Density correlations in ultracold Fermi systems within the exact Richardson solution

TL;DR

This paper analyzes occupation number correlations in ultracold fermionic systems using the exact Richardson solution, revealing predominantly anti-correlated occupations with multinomial statistics for specific energy-level distributions.

Contribution

It provides explicit correlation function expressions for a two-level degenerate system using the exact ground state of the reduced BCS Hamiltonian, including analytical results in certain limits.

Findings

Occupations are mainly anti-correlated due to fermionic nature.

Correlations follow a multinomial distribution.

Analytical expressions derived for specific limiting cases.

Abstract

We discuss the occupation number correlations in an ultracold system of interacting fermionic atoms. For a system with a special energy-level distribution, viz. two multiply-degenerate levels, explicit expressions for the correlation functions are derived in a canonical approach using the exact ground state wavefunction of the reduced BCS Hamiltonian. We evaluate the correlators numerically for different interaction strength and find analytical expressions in some limiting cases. Due to the underlying fermionic nature of the pairs the occupations are predominantly anti-correlated and their statistics is a multinomial distribution.