Browsing by Author "Kastner, Michael"

Now showing 1 - 11 of 11
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    Dynamical critical scaling of long-range interacting quantum magnets
    (American Physical Society, 2018) Defenu, Nicolo; Enss, Tilman; Kastner, Michael; Morigi, Giovanna
    Slow quenches of the magnetic field across the paramagnetic-ferromagnetic phase transition of spin systems produce heat. In systems with short-range interactions the heat exhibits universal power-law scaling as a function of the quench rate, known as Kibble-Zurek scaling. In this work we analyze slow quenches of the magnetic field in the Lipkin-Meshkov-Glick (LMG) model, which describes fully connected quantum spins. We analytically determine the quantum contribution to the residual heat as a function of the quench rate δ by means of a Holstein-Primakoff expansion about the mean-field value. Unlike in the case of short-range interactions, scaling laws in the LMG model are only found for a ramp starting or ending at the critical point. If instead the ramp is symmetric, as in the typical Kibble-Zurek scenario, then the number of excitations exhibits a crossover behavior as a function of δ and tends to a constant in the thermodynamic limit. Previous, and seemingly contradictory, theoretical studies are identified as specific limits of this dynamics. Our results can be tested on several experimental platforms, including quantum gases and trapped ions.
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    Entanglement-enhanced spreading of correlations
    (IOP Publishing, 2015-12-17) Kastner, Michael
    Starting from a product initial state, equal-time correlations in nonrelativistic quantum lattice models propagate within a light cone-like causal region. The presence of entanglement in the initial state can modify this behaviour, enhancing and accelerating the growth of correlations. In this paper we give a quantitative description, in the form of Lieb-Robinson-type bounds on equal-time correlation functions, of the interplay of dynamics versus. initial entanglement in quantum lattice models out of equilibrium. The bounds are tested against model calculations, and applications to quantum quenches, quantum channels, and Kondo physics are discussed.
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    Integrable active atom interferometry
    (IOP Publishing, 2020) Kastner, Michael; Menet, Vincent; Krie, Johannes N.
    Active interferometers are designed to enhance phase sensitivity beyond the standard quantum limit by generating entanglement inside the interferometer. An atomic version of such a device can be constructed by means of a spinor Bose–Einstein condensate with an F = 1 groundstate manifold in which spin-changing collisions (SCCs) create entangled pairs of m = ±1 atoms. We use Bethe Ansatz techniques to find exact eigenstates and eigenvalues of the Hamiltonian that models such SCCs. Using these results, we express the interferometer's phase sensitivity, Fisher information, and Hellinger distance in terms of the Bethe rapidities. By evaluating these expressions we study scaling properties and the interferometer's performance under the full Hamiltonian that models the SCCs, i.e., without the idealising approximations of earlier works that force the model into the framework of SU(1,1) interferometry.
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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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    Noninvasive measurement of dynamic correlation functions
    (American Physical Society, 2017) Uhrich, Philipp; Castrignano, Salvatore; Uys, Hermann; Kastner, Michael
    The measurement of dynamic correlation functions of quantum systems is complicated by measurement backaction. To facilitate such measurements we introduce a protocol, based on weak ancilla-system couplings, that is applicable to arbitrary (pseudo)spin systems and arbitrary equilibrium or nonequilibrium initial states. Different choices of the coupling operator give access to the real and imaginary parts of the dynamic correlation function. This protocol reduces disturbances due to the early-time measurements to a minimum, and we quantify the deviation of the measured correlation functions from the theoretical, unitarily evolved ones. Implementations of the protocol in trapped ions and other experimental platforms are discussed. For spin-1/2 models and single-site observables we prove that measurement backaction can be avoided altogether, allowing for the use of ancilla-free protocols.
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    Prethermalization and persistent order in the absence of a thermal phase transition
    (American Physical Society, 2017) Halimeh, Jad C.; Zauner-Stauber, Valentin; McCulloch, Ian P.; De Vega, Ines; Schollwock, Ulrich; Kastner, Michael
    We numerically study the dynamics after a parameter quench in the one-dimensional transverse-field Ising model with long-range interactions (∝1/rα with distance r), for finite chains and also directly in the thermodynamic limit. In nonequilibrium, i.e., before the system settles into a thermal state, we find a long-lived regime that is characterized by a prethermal value of the magnetization, which in general differs from its thermal value. We find that the ferromagnetic phase is stabilized dynamically: as a function of the quench parameter, the prethermal magnetization shows a transition between a symmetry-broken and a symmetric phase, even for those values of α for which no finite-temperature transition occurs in equilibrium. The dynamical critical point is shifted with respect to the equilibrium one, and the shift is found to depend on α as well as on the quench parameters.
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    Quantum effects in the cooperative scattering of light by atomic clouds
    (American Physical Society, 2017) Pucci, Lorenzo; Roy, Analabha; Santo, Tiago Santiago do Espirito; Kaiser, Robin; Kastner, Michael; Bachelard, Romain
    Scattering of classical light by atomic clouds induces photon-mediated effective long-range interactions between the atoms and leads to cooperative effects even at low atomic densities. We introduce a simulation technique that allows us to investigate the quantum regime of the dynamics of large clouds of atoms. We show that the fluorescence spectrum of the cloud can be used to probe genuine quantum cooperative effects. Signatures of these effects are the occurrence, and the scaling behavior, of additional sidebands at twice the frequency of the classical Mollow sidebands, as well as an asymmetry of the Mollow triplet.
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    Quantum kinetic perturbation theory for near-integrable spin chains with weak long-range interactions
    (IOP Publishing, 2019) Duval, Clement; Kastner, Michael
    For a transverse-field Ising chain with weak long-range interactions we develop a perturbative scheme, based on quantum kinetic equations, around the integrable nearest-neighbour model. We introduce, discuss, and benchmark several truncations of the time evolution equations up to eighth order in the Jordan–Wigner fermionic operators. The resulting set of differential equations can be solved for lattices with O(10²) sites and facilitates the computation of spin expectation values and correlation functions to high accuracy, at least for moderate timescales. We use this scheme to study the relaxation dynamics of the model, involving prethermalisation and thermalisation. The techniques developed here can be generalised to other spin models with weak integrability-breaking terms.
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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.
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    Thermalization of a Lipkin-Meshkov-Glick model coupled to a bosonic bath
    (American Physical Society, 2019) Louw, Jan C.; Kriel, Johannes N.; Kastner, Michael
    We derive a Lindblad master equation that approximates the dynamics of a Lipkin-Meshkov-Glick (LMG) model weakly coupled to a bosonic bath. By studying the time evolution of operators under the adjoint master equation we prove that, for large system sizes, these operators attain their thermal equilibrium expectation values in the long-time limit, and we calculate the rate at which these values are approached. Integrability of the LMG model prevents thermalization in the absence of a bath, and our work provides an explicit proof that the bath indeed restores thermalization. Imposing thermalization on this otherwise nonthermalizing model outlines an avenue towards probing the unconventional thermodynamic properties predicted to occur in ultracold-atom-based realizations of the LMG model.
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    Universal equilibrium scaling functions at short times after a quench
    (American Physical Society, 2017) Karl, Markus; Cakir, Halil; Halimeh, Jad C.; Oberthaler, Markus K.; Kastner, Michael; Gasenzer, Thomas
    By analyzing spin-spin correlation functions at relatively short distances,we showthat equilibrium near-critical properties can be extracted at short times after quenches into the vicinity of a quantum critical point. The time scales after which equilibrium properties can be extracted are sufficiently short so that the proposed scheme should be viable for quantum simulators of spin models based on ultracold atoms or trapped ions. Our results, analytic as well as numeric, are for one-dimensional spin models, either integrable or nonintegrable, but we expect our conclusions to be valid in higher dimensions as well.