Spatial structure of the pair wavefunction and the density correlation functions at the BEC-BCS crossover

TL;DR

This paper provides a detailed numerical and analytical study of the spatial structure of pair wavefunctions and density correlations across the BEC-BCS crossover, revealing distinct behaviors and characteristic lengths.

Contribution

It offers the first comprehensive analysis combining exact numerical calculations with analytic expressions for correlation lengths and pair sizes across the crossover.

Findings

Long-range correlations on the BCS side.

Tight pair formation dominates in the BEC region.

Distinct oscillatory and decay behaviors in correlation functions.

Abstract

By an exact numerical calculation of the BCS pair wavefunction and the density correlation functions both between atoms in the same and in different spin states, we extract the spatial large distance behavior of the respective functions. After different initial transients, those distributions show an algebraic dependence accompanied with their own exponential decay and a well defined periodic oscillatory behavior. While in general, in the BCS side there are long-range correlations and in the BEC region the behavior is dominated by tight pairs formation, each distribution shows its own overall behavior. We derive analytic expressions for the mean pair size and the correlation lengths of the same and different density correlation functions. The whole analysis yields a quite complete description of the spatial structure of the superfluid along the crossover.