Interference pattern and visibility of a Mott insulator

TL;DR

This paper provides a theoretical analysis of the interference pattern observed in a Mott insulator of cold atoms, linking it to particle-hole pairs and explaining experimental results with a focus on coherence and inhomogeneity effects.

Contribution

It introduces a detailed theoretical model using a random phase approximation to explain interference patterns in Mott insulators, including effects of inhomogeneity and particle-hole pairs.

Findings

Reproduces experimental interference visibility at moderate lattice depths

Shows particle-hole pairs influence the coherence properties

Identifies non-adiabatic effects as cause for deviations at large lattice depths

Abstract

We analyze theoretically the experiment reported in [F. Gerbier et al, cond-mat/0503452], where the interference pattern produced by an expanding atomic cloud in the Mott insulator regime was observed. This interference pattern, indicative of short-range coherence in the system, could be traced back to the presence of a small amount of particle/hole pairs in the insulating phase for finite lattice depths. In this paper, we analyze the influence of these pairs on the interference pattern using a random phase approximation, and derive the corresponding visibility. We also account for the inhomogeneity inherent to atom traps in a local density approximation. The calculations reproduce the experimental observations, except for very large lattice depths. The deviation from the measurement in this range is attributed to the increasing importance of non-adiabatic effects.