Probing local relaxation of cold atoms in optical superlattices

TL;DR

This paper investigates the local relaxation dynamics of cold atoms in optical superlattices under the Bose-Hubbard model, revealing how local observables relax to maximum entropy states while global information is preserved.

Contribution

It provides analytical solutions in non-interacting and hard core limits and numerical results for finite interactions, enhancing understanding of local relaxation in quenched quantum systems.

Findings

Local relaxation signatures are experimentally accessible.

System relaxes locally to maximum entropy states.

Finite interactions show combined relaxation features.

Abstract

In the study of relaxation processes in coherent non-equilibrium dynamics of quenched quantum systems, ultracold atoms in optical superlattices with periodicity two provide a very fruitful test ground. In this work, we consider the dynamics of a particular, experimentally accessible initial state prepared in a superlattice structure evolving under a Bose-Hubbard Hamiltonian in the entire range of interaction strengths, further investigating the issues raised in Ref. [Phys. Rev. Lett. 101, 063001 (2008)]. We investigate the relaxation dynamics analytically in the non interacting and hard core bosonic limits, deriving explicit expressions for the dynamics of certain correlation functions, and numerically for finite interaction strengths using the time-dependent density-matrix renormalization (t-DMRG) approach. We can identify signatures of local relaxation that can be accessed experimentally with present technology. While the global system preserves the information about the initial condition, locally the system relaxes to the state having maximum entropy respecting the constraints of the initial condition. For finite interaction strengths and finite times, the relaxation dynamics contains signatures of the relaxation dynamics of both the non-interacting and hard core bosonic limits.