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arXiv:1607.07513 · Physical Review A

Quantum defect theory for the orbital Feshbach resonance

Yanting Cheng, Ren Zhang, Peng Zhang

Published Jan 23, 2017• 12 citations
arXivHTMLPDF

Abstract

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 $^{173}\mathrm{Yb}$ atoms [R. Zhang et al., Phys. Rev. Lett. 115, 135301 (2015)]. When the OFR of the $^{173}\mathrm{Yb}$ 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.

DOI
10.1103/physreva.95.013624

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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.
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.
A comprehensive search for broad Feshbach resonances (FRs) in all possible combinations of stable alkali-metal atoms is carried out, using a multichannel quantum-defect theory assisted by the analytic wave functions for a long-range van der Waals potential. A number of broad sss-, ppp-, and ddd-wave FRs in the lowest-energy scattering channels, which are stable against two-body dipolar spin-flip loss, are predicted and characterized. Our results also show that broad FRs of ppp- or ddd-wave type that are free of two-body loss do not exist between fermionic alkali-metal atoms for a magnetic field up to 1000 G. These findings constitute helpful guidance on efforts towards the experimental study of high-partial-wave coupling-induced many-body physics.
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 have developed a model of Feshbach resonances in gases of ultracold alkali-metal atoms using the ideas of multichannel quantum-defect theory. Our model requires just three parameters describing the interactions---the singlet and triplet scattering lengths, and the long-range van der Waals coefficient---in addition to known atomic properties. Without using any further details of the interactions, our approach can accurately predict the locations of resonances. It can also be used to find the singlet and triplet scattering lengths from measured resonance data. We apply our technique to 6Li-40K^{6}\text{L}\text{i-}^{40}\text{K}6Li-40K and $^{40}\text{K}\text{\ensuremath{-}}^{87}\text{R}\text{b}$ scattering, obtaining good agreement with experimental results, and with the more computationally intensive coupled channels technique.
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.
Multichannel quantum-defect theory (MQDT) provides a powerful toolkit for describing and understanding collisions of cold alkali-metal atoms. Various MQDT approximations differ primarily in how they characterize the so-called short-ranged KKK matrix Ksr{\mathbf{K}}_{\text{sr}}Ksr​, which encapsulates the short-ranged physics into a handful of low-energy parameters that exhibit simple and smooth dependence on energy and field. Here, we compare three different methods for computing Ksr{\mathbf{K}}_{\text{sr}}Ksr​ for homonuclear collisions of alkali-metal atoms, from lithium to cesium. The MQDT calculations are benchmarked against numerically converged coupled-channels calculations that use a log-derivative propagator out to the asymptotic region. We study how well these approximations reproduce positions of sss-wave magnetic Feshbach resonances, comparing with experiment where possible, and identify the limitations of various approximations.