Density correlations in ultracold atomic Fermi gases

TL;DR

This paper analyzes density fluctuations in ultracold fermionic gases across the BEC-BCS crossover using full counting statistics, providing exact and analytical results that reveal how fluctuations vary with pairing and temperature.

Contribution

It introduces a novel application of full counting statistics to fermionic gases, deriving exact cumulant-generating functions across the BEC-BCS crossover.

Findings

Poissonian fluctuations are suppressed on the BCS side.

Fluctuation size measures pairing potential in the BCS limit.

Third cumulant and temperature effects are characterized.

Abstract

We investigate density fluctuations in a coherent ensemble of interacting fermionic atoms. Adapting the concept of full counting statistics, well-known from quantum optics and mesoscopic electron transport, we study second-order as well as higher-order correlators of density fluctuations. Using the mean-field BCS state to describe the whole interval between the BCS limit and the BEC limit, we obtain an exact expression for the cumulant-generating function of the density fluctuations of an atomic cloud. In the two-dimensional case, we obtain a closed analytical expression. Poissonian fluctuations of a molecular condensate on the BEC side are strongly suppressed on the BCS side. The size of the fluctuations in the BCS limit is a direct measure of the pairing potential. We also discuss the BEC-BCS crossover of the third cumulant and the temperature dependence of the second cumulant.