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.

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.