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Density correlations in ultracold atomic Fermi gases

W. Belzig·C. Schroll·C. Bruder
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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.

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W. Belzig, C. Schroll, C. Bruder. 2007-05-23. Density correlations in ultracold atomic Fermi gases. https://doi.org/10.1103/physreva.75.063611

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