Nonlinear Schrödinger equation for a superfluid Fermi gas from BCS to Bose crossover

Abstract

We introduce a quasi-analytic nonlinear Schrödinger equation with beyond mean-field corrections to describe the dynamics of a zero-temperature dilute superfluid Fermi gas in the crossover from the weak-coupling Bardeen-Cooper-Schrieffer (BCS) regime, where $k_F|a|\ll 1$ with $a$ the s-wave scattering length and $k_F$ the Fermi momentum, through the unitarity limit, $k_{F}a\to \pm \infty$, to the Bose regime where $k_{F}a>0$. The energy of our model is parametrized using the known asymptotic behavior in the BCS, Bose, and the unitarity limits and is in excellent agreement with accurate Green function Monte Carlo calculations. The model generates good results for frequencies of collective breathing oscillation of a trapped Fermi superfluid.

4 pages, 5 figures

References in corpus (6)

• Crossover from a molecular Bose-Einstein condensate to a degenerate Fermi gas
• Weakly bound dimers of fermionic atoms
• Collective excitations of a degenerate gas at the BEC-BCS crossover
• The potential energy of a ${}^{40}$K Fermi gas in the BCS-BEC crossover
• Collective modes and ballistic expansion of a Fermi gas in the BCS-BEC crossover
• Time-dependent Gross-Pitaevskii equation for composite bosons as the strong-coupling limit of the fermionic BCS-RPA approximation

Cited by in corpus (3)

• Superfluid Bose-Fermi mixture from weak-coupling to unitarity
• Effective Nonlinear Schrödinger Equations for Cigar-Shaped and Disk-Shaped Fermi Superfluids at Unitarity
• Universal behavior of a trapped Fermi superfluid in the BCS-unitarity crossover