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Double light-cone dynamics establish thermal states in integrable 1D Bose gases

Tim Langen, Schweigler, Thomas, Eugene Demler, Jörg Schmiedmayer

Published Jan 1, 2018• 16 citations
Publisher

Abstract

We theoretically investigate the non-equilibrium dynamics in a quenched pair of one-dimensional Bose gases with density imbalance. We describe the system using its low-energy effective theory, the Luttinger liquid model. In this framework the system shows strictly integrable relaxation dynamics via dephasing of its approximate many-body eigenstates. In the balanced case, this leads to the well-known light-cone-like establishment of a prethermalized state, which can be described by a generalized Gibbs ensemble. In the imbalanced case the integrable dephasing leads to a state that, counter-intuitively, closely resembles a thermal equilibrium state. The approach to this state is characterized by two separate light-cone dynamics with distinct characteristic velocities. This behavior is a result of the fact that in the imbalanced case observables are not aligned with the conserved quantities of the integrable system. We discuss a concrete experimental realization to study this effect using matterwave interferometry and many-body revivals on an atom chip.

DOI
10.18419/opus-18252

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We theoretically investigate the non-equilibrium dynamics in a quenched pair of one-dimensional Bose gases with density imbalance. We describe the system using its low-energy effective theory, the Luttinger liquid model. In this framework the system shows strictly integrable relaxation dynamics via dephasing of its approximate many-body eigenstates. In the balanced case, this leads to the well-known light-cone-like establishment of a prethermalized state, which can be described by a generalized Gibbs ensemble. In the imbalanced case the integrable dephasing leads to a state that, counter-intuitively, closely resembles a thermal equilibrium state. The approach to this state is characterized by two separate light-cone dynamics with distinct characteristic velocities. This behavior is a result of the fact that in the imbalanced case observables are not aligned with the conserved quantities of the integrable system. We discuss a concrete experimental realization to study this effect using matterwave interferometry and many-body revivals on an atom chip.
We theoretically investigate the non-equilibrium dynamics in a quenched pair of one-dimensional Bose gases with density imbalance. We describe the system using its low-energy effective theory, the Luttinger liquid model. In this framework the system shows strictly integrable relaxation dynamics via dephasing of its approximate many-body eigenstates. In the balanced case, this leads to the well-known light-cone-like establishment of a prethermalized state, which can be described by a generalized Gibbs ensemble. In the imbalanced case the integrable dephasing leads to a state that, counter-intuitively, closely resembles a thermal equilibrium state. The approach to this state is characterized by two separate light-cone dynamics with distinct characteristic velocities. This behavior is a result of the fact that in the imbalanced case observables are not aligned with the conserved quantities of the integrable system. We discuss a concrete experimental realization to study this effect using matterwave interferometry and many-body revivals on an atom chip.
Abstract. We detail the experimental observation of the non-equilibrium many-body phenomenon prethermalization. We study the dynamics of a rapidly and coherently split one-dimensional Bose gas. An analysis based on the use of full quantum mechanical probability distributions of matter wave interference contrast reveals that the system evolves towards a quasi-steady state. This state, which can be characterized by an effective temperature, is not the final thermal equilibrium state. We compare the evolution of the system to an integrable Tomonaga-Luttinger liquid model, and show that the system dephases to a prethermalized state rather than undergoing thermalization towards a final thermal equilibrium state.
We detail the experimental observation of the non-equilibrium many-body phenomenon prethermalization.We study the dynamics of a rapidly and coherently split one-dimensional Bose gas.An analysis based on the use of full quantum mechanical probability distributions of matter wave interference contrast reveals that the system evolves toward a quasi-steady state.This state, which can be characterized by an effective temperature, is not the final thermal equilibrium state.We compare the evolution of the system to an integrable Tomonaga-Luttinger liquid model, and show that the system dephases to a prethermalized state rather than undergoing thermalization toward a final thermal equilibrium state.
Abstract We consider the non-equilibrium dynamics of two-component one dimensional quantum gases in the limit of extreme population imbalance where the minority species has but a single particle. We consider the situation where the gas is prepared in a state with a single spatially localized exciton: the single particle of the minority species is spatially localized while the density of the majority species in the vicinity of the minority particle sees a depression. Remarkably, we are able to consider cases where the gas contains on the order of N = 100 particles, comparable to that studied in experiments on cold atomic gases. We are able to do so by exploiting the integrability of the gas together with the observation that the excitonic state can be constructed through a simple superposition of exact eigenstates of the gas. The number of states in this superposition, rather than being exponentially large in the number of particles, scales linearly with N . We study the evolution of such spatially localized states in both strongly interacting Bose and Fermi gases. The behavior of the light cones when the interaction strength and density of the gas is varied can be understood from exact results for the spin excitation spectrum in these systems. We argue that the light cone in both cases exhibits scaling collapse. However unique to the Bose gas, we show that the presence of gapped finite-momentum roton-like excitations provide the Bose gas dynamics with secondary light cones.
We describe the relaxation dynamics of a coherently split one-dimensional (1D) Bose gas in the harmonic approximation. A dephased, prethermalized state emerges in a light-cone-like evolution which is connected to the spreading of correlations with a characteristic velocity. In our description we put special emphasis on the influence of the longitudinal trapping potential and the finite size of the system, both of which are highly relevant in experiments. In particular, we quantify their influence on the phase correlation properties and the characteristic velocity with which the prethermalized state is established. Finally, we show that the trapping potential has an important effect on the recurrences of coherence which are expected to appear in a finite size system.
We consider the low-temperature transport properties of critical one-dimensional systems that can be described, at equilibrium, by a Luttinger liquid. We focus on the prototypical setting where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. At large distances x and times t, conformal field theory characterizes the energy transport in terms of a single light cone spreading at the sound velocity v. Energy density and current take different constant values inside the light cone, on its left, and on its right, resulting in a three-step form of the corresponding profiles as a function of ζ=x/t. Here, using a nonlinear Luttinger liquid description, we show that for generic observables this picture is spoiled as soon as a nonlinearity in the spectrum is present. In correspondence of the transition points x/t=±v, a novel universal region emerges at infinite times, whose width is proportional to the temperatures on the two sides. In this region, expectation values have a different temperature dependence and show smooth peaks as a function of ζ. We explicitly compute the universal function describing such peaks. In the specific case of interacting integrable models, our predictions are analytically recovered by the generalized hydrodynamic approach.