Pseudopotentials for Two-dimentional Ultracold Scattering in the Presence of Synthetic Spin-orbit-coupling

TL;DR

This paper develops a new 2D pseudopotential incorporating Rashba spin-orbit coupling, enabling accurate analytical and numerical scattering calculations in ultracold atomic systems with synthetic SOC.

Contribution

It introduces a novel 2D pseudopotential framework that accounts for spin-orbit coupling effects, improving the accuracy of scattering predictions in ultracold gases.

Findings

The pseudopotential accurately reproduces scattering observables across various energies and SOC strengths.

Comparison with numerical calculations shows perfect agreement, validating the approach.

Differences from free-space pseudopotentials are crucial for correct scattering descriptions.

Abstract

We derive a pseudopotential in two dimensions (2D) with the presence of a 2D Rashba spin-orbit-coupling (SOC), following the same spirit of frame transformation in {[}Phys. Rev. A 95, 020702(R) (2017){]}. The frame transformation correctly describes the non-trivial phase accumulation and partial wave couplings due to the presence of SOC and gives rise to a different pseudopotential than the free-space one, even when the length scale of SOC is significantly larger than the two-body potential range. As an application, we apply our pseudopotential with the Lippmann-Schwinger equation to obtain an analytical scattering matrix. To demonstrate the validity, we compare our results with a numerical scattering calculation of finite-range potential and show perfect agreement over a wide range of scattering energy and SOC strength. Our results also indicate that the differences between our pseudopotential and the original free-space pseudopotential are essential to reproduce scattering observables correctly.