Properties of the strongly paired fermionic condensates

TL;DR

This paper analyzes a fermionic gas in the BEC regime of the BCS-BEC crossover, calculating key properties like chemical potential and sound speed, and highlighting limitations of existing gap equations and low density approximations.

Contribution

It provides a detailed low density theoretical framework for strongly paired fermionic condensates and clarifies the invalidity of the standard BCS-BEC gap equation in the BEC regime.

Findings

Calculated chemical potential and sound speed in the BEC regime

Demonstrated the invalidity of the standard BCS-BEC gap equation in this regime

Derived the bosonic scattering length diagrammatically and confirmed no two-boson bound states

Abstract

We study a gas of fermions undergoing a wide resonance s-wave BCS-BEC crossover, in the BEC regime at zero temperature. We calculate the chemical potential and the speed of sound of this Bose-condensed gas, as well as the condensate depletion, in the low density approximation. We discuss how higher order terms in the low density expansion can be constructed. We demonstrate that the standard BCS-BEC gap equation is invalid in the BEC regime and is inconsistent with the results obtained here. We indicate how our theory can in principle be extended to nonzero temperature. The low density approximation we employ breaks down in the intermediate BCS-BEC crossover region. Hence our theory is unable to predict how the chemical potential and the speed of sound evolve once the interactions are tuned towards the BCS regime. As a part of our theory, we derive the well known result for the bosonic scattering length diagrammatically and check that there are no bound states of two bosons.