The contact in the BCS–BEC crossover for finite range interacting ultracold Fermi gases

Abstract

Using mean-field theory for the Bardeen-Cooper-Schriefer (BCS) to the Bose-Einstein condensate (BEC) crossover we investigate the ground state thermodynamic properties of an interacting homogeneous Fermi gas. The interatomic interactions modeled through a finite range potential allows us to explore the entire region from weak to strong interacting regimes with no approximations.To exhibit the thermodynamic behavior as a function of the potential parameters in the whole crossover region, we concentrate in studying the Contact variable, the thermodynamic conjugate of the inverse of the s-wave scattering length. Our analysis allows us to validate the mean-field approach across the whole crossover. It also leads to predict a quantum phase transition-like in the case when the potential range becomes large. This finding is a direct consequence of the k-dependent energy gap for finite interaction range potentials.

Spatial structure of the pair wave function and the density correlation functions throughout the BEC-BCS crossover

“…As an extension of this work, it will be of interest to study the large distance behavior of the correlation functions in quasi-2D geometries, which are of current interest for understanding the evolution from 3D to 2D [2]. Also, it is of interest to see how the large-distance properties are modified by beyond mean-field corrections, and the use of a short-range potential [36,40,41,[43][44][45][46]. equation (28) we get…”

Re-examining the quadratic approximation in theory of a weakly interacting Bose gas with condensate: the role of nonlocal interaction potentials

“…Yet another model potential V 5 (r) = −(g/8πr 3 0 )e −r/r0 is sometimes used in the ultracold gases literature [38], in particular, to reproduce an attractive tail of interaction. This potential has well defined analytic expressions for the corresponding scattering length, a s = a s (g, r 0 ) [63], and its Fourier transform, ν 5 (p) = −g/[1 + (pr 0 / ) 2 ] 2 .…”

Effective-range dependence of resonantly interacting fermions

“…To extract the unitary parameters thus requires an extrapolation to zero effective range. Range effects in the ufg are also discussed in [14] (large r e ), [4] (Fixed-Node qmc (fnqmc)), and in [15,16] (Bogoliubov-de Gennes (bdg) approximation).…”