A new many-body wave function for BCS-BEC crossover in Fermi gases

TL;DR

This paper introduces a novel many-body wave function formalism for the BCS-BEC crossover in Fermi gases, capturing key correlations and behaviors across regimes, and aligning with experimental data.

Contribution

It develops a modified BCS-Leggett wave function including higher fermion correlations, unifying BEC and BCS physics with experimental observations.

Findings

Reproduces Petrov et al's 4-fermion behavior and scattering length at short distances

Reduces to composite-boson Bogoliubov physics at long distances

Matches the Lee-Yang correction and explores higher-order effects

Abstract

We present a new many body formalism for BCS-BEC crossover, which represents a modification of the BCS-Leggett ground state to include 4-fermion, and higher correlations. In the BEC regime, we show how our approach contains the \textit{Petrov et al} 4-fermion behavior and associated scattering length $a_{dd}$ at short distances, and secondly reduces to composite-boson Bogoliubov physics at long distances. It reproduces the Lee-Yang term, whose numerical value is also fixed by $a_{dd}$. We have also examined the next term beyond the Lee-Yang correction in a phenomenological fashion, building on cloud size data and collective mode experiments. However, one has to view this phenomenological analysis with some caution since experiments are in a state of flux and are performed close to unitarity.