Renormalization of interactions of ultracold atoms in simulated Rashba gauge fields

TL;DR

This paper investigates how interactions in ultracold atoms with Rashba spin-orbit coupling can be renormalized, revealing the ultraviolet and infrared behaviors and their implications for effective interactions.

Contribution

It provides a detailed renormalization analysis of interactions in Rashba-coupled ultracold atoms, including the relation to scattering lengths and the impact of spin-orbit coupling.

Findings

Ultraviolet divergences are renormalized using low-energy scattering lengths.

Infrared divergences cause the effective interaction to vanish at zero center-of-mass momentum.

The study clarifies the connection between mean-field interactions and physical scattering parameters.

Abstract

Interactions of ultracold atoms with Rashba spin-orbit coupling, currently being studied with simulated (artificial) gauge fields, have nontrivial ultraviolet and infrared behavior. Examining the ultraviolet structure of the Bethe-Salpeter equation, we show that the linear ultraviolet divergence in the bare interaction can be renormalized as usual in terms of low-energy scattering lengths, and that for both bosons and fermions ultraviolet logarithmic divergences are absent. Calculating the leading order effective interaction with full dependence on the spin-orbit coupling strength and the center-of-mass momentum of the colliding pair, we elucidate the relation between mean-field interactions and physical three-dimensional scattering lengths. As a consequence of infrared logarithmic divergences in the two-particle propagator, the effective interaction vanishes as the center-of-mass momentum approaches zero.