Correlation length and universality in the BCS-BEC crossover for energy-dependent resonance superfluidity

Abstract

We consider the BCS-BEC crossover of a quantum Fermi gas at T = 0 in the presence of an energy-dependent Fano-Feshbach resonance, driving the system from broad to narrow limits. We choose a minimal microscopic potential reproducing the two-particle resonance physics in terms of the scattering length a and the effective range R * representing the resonance width, and solve the BCS mean-field equations varying a, R * and the density. We show that the condensate fraction manifests a universal behavior when the correlation length, measuring the pair size, is used as the crossover parameter. Generally, a negative effective range has the effect of stretching the crossover region between the two extreme regimes, as evidenced by the behavior of the chemical potential. These results can be useful in view of the more recent perspectives of realizing narrow resonances also by optical means and amenable as a base Quantum Monte Carlo simulations. a

Generalized Crossover in Interacting Fermions within the Low-Energy Expansion

“…( 1) becomes non-Hermitian and we cannot obtain a thermodynamic equilibrium state in our homogeneous model. We also note that while such a singularity was overlooked in the previous mean-field study at T = [50], interestingly a cluster formation has been predicted in a similar region where r e > 0.46a in trapped Fermi gases [67]. Indeed, µ approaches the half of a critical binding energy −E b,c /2 = −2/(ma 2 ) at this boundary r e = a/2 (p c = r −1 e ) in the strong-coupling side.…”

“…While r e in ultracold Fermi gases near a broad Feshbach resonance is negligible, that in neutron matter given by r e = 2.8 fm [44] largely affects system's properties even around the subnuclear density [40]. On the other hand, a narrow Feshbach resonance in ultracold atoms gives a large and negative effective range [45].Since r e is directly related to the phase shift δ(p) (where p is the momentum), one can expect that the negative (positive) effective range induces a strong (weak) attraction [40,[46][47][48][49][50]. In this sense, a natural question arises: How does the superfluid transition behave if one arbitrarily changes the effective range?The purpose of this work is to answer this question and show that another crossover of the superfluid phase transition from the BCS pairing to the molecular BEC occurs when changing the effective range r e .…”

“…On the other hand, a narrow Feshbach resonance in ultracold atoms gives a large and negative effective range [45]. Since r e is directly related to the phase shift δ(p) (where p is the momentum), one can expect that the negative (positive) effective range induces a strong (weak) attraction [40,[46][47][48][49][50]. In this sense, a natural question arises: How does the superfluid transition behave if one arbitrarily changes the effective range?…”

Universal correlations along the BEC-BCS crossover

“…Thus, based on these previous results we searched for a similar fitting, finding that the gap in (15) must be evaluated at zero momentum for finite range interactions. It is relevant to recall that characteristic lengths of the correlation functions, as well as the Cooper pair-size have certainly been the subject of several studies, see [22,[50][51][52][53].…”

“…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.…”