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arXiv:1606.07168 · Physical Review A

Collective modes in a two-band superfluid of ultracold alkaline-earth-metal atoms close to an orbital Feshbach resonance

Yi‐Cai Zhang, Shan–Shan Ding, Shizhong Zhang

Published Apr 27, 2017• 21 citations
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Abstract

We discuss the collective modes in an alkaline-earth-metal Fermi gas close to an orbital Feshbach resonance. Unlike the usual Feshbach resonance, the orbital Feshbach resonance in alkaline-earth-metal atoms realizes a two-band superfluid system where the fermionic nature of both the open and the closed channel has to be taken into account. We show that, apart from the usual Anderson-Bogoliubov mode which corresponds to the oscillation of total density, there also appears the long-sought Leggett mode corresponding to the oscillation of relative density between the two channels. The existence of the phonon and the Leggett modes and their evolution are discussed in detail. We show how these collective modes are reflected in the density response of the system.

DOI
10.1103/physreva.95.041603

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We discuss the collective modes in an alkaline-earth-metal Fermi gas close to an orbital Feshbach resonance. Unlike the usual Feshbach resonance, the orbital Feshbach resonance in alkaline-earth-metal atoms realizes a two-band superfluid system where the fermionic nature of both the open and the closed channel has to be taken into account. We show that, apart from the usual Anderson-Bogoliubov mode which corresponds to the oscillation of total density, there also appears the long-sought Leggett mode corresponding to the oscillation of relative density between the two channels. The existence of the phonon and the Leggett modes and their evolution are discussed in detail. We show how these collective modes are reflected in the density response of the system.
We investigate the nature of superfluid pairing in a strongly interacting Fermi gas near orbital Feshbach resonances with spin-population imbalance in three dimensions, which can be well described by a two-band or two-channel model. We show that a Sarma superfluid with gapless single-particle excitations is favored in the closed channel at large imbalance. It is thermodynamically stable against the formation of an inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov superfluid and features a well-defined Goldstone-Anderson-Bogoliubov phonon mode and a massive Leggett mode as collective excitations at low momentum. At large momentum, the Leggett mode disappears and the phonon mode becomes damped at zero temperature, due to the coupling to the particle-hole excitations. We discuss possible experimental observation of a strongly interacting Sarma superfluid with ultracold alkaline-earth-metal Fermi gases.
We theoretically investigate the superfluid properties of a two-band gas of 173Yb^{173}\mathrm{Yb}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^{173}\mathrm{Yb}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 first show that the many-body Hamiltonian governing the physical properties of an alkaline-earth 173Yb^{173}\mathrm{Yb}173Yb Fermi gas across the recently realized orbital Feshbach resonance is exactly analogous to that of two-band sss-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 propose to realize a strongly interacting Fermi superfluid near a narrow Feshbach resonance using the recently discovered ``orbital Feshbach resonance.'' The orbital Feshbach resonance is a type of magnetic field tunable scattering resonance theoretically predicted and experimentally observed recently in the alkaline-earth-metal-like 173Yb^{173}\mathrm{Yb}173Yb atom. We first show that the orbital Feshbach resonance is a narrow resonance in energy, while it is hundreds Gauss wide in terms of magnetic field strength, taking the advantage that the magnetic moment difference between the open and closed channels is quite small. Therefore, this is an ideal platform for the experimental realization of a strongly interacting Fermi superfluid with narrow resonance. We further show that the transition temperature for the Fermi superfluid in this system, especially at the BCS side of the resonance, is even higher than that in a wide resonance, which is also due to the narrow character of this resonance. Our results will encourage experimental efforts to realize Fermi superfluid in the alikaline-earth-metal-like 173Yb^{173}\mathrm{Yb}173Yb system, the properties of which will be complementary to extensively studied Fermi superfluids nearby a wide resonance in alkali-metal 40K^{40}\mathrm{K}40K and 6Li^{6}\mathrm{Li}6Li systems.
Recently, a new type of Feshbach resonance, i.e., orbital Feshbach resonance (OFR), was proposed for the ultracold alkaline-earth-metal--like atoms and was experimentally observed in the ultracold gases of 173Yb^{173}\mathrm{Yb}173Yb atoms. Unlike most of the magnetic Feshbach resonances of ultracold alkali atoms, when the OFR of 173Yb^{173}\mathrm{Yb}173Yb atoms appears, the energy gap between the thresholds of the open channel (OC) and the closed channel (CC) is much smaller than the characteristic energy of the interatomic interaction, i.e., the van der Waals energy. In this paper we study the OFR in systems with a small CC-OC threshold gap. We show that in these systems the OFR can be induced by the coupling between the OC and either an isolated bound state of the CC or the scattering states of the CC. Moreover, we also show that in each case the two-channel Huang-Yang pesudopotential is always applicable for the approximate calculation of the low-energy scattering amplitude. Our results imply that in the two-channel theoretical calculations for these systems it is appropriate to take into account the contributions from the scattering states of the CC.
We theoretically study the superfluid phase of a strongly correlated 173Yb^{173}\mathrm{Yb}173Yb Fermi gas near its orbital Feshbach resonance by developing a quantitative pair-fluctuation theory within a two-band model. We examine the density excitation spectrum of the system and determine a stability phase diagram. We find that the 173Yb^{173}\mathrm{Yb}173Yb Fermi gas is intrinsically metastable and has a peculiar equation of state, due to the small but positive singlet scattering length. The massive Leggett mode, arising from the fluctuation of the relative phase of two order parameters, is severely damped. We discuss the parameter space where an undamped Leggett mode may exist.