Quantum Spin Dynamics in a Normal Bose Gas with Spin-orbit Coupling

TL;DR

This paper analyzes the spin dynamics of a two-component Bose gas with spin-orbit coupling, deriving hydrodynamic equations and providing analytic solutions for spin behavior in different regimes, with potential experimental observation.

Contribution

It introduces coupled hydrodynamic equations for spin and density in a Bose gas with spin-orbit coupling and provides analytic solutions for spin helix dynamics in quasi-one-dimensional systems.

Findings

Transverse spin decays parabolically and exponentially in adiabatic regime.

Transverse spin oscillates in diabatic regime similar to LC circuit.

Spin dynamics occur on millisecond to second timescales in realistic experiments.

Abstract

In this Letter, we investigate spin dynamics of a two-component Bose gas with spin-orbit coupling realised in cold atom experiments. We derive coupled hydrodynamic equations for number and spin densities as well as their associated currents. Specialising to quasi-one-dimensional situation, we obtain analytic solutions of the spin helix structure and its dynamics in both adiabatic and diabatic regimes. In the adiabatic regime, the transverse spin decays parabolically in the short-time limit and exponentially in the long time limit, depending on initial polarisation. In contrast, in the diabatic regime, transverse spin density and current oscillate in a way similar to the charge-current oscillation in an undamped LC circuit. The effects of Rabi coupling on the short-time spin dynamics is also discussed. Finally, using realistic experimental parameters for $^{87}$Rb, we show that the time scales for spin dynamics is of order of milliseconds to a few seconds and can be observed experimentally.