BCS,BEC states and Feshbach resonance in atomic Fermi gases

Abstract

To study the behavior of atomic Fermi gases in the vicinity of Feshbach resonance, M. Holland et al. [12] and S. J. J. M. F. Kokkelmans et al. [22] proposed resonance mean field theory in which the molecules formed by Feshbach resonance are considered in the many-body Hamiltonian. Motivated by microscopic scattering theory and resonance mean field theory, we develop a thermodynamic method to study this system. In this method we treat atomic Fermi gases near resoance as a atom-molecule mixture. We can use BCS Hamiltonian and Bose- Einstein statistics to describe the behavior of atoms and molecules respectively. Chemical equilibrium can be achieved between atoms and molecules due to hypefine interaction. We use this method to study the system behavior under different temperature and detuning energy and find that at low temperature a smooth BCS-BEC crossever can occure with decreasing detuning energy. We further calculate a measurable quantity, molecular condensation fraction, and find its behavior matches qualitatively with the experimental result [16].