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arXiv:1809.00471 · Physical Review A

Confinement-induced resonance of alkaline-earth-metal-like atoms in anisotropic quasi-one-dimensional traps

Qing Ji, Ren Zhang, Xiang Zhang, Wei Zhang

Published Nov 12, 2018• 3 citations
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Abstract

We study the confinement-induced resonance (CIR) of $^{173}\mathrm{Yb}$ atoms near an orbital Feshbach resonance in a quasi-one-dimensional tube with transversal anisotropy. By solving the two-body scattering problem, we obtain the location of CIR for various anisotropy ratios and magnetic fields. Our results show that the anisotropy of the trapping potential can serve as an additional knob to tune the location of CIR. In particular, one can shift the location of CIR to the region attainable in the current experiment. We also study the energy spectrum of the system and analyze the properties of CIR from the perspective of bound states. We find that as the orbital Feshbach resonance acquires two nearly degenerate scattering channels, which in general have different threshold energies, CIR takes place when the closed-channel bound-state energy becomes degenerate with one of the thresholds.

DOI
10.1103/physreva.98.053613

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We study the confinement-induced resonance (CIR) of 173Yb^{173}\mathrm{Yb}173Yb atoms near an orbital Feshbach resonance in a quasi-one-dimensional tube with transversal anisotropy. By solving the two-body scattering problem, we obtain the location of CIR for various anisotropy ratios and magnetic fields. Our results show that the anisotropy of the trapping potential can serve as an additional knob to tune the location of CIR. In particular, one can shift the location of CIR to the region attainable in the current experiment. We also study the energy spectrum of the system and analyze the properties of CIR from the perspective of bound states. We find that as the orbital Feshbach resonance acquires two nearly degenerate scattering channels, which in general have different threshold energies, CIR takes place when the closed-channel bound-state energy becomes degenerate with one of the thresholds.
We derive one-dimensional effective Hamiltonians for spin-orbit-coupled Fermi gases confined in quasi-one-dimensional trapping potentials. For an energy regime around the two-body bound-state energy, the effective Hamiltonian takes a two-channel form, where the populations in transverse excited levels are described by dressed molecules in the closed channel. For an energy regime slightly above the continuum threshold, the effective Hamiltonian takes a single-channel form, where low-energy physics is governed by the one-dimensional interacting strength determined by three-dimensional scattering length and transverse confinement. We further discuss the effect of spin-orbit coupling and effective Zeeman field on the position of confinement-induced resonances and show that these resonances can be understood as Feshbach resonances between the threshold of the transverse ground state and the two-body bound state associated with the transverse excited states. We expect that the shift of confinement-induced resonances can be observed under present experimental technology at attainable temperatures.
We theoretically study two atoms with ppp-wave interaction in a one-dimensional waveguide, investigating how the transverse anisotropy of the confinement affects the two-body state, especially the properties of the resonance. For a bound-state solution, we find there are a total of three two-body bound states due to the richness of the orbital magnetic quantum number of the ppp-wave interaction, while only one bound state is supported by the sss-wave interaction. Two of them become nondegenerate due to the breaking of the rotation symmetry under a transversely anisotropic confinement. For a scattering solution, the effective one-dimensional scattering amplitude and scattering length are derived. We find the position of the ppp-wave confinement-induced resonance shifts apparently versus the transverse anisotropy. In addition, a two-channel mechanism for the confinement-induced resonance in a one-dimensional waveguide is generalized to the ppp-wave interaction, which was previously proposed only for the sss-wave interaction. All our calculations are based on the parametrization of the 40K^{40}\mathrm{K}40K-atom experiments and can thus be confirmed in future experiments.
We studied the scattering problem of two distinguishable atoms with unequal mass, where one atom (atom $\ensuremath{\alpha}$) is trapped in a quasi-one-dimensional (quasi-1D) tube and the other one (atom $\ensuremath{\beta}$) is localized by a 3D harmonic trap. We show that in such a system if atom $\ensuremath{\alpha}$ is much heavier than $\ensuremath{\beta}$, confinement-induced resonance (CIR) can appear when the 3D sss-wave scattering length as{a}_{s}as​ of these two atoms is much smaller than the characteristic lengths (CLs) of the confinements, for either as>0{a}_{s}>0as​>0 or as<0{a}_{s}<0as​<0. This is quite different from the usual CIRs which occur only when as{a}_{s}as​ is comparable with the CL of confinement. Moreover, the CIRs we find are broad enough to serve as a tool for the control of effective interatomic interaction. We further show the mechanism of these CIRs via the Born-Oppenheimer approximation. Our results can be used for the realization of strongly interacting systems with ultracold atoms with weak 3D background interaction (i.e., small as{a}_{s}as​), e.g., the realization of ultracold gases with strong spin-dependent interaction at zero magnetic fields.
A nuclear-spin-exchange interaction exists between two ultracold fermionic alkali-earth-metal-like atoms in the electronic 1S0{}^{1}{S}_{0}1S0​ state (ggg state) and 3P0{}^{3}{P}_{0}3P0​ state (eee state) and is an essential ingredient for the quantum simulation of the Kondo effect. We study the control of this spin-exchange interaction for two atoms simultaneously confined in a quasi-one-dimensional (quasi-1D) tube, where the ggg atom is freely moving in the axial direction while the eee atom is further localized by an additional axial trap and behaves as a quasi-0D impurity. In this system, the two atoms experience effective 1D spin-exchange interactions in both even and odd partial-wave channels, whose intensities can be controlled by the characteristic lengths of the confinements via confinement-induced resonances (CIRs). In a previous work, we studied this problem with a simplified pure 1D model [Y. Cheng et al., Phys. Rev. A 96, 063605 (2017)]. In the present work, we go beyond that pure 1D approximation. We model the transverse and axial confinements by harmonic traps with finite characteristic lengths ${a}_{\ensuremath{\perp}}$ and az{a}_{z}az​, respectively, and exactly solve the quasi-1D--quasi-0D scattering problem between these two atoms. Using the solutions, we derive the effective 1D spin-exchange interaction and investigate the locations and widths of the even-odd wave CIRs for our system. It is found that when the ratio ${a}_{z}/{a}_{\ensuremath{\perp}}$ is larger, the CIRs can be induced by weaker confinements, which are easier to be realized experimentally. The comparison between our results and a recent experiment by L. Riegger et al. [Phys. Rev. Lett. 120, 143601 (2018)] shows that the two experimentally observed resonance branches of the spin-exchange effect are due to an even-wave CIR and an odd-wave CIR, respectively. Our results are advantageous for the control and description of either the effective spin-exchange interaction or other types of interactions between ultracold atoms in quasi-(1+0)-dimensional systems.
We study atom-atom scattering in quasi-one-dimensional geometries with transverse anisotropy. By assuming an sss-wave pseudopotential of contact interaction, we show that the system would exhibit a single confinement-induced resonance, where the scattering process degenerates to a total reflection as a one-dimensional gas of impenetrable bosons. For a general form of interaction, we present a formal calculation based on the two-channel model and draw the same qualitative conclusion of only one confinement-induced resonance. Our findings are inconsistent with a recent experiment by Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)], where a splitting of confinement-induced resonances has been observed in an anisotropic quasi-one-dimensional quantum gas of Cs atoms.
We theoretically investigate the confinement-induced resonance for quasi-one-dimensional quantum systems under transversely anisotropic confinement, using a two-body sss-wave-scattering model in the zero-energy collision limit. We predict a single resonance for any transverse anisotropy, whose position shows a slight downshift with increasing anisotropy. We compare our prediction with the recent experimental result by Haller et al. [Phys. Rev. Lett. 104, 153203 (2010)], in which two resonances are observed in the presence of transverse anisotropy. The discrepancy between theory and experiment remains to be resolved.