Superfluid equation of state of cold fermionic gases in the Bose-Einstein regime

TL;DR

This paper develops an exact fermionic many-body theory for ultracold gases in the BEC regime, deriving the equation of state including mean-field and Lee-Huang-Yang corrections, highlighting the composite nature of dimers.

Contribution

It provides a systematic fermionic approach to derive the equation of state of fermionic gases in the BEC regime, including higher-order corrections.

Findings

Mean-field contribution matches standard dimer-dimer scattering results.

Lee-Huang-Yang correction retains form for composite dimers.

Next-order term reveals effects of dimer composite nature.

Abstract

We present an exact many-body theory of ultracold fermionic gases for the Bose-Einstein condensation (BEC) regime of the BEC-BCS crossover. This is a purely fermionic approach which treats explicitely and systematically the dimers formed in the BEC regime as made of two fermions. We consider specifically the zero temperature case and calculate the first terms of the expansion of the chemical potential in powers of the density $n$. We derive first the mean-field contribution, which has the expected standard expression when it is written in terms of the dimer-dimer scattering length $a_M$. We go next in the expansion to the Lee-Huang-Yang order, proportional to $n^{3/2}$. We find the far less obvious result that it retains also the same expression in terms of $a_M$ as for elementary bosons. The composite nature of the dimers appears only in the next term proportional to $n^2$.