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Compressibility and spin susceptibility in the evolution from BCS to BEC superfluids

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 critical exponents for the compressibility can be extracted via an analysis of the density fluctuations when phase transitions occur as a function of population imbalance or interaction parameter. In addition, we demonstrate that in the presence of trapping potentials, the local compressibility, local spin-susceptibility and local density-density correlations can be extracted from experimental data via a generalized local fluctuation-dissipation theorem which is valid beyond the local density approximation. Lastly, we use the local density approximation to calculate theoretically the local compressibility, local spin-susceptibility and local density-density fluctuations to compare with experimental results as they become available.