Density fluctuations and compressibility matrix for population or mass imbalanced Fermi-Fermi mixtures

TL;DR

This paper establishes a generalized fluctuation-dissipation theorem linking density fluctuations to compressibility in imbalanced Fermi-Fermi mixtures, enabling phase boundary and critical behavior analysis through fluctuation measurements.

Contribution

It introduces a generalized fluctuation-dissipation theorem applicable to imbalanced Fermi mixtures and demonstrates how to extract local compressibility and correlations in trapped systems.

Findings

Derived a generalized fluctuation-dissipation theorem for imbalanced mixtures

Showed how to determine phase boundaries from density fluctuations

Demonstrated local compressibility extraction in trapped gases

Abstract

We describe the relation between the isothermal atomic compressibility and density fluctuations in mixtures of two-component fermions with population or mass imbalance. We derive a generalized version of the fluctuation-dissipation theorem which is valid for both balanced and imbalanced Fermi-Fermi mixtures. Furthermore, we show that the compressibility, its critical exponents, and phase boundaries can be extracted via an analysis of the density fluctuations as a function of population imbalance, interaction parameter or temperature. Lastly, we demonstrate that in the presence of trapping potentials, the local compressibility and local density-density correlations can be extracted via a generalized fluctuation-dissipation theorem valid within the local density approximation.