Browsing by Author "Van den Worm, Mauritz"

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    Dynamics of long-range interacting quantum spin systems
    (Stellenbosch : Stellenbosch University, 2015-12) Van den Worm, Mauritz; Kastner, Michael; Stellenbosch University. Faculty of Science. Dept. of Physics.
    ENGLISH ABSTRACT: In this thesis we study the time evolution of correlation functions in quantum lattice models in the presence of long-range interactions or hopping decaying asymptotically as a power law. For a large class of initial conditions, exact analytic results are obtained in arbitrary lattice dimension for the longrange Ising model. In contrast to the nearest-neighbour case, we find that correlations decay like stretched or compressed exponentials in time. Provided the long-range character of the interactions is sufficiently strong, pronounced prethermalization plateaus are observed and relaxation timescales are widely separated. Starting from uncorrelated states that are easily prepared in experiments, we show the dynamical emergence of correlations and entanglement in these far-from-equilibrium interacting quantum systems. We characterize these correlations by the entanglement entropy, concurrence, and squeezing, which are inequivalent measures of entanglement corresponding to different quantum resources. For interaction exponents larger than the lattice dimensionality, a Lieb- Robinson-type bound effectively restricts the spreading of correlations to the interior of a causal region, but allows supersonic (faster than linear) propagation. Using tools of quantum metrology, for any exponents smaller than the lattice dimension, we construct Hamiltonians giving rise to quantum channels with capacities not restricted to any causal region. An analytic analysis of long-range Ising models illustrates the disappearance of the causal region and the creation of correlations becoming distance-independent. In all models we analyzed the spreading of correlations follows a power law, and not the exponential increase of the long-range Lieb-Robinson bound. Lieb-Robinson-type bounds are extended to strongly long-range interactions where the interaction exponent is smaller than the lattice dimension, and we report particularly sharp bounds that are capable of reproducing regimes with soundcone as well as supersonic dynamics. Our results provide guidance for optimizing experimental efforts to harness long-range interactions in a variety of quantum information and signaling tasks.
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    Interplay of soundcone and supersonic propagation in lattice models with power law interactions
    (Bristol : IOP Publishing, 2015-06-16) Storch, David-Maximilian; Van den Worm, Mauritz; Kastner, Michael
    Westudy the spreading of correlations and other physical quantities in quantum lattice models with interactions or hopping decaying like r−α with the distance r.Our focus is on exponents α between 0 and 6, where the interplay of long- and short-range features gives rise to a complex phenomenology and interesting physical effects, and which is also the relevant range for experimental realizations with cold atoms, ions, or molecules.Wepresent analytical and numerical results, providing a comprehensive picture of spatio-temporal propagation. Lieb–Robinson-type bounds are extended to strongly long-range interactions where α is smaller than the lattice dimension, and we report particularly sharp bounds that are capable of reproducing regimes with soundcone as well as supersonic dynamics. Complementary lower bounds prove that faster-than-soundcone propagation occurs for α < 2 in any spatial dimension, although cone-like features are shown to also occur in that regime. Our results provide guidance for optimizing experimental efforts to harness long-range interactions in a variety of quantum information and signaling tasks.
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    Relaxation timescales and decay of correlations in a long-range interacting quantum simulator
    (IOP, 2013) Van den Worm, Mauritz; Sawyer, Brian C.; Bollinger, John J.; Kastner, Michael
    We study the time evolution of correlation functions in long-range interacting quantum Ising models. For a large class of initial conditions, exact analytic results are obtained in arbitrary lattice dimension, both for ferromagnetic and antiferromagnetic coupling, and hence also in the presence of geometric frustration. In contrast to the nearest-neighbour case, we find that correlations decay like stretched or compressed exponentials in time. Provided the long-range character of the interactions is sufficiently strong, pronounced prethermalization plateaus are observed and relaxation timescales are widely separated. Specializing to a triangular lattice in two spatial dimensions, we propose to utilize these results for benchmarking a recently developed ion-trap-based quantum simulator.