Semiclassical quench dynamics of Bose gases in optical lattices

TL;DR

This paper investigates the non-equilibrium dynamics of Bose gases in optical lattices after a quantum quench, using semiclassical simulations to match experimental observations and analyze correlation spreading.

Contribution

It applies the truncated-Wigner approximation to simulate short-time dynamics of the Bose-Hubbard model, providing quantitative agreement with experiments and insights into correlation propagation.

Findings

Semiclassical approach accurately reproduces energy redistribution dynamics.

Propagation velocity of correlations depends on initial state and interaction strength.

Velocity bounds are related to elementary excitation group velocities.

Abstract

We analyze the time evolution of the Bose-Hubbard model after a sudden quantum quench to a weakly interacting regime. Specifically, motivated by a recent experiment at Kyoto University, we numerically simulate redistribution of the kinetic and onsite-interaction energies at an early time, which was observed in non-equilibrium dynamics of ultracold Bose gases in a cubic optical lattice starting with a singly-occupied Mott-insulator state. In order to compute the short-time dynamics corresponding to the experimental situation, we apply the truncated-Wigner approximation (TWA) to the Bose-Hubbard model on a cubic lattice. We show that our semiclassical approach quantitatively reproduces the fast redistribution dynamics. We further analyze spatial spreading of density-density correlations at equal time in the Bose-Hubbard model on a square lattice with a large filling factor. When the system is initially prepared in a coherent state, we find that a propagation velocity of the correlation wave packet in the correlation function strongly depends on the final interaction strength, and it is bounded by twice the maximum group velocity of the elementary excitations. In contrast, when the system is initially in a Mott-insulator state, the propagation velocity of the wave packet is approximately independent of the final interaction strength.