Starting with the two-band description of an orbital Feshbach resonance, we study superfluid properties of a trapped
173Yb Fermi gas under the assumptions of a local-density approximation for the trapping potential and a mean-field approximation for the intra-band Cooper pairings. In particular, we investigate the competition and interplay between the pair-breaking effect that is caused by the inter-band detuning energy, and the pair-breaking and thermal-broadening effects that are simultaneously caused by the temperature. We predict several experimental signatures that are directly caused by this interplay including a superfluid-normal phase separation within the trap, and could play decisive roles in probing two-band superfluidity in these systems.
In this paper, we study the orbital Feshbach resonance of ultracold two-electron 173 Yb Fermi gas in a one-dimensional optical lattice. We consider a two-band model under the assumptions of a local-density approximation for the optical lattice potential and a mean-field approximation for the intraband Cooper pairings. We get three crucially important properties for the system, the superfluid-Landau–Fermi-liquid (LFL) crossover corresponding to the tunneling energy, the particle condensation in the momentum space, and the superfluid-LFL phase transition corresponding to the temperature. We explain how to realize and manipulate these properties.
We first show that the many-body Hamiltonian governing the physical properties of an alkaline-earth
173Yb Fermi gas across the recently realized orbital Feshbach resonance is exactly analogous to that of two-band
s-wave superconductors with contact interactions; i.e., even though the free-particle bands have a tunable energy offset in between and are coupled by a Josephson-type attractive interband pair scattering, the intraband interactions have exactly the same strength. We then introduce two intraband order parameters within the BCS mean-field approximation and investigate the competition between their in-phase and out-of-phase (i.e., the so-called $\ensuremath{\pi}$-phase) solutions in the entire BCS-BEC evolution at zero temperature.
We theoretically investigate the superfluid properties of a two-band gas of
173Yb Fermi atoms with an orbital Feshbach resonance (OFR). To describe the BCS-BEC crossover region, we include superfluid fluctuations caused by interband and intraband 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, the effects of an experimentally inaccessible deep bound state are removed to model a real
173Yb 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 interband interaction. In addition to these superfluid quantities, we also examine collective modes, such as the Goldstone mode, the Schmid (Higgs) mode, and Leggett mode, to clarify how they appear in the spectral weights of pair-correlation functions in each band. Since the realization of a multiband 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.
We study static superfluid properties of alkali-earth-like Fermi atomic systems in the presence of orbital Feshbach resonance. Using a two-band description of the ground state and excited state and a mean-field approximation of the intraband atomic pairing, we investigate the phase transitions and crossover between BCS and Bose-Einstein-condensate (BEC) superfluidity. At zero temperature, we find exact BCS analytical solutions for the mean-field gap equations and number equations. Using these exact solutions, we calculate various static properties, such as superfluid order parameters, chemical potentials, density variations, density profiles, correlation and coherence lengths, ground-state energy, and Tan's contact density across the entire BCS-BEC crossover region. We anticipate that our closed-form analytical results can be used as a benchmark for future experimental and theoretical investigations and will have an impact on the current understanding of two-band superconductors such as
MgB2.
We investigate the single-particle properties at
T=0 of a trapped superfluid gas of Fermi atoms with a Feshbach resonance. A tunable pairing interaction associated with the Feshbach resonance leads to the BCS--Bose-Einstein condensate (BEC) crossover, where the character of superfluidity continuously changes from the BCS-type to a BEC of composite bosons. In this paper, we extend our previous work for a uniform superfluid Fermi gas [Y. Ohashi and A. Griffin, Phys. Rev. A 67, 063612 (2003)] to include the effect of a harmonic trap. We do not use the local density approximation (LDA), but directly solve the Bogoliubov--de Gennes (BdG) coupled equations. While our explicit numerical solutions are for a weak (narrow) Feshbach resonance, we argue that the single-particle BdG excitation spectrum will exhibit the same features for a strong (broad) Feshbach resonance. Using these equations, we find self-consistent values for the spatially dependent local density
n(r) as well as the composite BCS order parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(\mathbf{r})$, the latter describing both the Cooper-pair and molecular condensate contributions. Using these results, we calculate the single-particle density of states in the crossover region, and from this determine the true single-particle energy gap
(Eg) of the trapped Fermi superfluid. This is associated with the in-gap (or Andreev) states in the low-density region at the edge of the trap. We calculate the laser-induced tunneling current $I(\ensuremath{\omega})$ into another hyperfine state, as measured in recent rf spectroscopy experiments. This rf spectrum gives a direct probe of the quasiparticle spectrum. We show how the high-energy part of $I(\ensuremath{\omega})$ gives information about $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(r=0)$ at the center of the trap (which is comparable to the Fermi energy ${\ensuremath{\epsilon}}_{F}$ in the crossover region). We show that $I(\ensuremath{\omega})$ is very dependent on the spatial profile of the pair potential $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\Delta}}(r)$ that is used. We also emphasize that the narrow ``unpaired atom" peak in the rf data gives information about
Eg and the low-energy $(⪡{\ensuremath{\epsilon}}_{F})$ in-gap states of a Fermi superfluid. While our calculations are limited to
T=0, we use them to discuss the recent data of Chin et al. and the LDA calculations of T\"orm\"a and co-workers. The LDA, while useful, can lead to an incorrect physical picture of the low-density surface region of the Fermi superfluid.