Characters of basic steady state solutions for superfluid Fermi gas in Bessel optical lattices

Abstract

We consider a dynamical model for superfluid Fermi gas, trapped in the central well of an axially symmetric Bessel optical lattice potential. The equation includes nonlinear power-law form of the chemical potential [Formula: see text], for [Formula: see text], which accounts for Fermi pressure. Reducing the equation to two-dimensional (2D) form, we obtain the basic steady state solutions of the system along the Bose–Einstein condensation (BEC) side to Bardeen–Cooper–Schrieffer (BCS) side by employing the energy balance condition, which are guided by the variational approximation. It is found that the strength [Formula: see text] and the radial scale [Formula: see text] of the Bessel optical lattice have an extreme effect on the characters of basic steady state solution. Analytically, we deduce the atomic density distribution, the average atom number and the average energy of basic steady state, where the atom distribution of the system presents on periodic change with [Formula: see text], and increases faster at unitarity than in the BEC limit. Furthermore, because of the Fermi pressure, the atomic density distribution at the unitarity is more extensive than that in the BEC limit. In particular, there exist very interesting changes, the average energy intends to collapse state with [Formula: see text], however it emerges as a stable state with varying [Formula: see text] both in the BEC limit and at unitarity.