Reliability of the Ginzburg–Landau Theory in the BCS-BEC Crossover by Including Gaussian Fluctuations for 3D Attractive Fermions

Filippo Pascucci,Luca Salasnich,Andrea Perali

doi:10.3390/condmat6040049

Abstract

We calculate the parameters of the Ginzburg–Landau (GL) equation of a three-dimensional attractive Fermi gas around the superfluid critical temperature. We compare different levels of approximation throughout the Bardeen–Cooper–Schrieffer (BCS) to the Bose–Einstein Condensate (BEC) regime. We show that the inclusion of Gaussian fluctuations strongly modifies the values of the Ginzburg–Landau parameters approaching the BEC regime of the crossover. We investigate the reliability of the Ginzburg–Landau theory, with fluctuations, studying the behavior of the coherence length and of the critical rotational frequencies throughout the BCS-BEC crossover. The effect of the Gaussian fluctuations gives qualitative correct trends of the considered physical quantities from the BCS regime up to the unitary limit of the BCS-BEC crossover. Approaching the BEC regime, the Ginzburg–Landau equation with the inclusion of Gaussian fluctuations turns out to be unreliable.

Highlights

The last two decades of developments in the confinement, cooling, and control of the interaction in alkali-metal atomic gases have powered the interest in the BCS-Bose–Einstein Condensate (BEC) crossover [1,2]
We studied the behavior of the Ginzburg–Landau parameters around the superfluid critical temperature throughout the BCS-BEC crossover by solving the gap equation and the number equation in the mean-field and beyond-mean-field approximation
We found that the effects of the Gaussian fluctuations on the Ginzburg–Landau parameters A and B

Summary

Introduction

The last two decades of developments in the confinement, cooling, and control of the interaction in alkali-metal atomic gases have powered the interest in the BCS-BEC crossover [1,2]. The main motivation of our work rests on the formulation of an alternative, simpler approach for the calculation of complex superfluid properties throughout the BCS-BEC crossover close to the critical temperature. To investigate the reliability of the GL theory with fluctuations throughout the BCS-BEC crossover, we compared the result obtained from the GL theory with the microscopic approach for the coherence length and the critical rotational frequencies. We calculated the Ginzburg–Landau parameters in the BCS-BEC crossover through the integral functional approach as in [14,15,16]. Through GL parameters, we investigated the behavior of the coherence length, comparing our results with the one obtained by Palestini and Strinati through the microscopic diagrammatic approach in [17]. We analyzed the critical rotational frequencies that are the neutral system analogue of the critical magnetic fields for superconductors [18]

Methods

Gap Equation and Number Equation

Ginzburg–Landau Parameters and Characteristic Quantities

Conclusions