our two-lens design is remarkably insensitive to mechanical tolerances in spite of the large NA. Additionally, we demonstrate the application of a tapered optical fiber tip, as used in scanning near-field optical microscopy, to measure the point spread function of a high NA optical system. From the point spread function, we infer the wavefront aberration for the entire field of view of about 75 μm. Pushing the NA of an optical system to its ultimate limit enables novel applications in quantum technolo- gies such as quantum control of atoms in optical mi- crotraps with an unprecedented spatial resolution and photon collection efficiency.

  • J. Asbóth and A. Alberti
    Spectral flow and global topology of the Hofstadter butterfly, Phys. Rev. Lett. 118, 216801 (2017)arXivBibTeXPDF
    ABSTRACT »

    We study the relation between the global topology of the Hofstadter butterfly of a multiband insulator and the topological invariants of the underlying Hamiltonian. The global topology of the butterfly, i.e., the displacement of the energy gaps as the magnetic field is varied by one flux quantum, is determined by the spectral flow of energy eigenstates crossing gaps as the field is tuned. We find that for each gap this spectral flow is equal to the topological invariant of the gap, i.e., the net number of edge modes traversing the gap. For periodically driven systems, our results apply to the spectrum of quasienergies. In this case, the spectral flow of the sum of all the quasienergies gives directly the Rudner-Lindner-Berg-Levin invariant that characterizes the topological phases of a periodically driven system.

  • T. Rakovszky, J. Asbóth and A. Alberti
    Detecting topological invariants in chiral symmetric insulators via losses, Phys. Rev. B: Rapid Comm. 95, 201407(R) (2017)arXivBibTeXPDF
    ABSTRACT »

    We show that the bulk winding number characterizing one-dimensional topological insulators with chiral symmetry can be detected from the displacement of a single particle, observed via losses. Losses represent the effect of repeated weak measurements on one sublattice only, which interrupt the dynamics periodically. When these do not detect the particle, they realize negative measurements. Our repeated measurement scheme covers both time-independent and periodically driven (Floquet) topological insulators, with or without spatial disorder. In the limit of rapidly repeated, vanishingly weak measurements, our scheme describes non-Hermitian Hamiltonians, as the lossy Su-Schrieffer-Heeger model of Rudner and Levitov, [Phys. Rev. Lett. 102, 065703 (2009)]. We find, contrary to intuition, that the time needed to detect the winding number can be made shorter by decreasing the efficiency of the measurement. We illustrate our results on a discrete-time quantum walk, and propose ways of testing them experimentally.

  • F. Bleckmann, Z. Cherpakova, S. Linden and A. Alberti
    Spectral imaging of topological edge states in plasmonic waveguide arrays, Phys. Rev. B 96, 045417 (2017)arXivBibTeXPDF
    ABSTRACT »

    We report on the observation of a topologically protected edge state at the interface between two topologically distinct domains of the Su-Schrieffer-Heeger model, which we implement in arrays of evanescently coupled dielectric-loaded surface plasmon polariton waveguides. Direct evidence of the topological character of the edge state is obtained through several independent experiments: Its spatial localization at the interface as well as the restriction to one sublattice is confirmed by real-space leakage radiation microscopy. The corresponding momentum-resolved spectrum obtained by Fourier imaging reveals the midgap position of the edge state as predicted by theory.

2016

  • T. Groh, S. Brakhane, W. Alt, D. Meschede, J. Asbóth and A. Alberti
    Robustness of topologically protected edge states in quantum walk experiments with neutral atoms, Phys. Rev. A (editor's suggestion) 94, 013620 (2016)arXivBibTeXPDF
    ABSTRACT »

    Discrete-time quantum walks allow Floquet topological insulator materials to be explored using controllable systems such as ultracold atoms in optical lattices. By numerical simulations, we study the robustness of topologically protected edge states in the presence of decoherence in one- and two-dimensional discrete-time quantum walks. We also develop a simple analytical model quantifying the robustness of these edge states against either spin or spatial dephasing, predicting an exponential decay of the population of topologically protected edge states. Moreover, we present an experimental proposal based on neutral atoms in spin-dependent optical lattices to realize spatial boundaries between distinct topological phases. Our proposal relies on a new scheme to implement spin-dependent discrete shift operations in a two-dimensional optical lattice. We analyze under realistic decoherence conditions the experimental feasibility of observing unidirectional, dissipationless transport of matter waves along boundaries separating distinct topological domains.

  • S. Brakhane and A. Alberti
    Technical Note: Stress-Induced Birefringence in Vacuum Systems, White paper, (2016)BibTeXPDF
    ABSTRACT »

    Even scientific grade optical glasses show birefringence when small external forces are applied to the sample. Stress-induced birefringence can be particularly detrimental to the state of polarization of light when a laser beam is transmitted through the glass. This is especially the case for glass windows of a vacuum chamber. Since compensation of spatially inhomogeneous birefringence is extremely challenging, it should be prevented by proper design of the vacuum chamber. Birefringence below 0.2 nm/cm can be achieved by thoroughly choosing glass material with low stress optical coefficient and mounting geometry. Applications strongly depend on light polarization are quantum technologies such as precision metrology, quantum computation and quantum simulations based on ions or atoms.

2015

  • S. Brakhane, W. Alt, D. Meschede, C. Robens, G. Moon and A. Alberti
    Ultra-low birefringence dodecagonal vacuum glass cell, Rev. Sci. Instrum. 86, 126108 (2015)arXivBibTeXPDF
    ABSTRACT »

    We report on an ultra-low birefringence dodecagonal glass cell for ultra-high vacuum applications. The epoxy-bonded trapezoidal windows of the cell are made of SF57 glass, which exhibits a very low stress-induced birefringence. We characterize the birefringence Δn of each window with the cell under vacuum conditions, obtaining values around 10-8. After baking the cell at 150 ºC, we reach a pressure below 10-10 mbar. In addition, each window is antireflection coated on both sides, which is highly desirable for quantum optics experiments and precision measurements.

  • S. Brakhane, W. Alt, D. Meschede, C. Robens and A. Alberti
    Polarisationserhaltende Vakuum-Zelle zur Anwendung oder Messung elektromagnetischer Wellen im Vakuum, Patent pending, (2015)BibTeX
    ABSTRACT »

    Die Erfindung betrifft ein Verfahren, eine Vorrichtung und die Verwendung einer Vorrichtung zur Anwendung oder Messung polarisierter elektromagnetischer Strahlung im Vakuum, wobei die Doppelbrechung Δn < 10-6 beträgt.

  • C. Robens, S. Brakhane, D. Meschede and A. Alberti
    Quantum Walks With Neutral Atoms: Quantum Interference Effects of One and Two Particles, Proceedings of the XXII International Conference ICOLS, (2015)arXivBibTeX
    ABSTRACT »

    We report on the state of the art of quantum walk experiments with neutral atoms in state-dependent optical lattices. We demonstrate a novel state-dependent transport technique enabling the control of two spin-selective sublattices in a fully independent fashion. This transport technique allowed us to carry out a test of single-particle quantum interference based on the violation of the Leggett-Garg inequality and, more recently, to probe two-particle quantum interference effects with neutral atoms cooled into the motional ground state. These experiments lay the groundwork for the study of discrete-time quantum walks of strongly interacting, indistinguishable particles to demonstrate quantum cellular automata of neutral atoms.

  • C. Robens, W. Alt, D. Meschede, C. Emary and A. Alberti
    Ideal Negative Measurements in Quantum Walks Disprove Theories Based on Classical Trajectories, Phys. Rev. X 5, 011003 (2015)arXivBibTeXPDF
    ABSTRACT »

    We report on a stringent test of the nonclassicality of the motion of a massive quantum particle, which propagates on a discrete lattice. Measuring temporal correlations of the position of single atoms performing a quantum walk, we observe a 6σ violation of the Leggett-Garg inequality. Our results rigorously excludes (i.e., falsifies) any explanation of quantum transport based on classical, well-defined trajectories. We use so-called ideal negative measurements—an essential requisite for any genuine Leggett-Garg test—to acquire information about the atom’s position, yet avoiding any direct interaction with it. The interaction-free measurement is based on a novel atom transport system, which allows us to directly probe the absence rather than the presence of atoms at a chosen lattice site. Beyond the fundamental aspect of this test, we demonstrate the application of the Leggett-Garg correlation function as a witness of quantum superposition. Here, we employ the witness to discriminate different types of walks spanning from merely classical to wholly quantum dynamics.

2014

  • A. Alberti, W. Alt, R. Werner and D. Meschede
    Decoherence Models for Discrete-Time Quantum Walks and their Application to Neutral Atom Experiments, New J. Phys. 16, 123052 (2014)arXivBibTeXPDF
    ABSTRACT »

    We discuss decoherence in discrete-time quantum walks in terms of a phenomenological model that distinguishes spin and spatial decoherence. We identify the dominating mechanisms that affect quantum-walk experiments realized with neutral atoms walking in an optical lattice.

    From the measured spatial distributions, we determine with good precision the amount of decoherence per step, which provides a quantitative indication of the quality of our quantum walks. In particular, we find that spin decoherence is the main mechanism responsible for the loss of coherence in our experiment. We also find that the sole observation of ballistic—instead of diffusive—expansion in position space is not a good indicator of the range of coherent delocalization.

    We provide further physical insight by distinguishing the effects of short- and long-time spin dephasing mechanisms. We introduce the concept of coherence length in the discrete-time quantum walk, which quantifies the range of spatial coherences. Unexpectedly, we find that quasi-stationary dephasing does not modify the local properties of the quantum walk, but instead affects spatial coherences.

    For a visual representation of decoherence phenomena in phase space, we have developed a formalism based on a discrete analogue of the Wigner function. We show that the effects of spin and spatial decoherence differ dramatically in momentum space.

2013

  • M. Genske, W. Alt, A. Steffen, A. H. Werner, R. F. Werner, D. Meschede and A. Alberti
    Electric quantum walks with individual atoms, Phys. Rev. Lett. 110, 190601 (2013)arXivBibTeXPDF
    ABSTRACT »
    We report on the experimental realization of electric quantum walks, which mimic the effect of an electric field on a charged particle in a lattice. Starting from a textbook implementation of discrete-time quantum walks, we introduce an extra operation in each step to implement the effect of the field. The recorded dynamics of such a quantum particle exhibits features closely related to Bloch oscillations and interband tunneling. In particular, we explore the regime of strong fields, demonstrating contrasting quantum behaviors: quantum resonances vs. dynamical localization depending on whether the accumulated Bloch phase is a rational or irrational fraction of 2π.
  • C. Cedzich, T. Rybár, A. H. Werner, A. Alberti, M. Genske and R. F. Werner
    Propagation of Quantum Walks in Electric Fields, Phys. Rev. Lett. 111, 160601 (2013)arXivBibTeXPDF
    ABSTRACT »
    We study one-dimensional quantum walks in a homogeneous electric field. The field is given by a phase which depends linearly on position and is applied after each step. The long time propagation properties of this system, such as revivals, ballistic expansion and Anderson localization, depend very sensitively on the value of the electric field Φ, e.g., on whether Φ/(2π) is rational or irrational. We relate these properties to the continued fraction expansion of the field. When the field is given only with finite accuracy, the beginning of the expansion allows analogous conclusions about the behavior on finite time scales.

2012

  • A. Ahlbrecht, A. Alberti, D. Meschede, V. B. Scholz, A. H. Werner and R. F. Werner
    Molecular binding in interacting quantum walks, New J. Phys. 14, 073050 (2012)arXivBibTeXPDF
    ABSTRACT »

    We show that the presence of an interaction in the quantum walk of two atoms leads to the formation of a stable compound, a molecular state. The wave-function of the molecule decays exponentially in the relative position of the two atoms, hence it constitutes a true bound state. Furthermore, for a certain class of interactions we develop an effective theory and find that the dynamics of the molecule is described by a quantum walk in its own right. We propose a setup for the experimental realization as well as sketch the possibility to observe quasi-particle effects in quantum many body systems.

2009

  • M. Karski, L. Förster, J. Choi, A. Steffen, W. Alt, D. Meschede and A. Widera
    Quantum Walk in Position Space with Single Optically Trapped Atoms, Science 325, 174 (2009)arXivBibTeX
    ABSTRACT »
    The quantum walk is the quantum analog of the well-known random walk, which forms the basis for models and applications in many realms of science. Its properties are markedly different from the classical counterpart and might lead to extensive applications in quantum information science. In our experiment, we implemented a quantum walk on the line with single neutral atoms by deterministically delocalizing them over the sites of a one-dimensional spin-dependent optical lattice. With the use of site-resolved fluorescence imaging, the final wave function is characterized by local quantum state tomography, and its spatial coherence is demonstrated. Our system allows the observation of the quantum-to-classical transition and paves the way for applications, such as quantum cellular automata.