Competition between BCS-pairing and “moth-eaten effect” in BEC–BCS crossover

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 sizable 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.

► Study condensation energy (ϵNϵN) of two-fermion system with Richardson–Gaudin equation.
► Trend of “moth-eaten” effect in ϵNϵN from one to many pairs.
► ϵNϵN first increases/emerges, then decreases to zero with increase of pair number in 3D.
► ϵNϵN always decreases with increase of pair number in 2D.
► Quantitative analysis of ϵNϵN for two pairs, in 2D and 3D.