Temporal and spatio-temporal correlation functions for trapped Bose gases

TL;DR

This paper investigates temporal and spatio-temporal density correlations in trapped Bose gases, accounting for measurement effects, revealing oscillation revivals and propagation of correlations, and proposing a realistic experimental protocol.

Contribution

It provides a detailed analysis of density correlation functions in Bose gases, including effects of finite measurement size and duration, and introduces a practical measurement protocol.

Findings

Shot-noise correlations revive after trap oscillation periods.

Bosonic correlations dominate at long times for non-overlapping regions.

Correlations propagate at finite speeds.

Abstract

Density correlations unambiguously reveal the quantum nature of matter. Here, we study correlations between measurements of density in cold-atom clouds at different times at one position, and also at two separated positions. We take into account the effects of finite-size and -duration measurements made by light beams passing through the atom cloud. We specialise to the case of Bose gases in harmonic traps above critical temperature, for weakly-perturbative measurements. For overlapping measurement regions, shot-noise correlations revive after a trap oscillation period. For non-overlapping regions, bosonic correlations dominate at long times, and propagate at finite speeds. Finally, we give a realistic measurement protocol for performing such experiments.