Exact Two-Body Solutions and Quantum Defect Theory of Polar Molecular Gases with Van der Waals Potentials

• URL: http://arxiv.org/abs/2202.08694v2
• Date: Thu, 24 Feb 2022 08:15:14 GMT
• Title: Exact Two-Body Solutions and Quantum Defect Theory of Polar Molecular Gases with Van der Waals Potentials
• Authors: Jianwen Jie, Ran Qi
• Abstract summary: We provide the two-body exact solutions for the 2D and 3D Schr"odinger equation with isotropic Van der Waals potentials. We then apply quantum defect theory to study the scattering properties and bound states of two ultracold polar molecules confined in quasi-2D and 3D geometries.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In a recent experiment [Matsuda et al, Science 370, 1324 (2020)], a quasi two-dimensional (2D), long-lived and strongly interacting diatomic polar molecular gas was successfully prepared via controllable electric field technique. Surprisingly, the effective repulsive and attractive Van der Waals interactions of two molecules would emerge when scanning the strength of the electric fields. Those results were also generalized to the three-dimensional (3D) case in a later experiment [J. Li et al, Nature Physics 17, 1144 (2021)]. Motivated by these experiments, in this paper we provide the two-body exact solutions for the 2D and 3D Schr\"{o}dinger equation with isotropic Van der Waals potentials ($\pm1/r^{6}$). Furthermore, base on these exact solutions, we build the analytical quantum defect theory (QDT) for quasi-2D and 3D geometries, and then apply QDT to study the scattering properties and bound states of two ultracold polar molecules confined in quasi-2D and 3D geometries. Interestingly, we find that for the attractive (repulsive) Van der Waals potential cases, the two-body short range potential can be approximated by an square barrier with infinity height (square potential with finite depth) which yields the wide (narrow) and dense (dilute) resonances of the quantum defect parameter. For the quasi-2D attractive case, the scattering resonances of different partial waves can orderly happen which is featured by the phase jumps when varying the scattering energy. The analytical expansions in the low energy limit shows a consistent agreement to the numerical results.

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