Thermodynamics and superfluid density in BCS-BEC crossover with and without population imbalance

TL;DR

This paper presents a fully consistent theoretical approach to the thermodynamics and superfluid density of trapped fermions in the BCS-BEC crossover, emphasizing the importance of pseudogap effects and addressing previous inconsistencies.

Contribution

It introduces a novel, consistent treatment of pseudogap effects that improves the physical accuracy of superfluid density and density profile calculations in the BCS-BEC crossover.

Findings

Superfluid density results are physically consistent at all temperatures.

The approach accounts for pseudogap effects, distinguishing $T^*$ and $T_c$.

Previous models showed ill-behaved superfluid density, now corrected.

Abstract

We address the thermodynamics, density profiles and superfluid density of trapped fermions undergoing BCS-BEC crossover, with and without population imbalance. Our approach represents a fully consistent treatment of "pseudogap effects", which reflect the distinction between the pair formation temperature $T^*$ and the pair condensation temperature $T_c$ and must be accommodated by modifying the fermionic excitation spectrum. This distinction has been omitted from all other many body approaches in the literature. We show how enforcing this corollary implies that pairing fluctuation contributions enter into both the gap and the number equations; this is necessary in order to be consistent with a generalized Ward identity. Furthermore, we demonstrate that we obtain physical results for the superfluid density $n_s(T)$ at all $T$. In contrast, previous work in the literature has led to ill-behaved $n_s(T)$. The superfluid density is a critical measure of the physicality of a given crossover theory. In order to properly address thermodynamic properties of a trapped Fermi gas, it is necessary to demonstrate that the particle density profiles are consistent with experiment. The lack of demonstrable consistency between theoretical and experimental density profiles, along with problematic behavior found for $n_s(T)$, casts doubt on previous claims in the literature concerning quantitative agreement between thermodynamical calculations and experiment.