Superfluidity and binary-correlations within clusters of fermions

TL;DR

This paper introduces a new variational method to simulate small fermionic clusters, capturing mean-field and binary correlations, and applies it to study the BCS-BEC crossover in a four-fermion system.

Contribution

The paper presents a novel variational approach that explicitly includes binary correlations, enabling detailed study of fermionic cluster dynamics and thermodynamics.

Findings

Particles prefer two distinct pair states in the crossover regime

Method accurately captures correlation effects beyond mean-field

Application to four-fermion system illustrates crossover behavior

Abstract

We propose a method for simulating the behaviour of small clusters of particles that explicitly accounts for all mean-field and binary-correlation effects. Our approach leads to a set of variational equations that can be used to study both the dynamics and thermodynamics of these clusters. As an illustration of this method, we explore the BCS-BEC crossover in the simple model of four fermions, interacting with finite-range potentials, in a harmonic potential. We find, in the crossover regime, that the particles prefer to occupy two distinct pair states as opposed to the one assumed by BCS theory.