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arXiv:1602.06513 · Physical Review A

Reaching a Fermi-superfluid state near an orbital Feshbach resonance

Junjun Xu, Ren Zhang, Yanting Cheng, Peng Zhang, Ran Qi, Hui Zhai

Published Sep 9, 2016• 36 citations
arXivHTMLPDF

Abstract

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 $^{173}\mathrm{Yb}$ 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 $^{173}\mathrm{Yb}$ system, the properties of which will be complementary to extensively studied Fermi superfluids nearby a wide resonance in alkali-metal $^{40}\mathrm{K}$ and $^{6}\mathrm{Li}$ systems.

DOI
10.1103/physreva.94.033609

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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.
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 theoretically investigate normal-state properties of an ultracold Fermi gas with an orbital Feshbach resonance (OFR). Recently, OFR has attracted much attention as a promising pairing mechanism to realize a superfluid 173Yb Fermi gas. Including pairing fluctuations within a T-matrix approximation, and removing effects of an experimentally inaccessible deep bound state, we evaluate strong-coupling corrections to single-particle excitations. With increasing the strength of an OFR-induced tunable pairing interaction, the open channel is shown to exhibit the pseudogap phenomenon in the BCS-BEC crossover region, as in the case of a broad magnetic Feshbach resonance (MFR) in 6Li and 40K Fermi gases. We also show that the strong pairing interaction affects the closed channel, leading to the coexistence of particle and hole branches in the single-particle spectral weight. Since the latter phenomenon cannot be observed in the conventional MFR case, it may be viewed as a characteristic strong-coupling phenomenon peculiar to the OFR case.
The orbital Feshbach resonance (OFR) is a recently developed scheme for magnetically tuning the interactions in closed-shell fermionic atoms. Remarkably, unlike the Feshbach resonances in alkali-metal atoms, the open and closed channels of the OFR are only very weakly detuned in energy. This leads to a unique effect whereby a medium in the closed channel can Pauli block---or frustrate---the two-body scattering processes. Here, we theoretically investigate the impact of frustration in the few- and many-body limits of the experimentally accessible three-dimensional 173Yb^{173}\mathrm{Yb}173Yb system. We find that by adding a closed-channel atom to the two-body problem the binding energy of the ground state is significantly suppressed, and by introducing a closed-channel Fermi sea to the many-body problem we can drive the system towards weaker fermion pairing. These results are potentially relevant to superconductivity in solid-state multiband materials, as well as to the current and continuing exploration of unconventional Fermi-gas superfluids near the OFR.
We address the phase of a highly polarized Fermi gases across a narrow Feshbach resonance starting from the problem of a single down-spin fermion immersed in a Fermi sea of up spins. Both polaron and pairing states are considered using the variational wave function approach, and we find that the polaron-to-pairing transition will take place on the BCS side of the resonance, strongly in contrast to a wide resonance where the transition is located at the BEC side. For the pairing phase, we find the critical strength of the repulsive interaction between pairs above which the mixture of pairs and fermions will not phase separate. Therefore, nearby a narrow resonance, it is quite likely that magnetism can coexist with sss-wave BCS superfluidity at large Zeeman fields, which is a remarkable property absent in conventional BCS superconductors (or fermion-pair superfluids).
We theoretically investigate strong-coupling properties of an ultracold Fermi gas with an orbital Feshbach resonance (OFR). Including tunable pairing interaction associated with an OFR within the framework of the strong-coupling theory developed by Nozières and Schmitt-Rink (NSR), we examine the occupation of the closed channel. We show that, although the importance of the closed channel is characteristic of the system with an OFR, the occupation number of the closed channel is found to actually be very small at the superfluid phase transition temperature T c , in the whole BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover region, when we use the scattering parameters for an ultracold 173 Yb Fermi gas. The occupation of the closed channel increases with increasing the temperature above T c , which is more remarkable for a stronger pairing interaction. We also present a prescription to remove effects of an experimentally inaccessible deep bound state from the NSR formalism, which we meet when we theoretically deal with a 173 Yb Fermi gas with an OFR.
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.