Competition between BCS-pairing and "moth-eaten effect" in BEC-BCS crossover

TL;DR

This paper investigates how the condensation energy in BEC-BCS crossover systems varies with pair number, revealing a competition between pairing correlations and the 'moth-eaten effect' across different dimensions.

Contribution

It introduces a detailed analysis of the interplay between pairing energy and state depletion ('moth-eaten effect') in BEC-BCS crossover, highlighting dimensional differences.

Findings

Condensation energy per pair first increases then decreases in 3D systems.

In 2D systems, the 'moth-eaten effect' dominates, causing a monotonic decrease.

The 'moth-eaten effect' significantly influences pairing behavior in many-body systems.

Abstract

We study the change in condensation energy from a single pair of fermionic atoms to a large number of pairs interacting via the reduced BCS potential. We find that the energy-saving due to correlations decreases when the pair number increases because the number of empty states available for pairing gets smaller ("moth-eaten effect"). However, this decrease dominates the 3D kinetic energy increase of the same amount of noninteracting atoms only when the pair number is a sizeable fraction of the number of states available for pairing. As a result, in BEC-BCS crossover of 3D systems, the condensation energy per pair first increases and then decreases with pair number while in 2D, it always is controlled by the "moth-eaten effect" and thus simply decreases.