Ultracold collisions between spin-orbit-coupled dipoles: General formalism and universality

Abstract

A theoretical study of the low-energy scattering properties of two aligned identical bosonic and fermionic dipoles in the presence of isotropic spin-orbit coupling (SOC) is presented. A general treatment of particles with arbitrary (pseudo-) spin is given in the framework of multi-channel scattering. At ultracold temperatures and away from shape resonances or closed-channel dominated resonances, the cross-section can be well described within the Born approximation to within corrections due to the s-wave scattering. We compare our findings with numerical calculations and find excellent agreement.

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

“…The analytical results shows a good agreement with a full numerical scatteirng calculation with the representation of SOC, using a similar procedure as Ref. [38]. The technical details are shown in the Supplemental Material.…”

“…We carry out a numerical calculation with finite range Lennard-Jones potentials U (ρ) to verify our analytical results, using a similar procedure as Ref. [38]. We expand the rescaled Hamiltonian h ≡ ρ 1/2 H rel ρ −1/2 with the channel functions that leads to a set of coupled differential equations for u = ρ 1/2 R SO : hu = Eu, where h = h fs + V SO has matrix elements…”

“…Via some numerical investigations, Cui concludes that free-space pseudopotentials, especially for higher partial waves such as p-wave, are not satisfactory. Ever since, several studies have carefully calculated two-body scattering with the presence of 3D [32][33][34][35][36][37][38] or 2D [39,40] SOC, paving the way for designing a pseudopotential model. One particularly enlightening study carried out by Guan and Blume reveals that a frame transformation approach (that we will detail later) can correctly calculate the scattering phase accumulated at short distances modified by SOC [41].…”

“…Following the spirit of Refs. [35][36][37][38]41], we focus on the scattering in the COM frame, where the relative Hamiltonian can be written as…”

Universal scattering phase shift in the presence of spin-orbit coupling

“…Two-body scattering problems in the presence of SO coupling have comprehensively been studied in the past few years [40,[48][49][50][51][52]. However, a unified description of the low-energy behavior of the scattering phase shift is still elusive.…”