Small quench dynamics as a probe for trapped ultracold atoms

TL;DR

This paper demonstrates that analyzing the temporal variance of site occupations after a quench effectively reveals phase boundaries between superfluid and Mott insulating regions in trapped ultracold atom systems, aiding experimental exploration.

Contribution

It introduces a novel method using out-of-equilibrium dynamics to identify spatial phase boundaries in Hubbard model systems with ultracold atoms.

Findings

Temporal variance accurately locates phase boundaries.

Method outperforms standard indicators like local compressibility.

Applicable to both integrable and nonintegrable models.

Abstract

Finite systems of bosons and/or fermions described by the Hubbard model can be realized using ultracold atoms confined in optical lattices. The ground states of these systems often exhibit a coexistence of compressible superfluid and incompressible Mott insulating regimes. We analyze such systems by studying the out-of-equilibrium dynamics following a weak sudden quench of the trapping potential. In particular, we show how the temporal variance of the site occupations reveals the location of spatial boundaries between compressible and incompressible regions. The feasibility of this approach is demonstrated for several models using numerical simulations. We first consider integrable systems, hard-core bosons (spinless fermions) confined by a harmonic potential, where space separated Mott and superfluid phases coexist. Then, we analyze a nonintegrable system, a $J-V-V'$ model with coexisting charge density wave and superfluid phases. We find that the temporal variance of the site occupations is a more effective measure than other standard indicators of phase boundaries such as a local compressibility. Based on these examples, we argue that analyzing temporal fluctuations is a valuable experimental tool for exploring phase boundaries in trapped atom systems.