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Journal of Statistical Mechanics Theory and Experiment

Prethermalization of weakly interacting bosons after a sudden interaction quench

Giuseppe Menegoz, Alessandro Silva

Published May 28, 2015• 15 citations
Publisher

Abstract

We calculate the dynamics of local and non-local correlation functions of a three dimensional weakly interacting Bose gas after an interaction quench. Within the Bogoliubov approximation we discuss the resulting quasi-steady prethermal state and relaxation to it. We finally discuss the decay rates of Bogoliubov quasi-particles characterizing the expected departure from the prethermal state towards a fully thermalized one.

DOI
10.1088/1742-5468/2015/05/p05035

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We calculate the dynamics of local and non-local correlation functions of a three dimensional weakly interacting Bose gas after an interaction quench. Within the Bogoliubov approximation we discuss the resulting quasi-steady prethermal state and relaxation to it. We finally discuss the decay rates of Bogoliubov quasi-particles characterizing the expected departure from the prethermal state towards a fully thermalized one.
We calculate the dynamics of local and non-local correlation functions of one and threedimensional weakly interacting Bose gas after an interaction quench. Within the Bogoliubov approximation we discuss the resulting quasi-steady prethermal state and relaxation to it. We discuss the deacay rates of Bogoliubov quasi-particles characterizing the expected departure from the prethermal state towards a fully thermalized one. We conclude that prethermalization in this situation manifest as a crossover.
The dynamics of a weakly interacting Bose gas at low temperatures is close to integrable due to the approximate quadratic nature of the many-body Hamiltonian. While the short-time physics after an abrupt ramp of the interaction constant is dominated by integrable dynamics, integrability is broken at longer times by higher-order interaction terms in the Bogoliubov Hamiltonian, in particular, by Beliaev-Landau scatterings involving three quasiparticles. The two-stage relaxation process is highlighted in the evolution of local observables such as the density-density correlation function: an integrable dephasing mechanism leads the system to a prethermal stage, followed by true thermalization conveyed by quasiparticle collisions. Our results bring the crossover from prethermalization to thermalization within reach of current experiments with ultracold atomic gases.
We study the relaxation of excitations in a system of one-dimensional weakly interacting bosons. Due to residual weak interactions, Bogoliubov quasiparticles in this system have finite lifetimes. As a result of the conservation laws in one dimension, at zero temperature the leading mechanism of decay of a quasiparticle is disintegration into three others. We focus on phonon quasiparticles and find that their decay rate is proportional to the seventh power of momentum. In the integrable case of contact interaction between the bosons, the decay rate vanishes.
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 study the dynamics of a quantum Ising chain after the sudden introduction of a nonintegrable long-range interaction. Via an exact mapping onto a fully connected lattice of hard-core bosons, we show that a prethermal state emerges and we investigate its features by focusing on a class of physically relevant observables. In order to gain insight into the eventual thermalization, we outline a diagrammatic approach which complements the study of the previous quasistationary state and provides the basis for a self-consistent solution of the kinetic equation. This analysis suggests that both the temporal decay towards the prethermal state and the crossover to the eventual thermal one may occur algebraically.
The dynamics of interacting bosons in one dimension following the sudden switching on of a weak disordered potential is investigated. On time scales before quasiparticles scatter (prethermalized regime), the dephasing from random elastic forward scattering causes all correlations to decay exponentially fast, but the system remains far from thermal equilibrium. For longer times, the combined effect of disorder and interactions gives rise to inelastic scattering and to thermalization. A novel quantum kinetic equation accounting for both disorder and interactions is employed to study the dynamics. Thermalization turns out to be most effective close to the superfluid-Bose-glass critical point where nonlinearities become more and more important. The numerically obtained thermalization times are found to agree well with analytic estimates.