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arXiv:1601.07726 · Physical Review A

Orbital Feshbach resonances with a small energy gap between open and closed channels

Yanting Cheng, Ren Zhang, Peng Zhang

Published Apr 22, 2016• 10 citations
arXivHTMLPDF

Abstract

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 $^{173}\mathrm{Yb}$ atoms. Unlike most of the magnetic Feshbach resonances of ultracold alkali atoms, when the OFR of $^{173}\mathrm{Yb}$ 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.

DOI
10.1103/physreva.93.042708

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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.
In the ultracold gases of alkali-earth-metal-like atoms, a new type of Feshbach resonance, i.e., the orbital Feshbach resonance (OFR), has been proposed and experimentally observed in ultracold 173Yb^{173}\mathrm{Yb}173Yb atoms [R. Zhang et al., Phys. Rev. Lett. 115, 135301 (2015)]. When the OFR of the 173Yb^{173}\mathrm{Yb}173Yb atoms occurs, the energy gap between the open and closed channels is smaller by two orders of magnitude than the van der Waals energy. As a result, quantitative accurate results for the low-energy two-body problems can be obtained via multichannel quantum defect theory (MQDT), which is based on the exact solution of the Schr\"odinger equation with the van der Waals potential. In this paper we use MQDT to calculate the two-atom scattering length, effective range, and binding energy of two-body bound states for the systems with OFR. With these results we further study the clock-transition spectrum for the two-body bound states, which can be used to experimentally measure the binding energy. Our results are helpful for the quantitative theoretical and experimental research for the ultracold gases of alkali-earth-metal-like atoms with OFR.
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 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.
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 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.