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arXiv:1907.07382 · Physical Review A

Confinement-induced resonance with weak background interaction

Ren Zhang, Peng Zhang

Published Dec 4, 2019• 4 citations
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Abstract

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 $s$-wave scattering length ${a}_{s}$ of these two atoms is much smaller than the characteristic lengths (CLs) of the confinements, for either ${a}_{s}>0$ or ${a}_{s}<0$. This is quite different from the usual CIRs which occur only when ${a}_{s}$ 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 ${a}_{s}$), e.g., the realization of ultracold gases with strong spin-dependent interaction at zero magnetic fields.

DOI
10.1103/physreva.100.063607

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We studied the scattering problem of two distinguishable atoms with unequal mass, where one atom (atom \ensuremathα\ensuremath{\alpha}\ensuremathα) is trapped in a quasi-one-dimensional (quasi-1D) tube and the other one (atom \ensuremathβ\ensuremath{\beta}\ensuremathβ) is localized by a 3D harmonic trap. We show that in such a system if atom \ensuremathα\ensuremath{\alpha}\ensuremathα is much heavier than \ensuremathβ\ensuremath{\beta}\ensuremathβ, 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.
We observe d-wave confinement-induced resonances (CIRs) of bosonic scattering in tightly confining harmonic waveguides. It is shown that the d-wave CIR emerges in the quasi-1D regime as an imprint of a 3D d-wave shape resonance. A scaling relation for the position of the d-wave CIR is provided. By changing the trap frequency, ultracold scattering can be continuously tuned from s-wave to d-wave CIRs. The effect can be utilized for the realization of ultracold atomic gases interacting via higher partial waves and opens a novel possibility for studying strongly correlated atomic systems beyond s-wave physics. PACS numbers: 03.75.Be, 34.10.+x, 34.50.-s
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.
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We solve the two-body problem of ultracold heteronuclear atoms in a quasi-two-dimensional (quasi-2D) geometry. The quasi-2D confinement is realized by a harmonic trap along the longitudinal (zzz-) direction, with different trap frequencies for the two atoms, as in many current experiments on ultracold heteronuclear gases. As a consequence, the longitudinal center-of-mass (CoM) motion is coupled to the relative motion, which significantly complicates the two-body problem. We solve this problem exactly and derive the 2D scattering length a2Da_{\rm 2D}a2D​, the 2D effective range parameter R2DR_{\rm 2D}R2D​, and the bound-state energies, as functions of the sss-wave scattering length and effective range of the two atoms in free three-dimensional (3D) space. We show that multiple 2D scattering resonances can be induced by the coupling between the longitudinal CoM and relative motion. Around these resonances, a2Da_{\rm 2D}a2D​ varies rapidly with the 3D scattering parameters, while R2DR_{\rm 2D}R2D​ is strongly enhanced. Since the effective pairwise interaction in quasi-2D ultracold gases is determined by i.e., the two-body scattering amplitudes and bound-state energies, our results can be used for manipulating the effective 2D interatomic interaction in quasi-2D ultracold heteronuclear gases by tuning the confinement frequencies and the 3D scattering parameters.
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We study quasi-1D effective scattering and bound states for two atoms confined individually by {\it separated} transverse traps. With equal trapping frequency for two atoms, we find that tuning the separation can induce {\it double} 1D scattering resonances when the ratio between the confinement length and s-wave scattering length is within (0.791,1.46](0.791,1.46](0.791,1.46]. The sign and amplitude of resonance width show nontrivial dependences on the resonance position. The universal properties of a many-body system at double resonances are manifested by studying the interaction effect of a localized impurity immersed in a Fermi sea of light atoms.