Dynamics of the Bose-Hubbard model: transition from Mott insulator to superfluid

TL;DR

This paper investigates the dynamics of phase transitions in the one-dimensional Bose-Hubbard model, focusing on how correlations develop during the transition from Mott insulator to superfluid phases under different quench rates.

Contribution

It combines variational wave functions, dynamical Bogoliubov theory, and numerical simulations to analyze correlation scaling during the transition, linking theory with measurable experimental signatures.

Findings

Correlation scaling relations are identified during the transition.

Fast and slow quenches produce distinct correlation dynamics.

Results are applicable to cold atom experiments in optical lattices.

Abstract

We study the dynamics of phase transitions in the one dimensional Bose-Hubbard model. To drive the system from Mott insulator to superfluid phase, we change the tunneling frequency at a finite rate. We investigate the build up of correlations during fast and slow transitions using variational wave functions, dynamical Bogoliubov theory, Kibble-Zurek mechanism, and numerical simulations. We show that time-dependent correlations satisfy characteristic scaling relations that can be measured in optical lattices filled with cold atoms.