One-Dimensional Quench Dynamics in an Optical Lattice: sine-Gordon and Bose-Hubbard Descriptions

TL;DR

This paper explores the non-equilibrium dynamics of one-dimensional bosonic systems in optical lattices, comparing sine-Gordon and Bose-Hubbard models, revealing distinct relaxation behaviors and correlation phenomena after a quench.

Contribution

It provides a numerical analysis of quench dynamics in 1D bosonic systems, distinguishing between sine-Gordon and Bose-Hubbard regimes through correlation and entropy measures.

Findings

Correlation dynamics show collapse-revival phenomena with different time scales.

Bose-Hubbard dynamics relax to a maximum entropy state, unlike sine-Gordon.

Sine-Gordon dynamics are too fast to show relaxation signatures.

Abstract

We investigate the dynamics of one-dimensional interacting bosons in an optical lattice after a sudden quench in the Bose-Hubbard (BH) and sine-Gordon (SG) regimes. While in higher dimension, the Mott-superfluid phase transition is observed for weakly interacting bosons in deep lattices, in 1D an instability is generated also for shallow lattices with a commensurate periodic potential pinning the atoms to the Mott state through a transition described by the SG model. The present work aims at identifying the SG and BH regimes. We study them by dynamical measures of several key quantities. We numerically exactly solve the time dependent Schr\"odinger equation for small number of atoms and investigate the corresponding quantum many-body dynamics. In both cases, correlation dynamics exhibits collapse revival phenomena, though with different time scales. We argue that the dynamical fragmentation is a convenient quantity to distinguish the dynamics specially near the pinning zone. To understand the relaxation process we measure the many-body information entropy. BH dynamics clearly establishes the possible relaxation to the maximum entropy state determined by the Gaussian orthogonal ensemble of random matrices (GOE). In contrast, the SG dynamics is so fast that it does not exhibit any signature of relaxation in the present time scale of computation.