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A strongly correlated Fermi superfluid near an orbital Feshbach resonance: The stability, universal equation of state and Leggett mode

Lianyi He, Jia Wang, Shi-Guo Peng, Xia-Ji Liu, Hui Hu

Published Jun 1, 2016• 0 citations
OpenAlex

Abstract

We theoretically study the superfluid phase of a strongly correlated $^{173}$Yb Fermi gas near orbital Feshbach resonances, by developing a quantitative fluctuation theory with the two-band model. We examine the low-energy density excitation spectrum of the system and determine a stability phase diagram. We find that the $^{173}$Yb Fermi gas is intrinsically metastable and has a new-type universal equation of state, due to the small but positive singlet scattering length. The massive Leggett mode, arising from the out-of-phase fluctuation of the relative phase of two pairing parameters, is severely damped. We discuss the parameter space where an undamped Leggett mode may exist.

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Strongly correlated Fermi superfluid near an orbital Feshbach resonance: Stability, equation of state, and Leggett mode

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We theoretically study the superfluid phase of a strongly correlated $^{173}\mathrm{Yb}$ 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 $^{173}\mathrm{Yb}$ 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.

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We theoretically investigate the superfluid properties of a two-band gas of $^{173}\mathrm{Yb}$ 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 $^{173}\mathrm{Yb}$ 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 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.

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

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.

arXiv:1606.07168•Physical Review A•Apr 27, 2017•21 citations
We theoretically study the superfluid phase of a strongly correlated 173^{173}173Yb Fermi gas near orbital Feshbach resonances, by developing a quantitative fluctuation theory with the two-band model. We examine the low-energy density excitation spectrum of the system and determine a stability phase diagram. We find that the 173^{173}173Yb Fermi gas is intrinsically metastable and has a new-type universal equation of state, due to the small but positive singlet scattering length. The massive Leggett mode, arising from the out-of-phase fluctuation of the relative phase of two pairing parameters, is severely damped. We discuss the parameter space where an undamped Leggett mode may exist.
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.
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 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.
Abstract The Leggett collective excitations for a two-band Fermi gas with s-wave pairing and Josephson interband coupling in the BCS-BEC crossover at finite temperatures are investigated within the Gaussian pair fluctuation approach. Eigenfrequencies and damping factors for Leggett modes are determined in a nonperturbative way, using the analytic continuation of the fluctuation propagator through a branch cut in the complex frequency plane, as in Kurkjian et al (2019 Phys. Rev. Lett. 122 093403). The treatment is performed beyond the low-energy expansion, which is necessary when the collective excitation energy reaches the pair-breaking continuum edge. The results are applied in particular to cold atomic gases at the orbital Feshbach resonance and in a regime far from BEC, which can be relevant for future experiments.
We theoretically investigate dynamic structure factors of a strongly interacting Fermi superfluid near an orbital Feshbach resonance with random phase approximation approach at zero temperature, and find their dynamical characters across the phase transition from a balanced conventional Bardeen-Cooper-Schrieffer (BCS) superfluid to a polarized Sarma superfluid by continuously varying the chemical potential difference of two spin components. In a Bose-Einstein-condensate-like regime of the Fermi superfluid, dynamic structure factors can help distinguish the in-phase ground state from the out-of-phase metastable state by the relative location of molecular excitation and Leggett mode, or the minimum energy to break a Cooper pair. In the phase transition from BCS to Sarma superfluid, we find the dynamic structure factor of Sarma superfluid has its own specific gapless excitation at a small transferred momentum where the collective phonon excitation acquires a finite width, and also a relatively strong atomic excitation at a large transferred momentum, because of the existence of unpaired Fermi atoms. Our results can be used to differentiate Sarma superfluid from BCS superfluid.
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.