# Beliaev Damping in Spin-$\frac{1}{2}$ Interacting Bosons with Spin-Orbit Coupling

## TL;DR

This paper analytically investigates Beliaev damping in spin-1/2 bosons with spin-orbit coupling, revealing unique decay features and phase boundary divergences, and connects these to observable dynamic structure factors for experimental validation.

## Contribution

It provides the first analytical calculation of Beliaev damping in spin-orbit coupled bosons, highlighting novel decay behaviors and phase boundary effects due to spin-orbit interactions.

## Key findings

- Beliaev damping rate depends explicitly on spin-density interactions.
- Decay rate diverges at the phase boundary between zero-momentum and plane-wave phases.
- Results are directly accessible through dynamic structure factor measurements.

## Abstract

Beliaev damping provides one of the most important mechanisms for dissipation of quasiparticles through beyond-mean-field effects at zero temperature. Here we present the first analytical result of Beliaev damping in low-energy excitations of spin-$\frac{1}{2}$ interacting bosons with equal Rashba and Dresslhaus spin-orbit couplings. We identify novel features of Beliaev decay rate due to spin-orbit coupling, in particular, it shows explicit dependence on the spin-density interaction and diverges at the interaction-modified phase boundary between the zero-momentum and plane-wave phases. This represents a manifestation of the effect of spin-orbit coupling in the beyond-mean-field regime, which by breaking Galilean invariance couples excitations in the density- and spin-channels. By describing the Beliaev damping in terms of the observable dynamic structure factors, our results allow direct experimental access within current facilities.