BEC-BCS crossover with Feshbach resonance for a three-hyperfine-species model
Guojun Zhu and Anthony J. Leggett
Accepted
We consider the behavior of an ultracold Fermi gas across a narrow Feshbach resonance, where the occupation of the closed channel may not be negligible. While the corrections to the single-channel formulae associated with the nonzero chemical potential and with particle conservation have been considered in the existing literature, there is a further effect, namely the "inter-channel Pauli exclusion principle" associated with the fact that a single hyperfine species may be common to the two channels. We focus on this effect and show that, as intuitively expected, the resulting corrections are of order EF/h, where EF is the Fermi energy of the gas in the absence of interactions and h is the Zeeman energy difference between the two channels. We also consider the related corrections to the fermionic excitation spectrum, and briefly discuss the collective modes of the system.