Application of the inhomogeneous Kibble-Zurek mechanism to quench dynamics in the transition from a Mott-insulator to a superfluid in a finite system

TL;DR

This paper investigates how the inhomogeneous Kibble-Zurek mechanism explains the nonuniform quench dynamics during the transition from a Mott insulator to a superfluid in cold Bose gases, using Gutzwiller simulations.

Contribution

It extends the inhomogeneous Kibble-Zurek theory to finite systems with harmonic traps and demonstrates its applicability through simulations.

Findings

Quench dynamics show positional dependence due to Mott-lobe structure.

Inhomogeneous Kibble-Zurek theory matches simulation results in shallow traps.

Growth of superfluid order parameter is spatially nonuniform.

Abstract

We apply the theory of inhomogeneous Kibble-Zurek mechanism to understand quench dynamics from the Mott insulator to the superfluid in a cold Bose gases confined in both a two-dimensional optical lattice and a harmonic trap. The local quench time and the freeze-out region associated with the nonadiabatic transition take a nontrivial positional dependence due to the Mott-lobe structure of the ground state phase diagram of the Bose-Hubbard model. We demonstrate that the quench dynamics through the time-dependent Gutzwiller simulations, revealing inhomogeneous properties of the growth of the superfluid order parameter. The inhomogeneous Kibble-Zurek theory is applicable for the shallow harmonic trap.