BCS-BEC crossover in a trapped Fermi super-fluid using a density-functional equation

Abstract

We derive a generalized time-dependent Galilean-invariant density-functional (DF) equation appropriate to study the stationary and non-stationary properties of a trapped Fermi super-fluid in the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensation (BCS) crossover. This equation is equivalent to a quantum hydrodynamical equation for a Fermi super-fluid. The bulk chemical potential of this equation has the proper (model-independent) dependence on the Fermi-Fermi scattering length in the BCS and BEC limits. We apply this DF equation to the study of stationary density profile and size of a cigar-shaped Fermi super-fluid of ${}^6$Li atoms and the results are in good agreement with the experiment of Bartenstein {\it et al.} in the BCS-BEC crossover. We also apply the DF equation to the study of axial and radial breathing oscillation and our results for these frequencies are in good agreement with experiments in the BCS-BEC crossover.

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Cited by in corpus (10)

• Localization of a Bose-Fermi mixture in a bichromatic optical lattice
• Dark solitons dynamics and snake instability in superfluid Fermi gases trapped by an anisotropic harmonic potential
• Slow interaction ramps in trapped many-particle systems: universal deviations from adiabaticity
• Interaction ramps in a trapped Bose condensate
• Effective equations for repulsive quasi-1D BECs trapped with anharmonic transverse potentials
• One- and two-dimensional reductions of the mean-field description of degenerate Fermi gases
• Dipolar Bose-Einstein condensate for large scattering length
• Dynamics of shock waves in a superfluid unitary Fermi gas
• Ultracold collisions between two light indistinguishable diatomic molecules: elastic and rotational energy transfer in HD+HD
• Dispersive effects in the unitary Fermi gas