Universal correlations along the BEC-BCS crossover

TL;DR

This paper demonstrates that the long-distance behavior of two-body correlations and Cooper-pair density in a balanced Fermi gas is universal across the BEC-BCS crossover, supported by numerical and analytical results.

Contribution

It provides the first demonstration of universality in correlation functions along the BEC-BCS crossover using mean-field theory and analytical expressions.

Findings

Correlation length expressed analytically in terms of chemical potential and energy gap.

Numerical solutions confirm universal behavior across different interaction potentials.

Long-distance correlations are independent of specific short-range interactions.

Abstract

We show that the long-distance behavior of the two-body density correlation functions and the Cooper-pair probability density of a balanced mixture of a two-component Fermi gas at $T = 0$, is universal along the BEC-BCS crossover. Our result is demonstrated by numerically solving the mean-field BCS model for different finite short-range atomic interaction potentials. We find an analytic expression for the correlation length in terms of the chemical potential and the energy gap at zero momentum.