Simplified contact pseudopotential for anisotropic interactions of polarized particles under harmonic confinement

TL;DR

This paper introduces a simplified contact pseudopotential model for anisotropic interactions of polarized particles under harmonic confinement, making it more practical for experimental and theoretical studies of polar molecules.

Contribution

The authors develop a simplified, wavefunction-smoothness-based pseudopotential that depends on the scattering K-matrix and accounts for anisotropic interactions in confined polarized particles.

Findings

The pseudopotential explicitly incorporates anisotropic effects via derivatives aligned with the polarizing field.

It is expressed as a sum over coupled partial waves, reflecting the anisotropic scattering process.

The model is suitable for practical calculations involving smooth wavefunctions in harmonic traps.

Abstract

Motivated by the recent progress in cooling and trapping polar molecules, we present a simplified version of the rigorous contact pseudopotential for anisotropically-interacting polarized particles [A. Derevianko, Phys. Rev. A 67, 033607 (2003); Phys. Rev. A 72, 039901(E) (2005)]. The simplifications are carried out for a practically important case of harmonically confined particles described by sufficiently smooth wavefunctions. The resulting contact pseudo-potential depends on the K-matrix of the underlying scattering process and is represented as a sum over pairs of partial waves coupled by the collision. The contribution of each pair of the coupled waves (l and l') involves a tensor product of derivatives of orders l and l'. The asymmetry in the derivatives reflects the anisotropy of the original interaction potential: there is a preferential appearance of the derivatives along the polarizing field.