Pairing and molecule formation along the BCS-BEC crossover for finite range potentials

Abstract

We analyze the BCS-BEC crossover transition of a balanced two component mixture of fermions interacting via a finite range potential, within a mean field approach. For the analysis we consider three finite range potentials cases describing the interaction between different Fermi species: a square well, an exponential and a Yukawa potential. The T = 0 thermodynamics analysis along the BCS-BEC crossover allow us to recognize the proper variables, for finite range interactions, that capture the transition from a thermodynamic non-universal behavior at unitarity, to its universal restoration. On the other side, the determination of the pair functions along the crossover suggests that the smooth transition occurs always between the scattering resonance and the change of sign of the chemical potential. This identification follows directly from the pair wave functions behavior, which in the BCS and BEC sides become exponentially localized and oscillatory slowly decaying respectively. * Electronic address: rosario@fisica.unam.mx 1 arXiv:1904.00135v1 [cond-mat.quant-gas]

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…”

“…This behavior differs from the 3D case [14], where the oscillation wave vectors decrease as we approach the BEC limit, with the disappearance of the Fermi-surface. We believe an explanation of this behavior in 2D requires further considerations, such as the use of a finite range interaction, instead of the contact interaction [40,41], and the inclusion of beyond mean-field corrections. The phase differences between the three functions show that their nodes (or maximums also) form a structure of concentric circles.…”

“…There are, however, natural extensions of this study that should be addressed. One is the consideration of realistic interatomic finite-range potentials [36,37] and the other is the inclusion of finite temperatures [38] still at the level of a mean-field description. For the case of finite temperatures there are already solid advances specially for the ↑↓ correlation function [16,38].…”

Universal correlations along the BEC-BCS crossover

“…In addition, correlation functions are of fundamental relevance to characterize the order of a phase transition as they directly track density-density fluctuations [9][10][11][12][13][14][15][16]. Within the ubiquitous crossover of fermionic superfluids that goes from a Bardeen-Cooper-Schrieffer (BCS) state to a molecular Bose-Einstein condensate (BEC), as the s-wave scattering length is varied through a Feshbach resonance [17][18][19][20][21][22][23][24], the analysis of density correlations has been a subject of relatively recent scrutiny, both at zero and finite temperature [19,20,[23][24][25][26][27][28][29][30][31], as well as varying interaction models [22,32], and space dimension [26,33,34], but mostly within the context of the contact interaction that depends solely on the scattering length. The modulation of such an effective interaction between fermions gives the possibility of the emergence of different quantum states like superfluidity, or superconductivity for charged fermions, and molecular formation, giving account of the rich many-body effects that can be found in nature.…”

“…That is, within the BCS-Leggett variational approach, we fully analyze the BEC-BCS crossover using four finite-range potentials that show representative features of typical atomic and nuclear interactions. We analyze a square well potential [20], which shows a discontinuity at a finite radius; an exponential potential [44], which is smooth over all space; the Yukawa potential [45], which has a divergence at the origin; and we also use a van der Waals tail potential [23,32], which bears the common atomic power-law decay. An important aspect is that we do not approximate these potentials in the gap equation and, while this introduces the inconvenience of dealing with numerical difficulties, these have been solved in [32,46].…”