Nonlinear Schrödinger equation for a superfluid Fermi gas in the BCS-BEC crossover

We introduce a quasianalytic 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 kF |a| 1 with a the s -wave scattering length and kF the Fermi momentum, through the unitarity limit kF a→± to the Bose-Einstein condensation (BEC) regime where kF a>0. The energy of our model is parametrized using the known asymptotic behavior in the BCS, BEC, and the unitarity limits and is in excellent agreement with accurate Green's-function Monte Carlo calculations. The model generates good results for frequencies of collective breathing oscillations of a trapped Fermi superfluid. © 2008 The American Physical Society.