Superfluid properties of an ultracold Fermi gas with an orbital Feshbach resonance in the BCS-BEC crossover region

Abstract

We theoretically investigate superfluid properties of a two-band gas of $^{173}$Yb Fermi atoms with an orbital Feshbach resonance (OFR). To describe the BCS-BEC crossover region, we include superfluid fluctuations caused by inter-band and intra-band pairing interactions associated with OFR, by extending the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink to the two-band case below the superfluid phase transition temperature; however, effects of an experimentally inaccessible deep bound state are removed, to model a real $^{173}$Yb Fermi gas near OFR. We show that the condensate fraction in the upper closed channel gradually becomes smaller than that in the lower open channel, as one moves from the strong- to the weak-coupling regime, because the OFR-pairing mechanism tunes the interaction strengths by adjusting the energy difference between the two bands. However, even when the closed-channel band is much higher in energy than the open-channel band in the weak-coupling regime, the magnitude of the superfluid order parameter in the closed channel is found to be still comparable to that in the open channel. As the reason for this, we point out a pair-tunneling effect by the OFR-induced inter-band interaction. Besides these superfluid quantities, we also examine collective modes, such as the Goldstone mode, Schmid (Higgs) mode, as well as Leggett mode, to clarify how they appear in the spectral weights of pair-correlation functions in each band. Since the realization of a multi-band superfluid Fermi gas is a crucial issue in cold Fermi gas physics, our results would contribute to the basic understanding of this type of Fermi superfluid in the BCS-BEC crossover region.