Scattering and Bound States of Two Heteronuclear Ultracold Atoms in a Quasi-Two-Dimensional Confinement

• URL: http://arxiv.org/abs/2606.02987v1
• Date: Tue, 02 Jun 2026 00:45:14 GMT
• Title: Scattering and Bound States of Two Heteronuclear Ultracold Atoms in a Quasi-Two-Dimensional Confinement
• Abstract summary: We solve the two-body problem of ultracold heteronuclear atoms in a quasi-two-dimensional (quasi-2D) geometry.<n>Multiple 2D scattering resonances can be induced by the coupling between the longitudinal CoM and relative motion.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 ($z$-) 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 $a_{\rm 2D}$, the 2D effective range parameter $R_{\rm 2D}$, and the bound-state energies, as functions of the $s$-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, $a_{\rm 2D}$ varies rapidly with the 3D scattering parameters, while $R_{\rm 2D}$ 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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