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Journal of Physics B Atomic Molecular and Optical Physics

Orbital Feshbach resonance of Fermi gases in an optical lattice

Haiyang Zhang, Fazal Badshah, Abdul Basit, Guo-Qin Ge

Published Aug 6, 2018• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1361-6455/aad83b

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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 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.
Abstract In this paper, we study the orbital Feshbach resonance of an ultracold two-electron 173 Yb Fermi gas in a one-dimensional optical lattice with the Raman coupling between two different nuclear spin states in a two-channel model, an open channel and a closed channel. We find that the Raman coupling strength can prevent formation of Cooper pairs and compress the system, compromising its superfluidity, while in the presence of a synthetic magnetic flux, the Raman laser can promote superfluidity by adjusting the interaction between Cooper pairs, especially for a large orbital Feshbach resonance detuning. Further, we show the significant consequences of the chiral edge current by introducing a synthetic two dimensional lattice. We find that the chiral edge currents vary periodically with the flux. We find that the chiral edge currents in the open channel case may change their directions versus the orbital Feshbach resonance detuning. In contrast, for a closed channel, the detuning merely supports the chiral edge current and the directions of the chiral currents do not change with the variation of the detuning, which means the chirality remains unchanged.
Starting with the two-band description of an orbital Feshbach resonance, we study superfluid properties of a trapped 173Yb^{173}\mathrm{Yb}173Yb Fermi gas under the assumptions of a local-density approximation for the trapping potential and a mean-field approximation for the intraband Cooper pairings. In particular, we investigate the competition and interplay between the pair-breaking effect that is caused by the interband 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 spatial separation of superfluid and normal phases within the trap, and could play decisive roles in probing two-band superfluidity in these systems.
Starting with the two-band description of an orbital Feshbach resonance, we study superfluid properties of a trapped 173^{173}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.
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{\mathrm{MgB}}_{2}MgB2​.
We have studied a system of ultracold fermionic potassium ( 40 K) atoms in a three-dimensional (3D) optical lattice in the vicinity of an s-wave Feshbach resonance. Close to resonance, the system is described by a multi-band Bose–Fermi Hubbard Hamiltonian. We derive an effective lowest-band Hamiltonian in which the effect of higher bands is incorporated by a self-consistent mean-field approximation. The resulting model is solved by means of generalized dynamical mean-field theory. In addition to the BEC–BCS crossover, we find a phase transition to a fermionic Mott insulator at half-filling, induced by the repulsive fermionic background scattering length. We also calculate the critical temperature of the BEC/BCS state and find it to be minimal at resonance.