Eur. Phys. J. B 82, 303-311 (2011)
https://doi.org/10.1140/epjb/e2011-10987-2

Finite vortex numbers and symmetric vortex structures in a rotating trapped Fermi gas in the BCS-BEC crossover

State Key Laboratory of Surface Physics and Department of Physics, Fudan University, Shanghai, 200433, P.R. China

Corresponding author: ^a ylma@fudan.edu.cn

Received: 17 December 2010
Revised: 8 July 2011
Published online: 17 August 2011

Abstract

The ground state of a three-dimensional (3D) rotating trapped superfluid Fermi gas in the BCS-BEC crossover is mapped to finite N_v-body vortex states by a simple ansatz. The total vortex energy is measured from the ground-state energy of the system in the absence of the vortices. The vortex state is stable since the vortex potential and rotation energies are attractive while the vortex kinetic energy and interaction between vortices are repulsive. By combining the analytical and numerical works for the minimal vortex energy, the 2D configurations of N_v vortices are studied by taking into account of the finite size effects both on xy-plane and on z-direction. The calculated vortex numbers as a function of the interaction strength are appropriate to the renew experimental results by Zwierlein in [High-temperature superfluidity in a ultracold Fermi gas, Ph.D. thesis, Massachusetts Institute of Technology, 2006]. The numerical results show that there exist two types of vortex structures: the trap center is occupied and unoccupied by a vortex, even in the case of N_v < 10 with regular polygon and in the case of N_v ≥ 10 with finite triangle lattice. The rotation frequency dependent vortex numbers with different interaction strengths are also discussed.