Phase-space curvature in spin-orbit-coupled ultracold atomic systems

Abstract

We consider a system with spin-orbit coupling and derive equations of motion which include the effects of Berry curvatures. We apply these equations to investigate the dynamics of particles with equal Rashba-Dresselhaus spin-orbit coupling in one dimension. In our derivation, the adiabatic transformation is performed first and leads to quantum Heisenberg equations of motion for momentum and position operators. These equations explicitly contain position-space, momentum-space, and phase-space Berry curvature terms. Subsequently, we perform the semiclassical approximation, and obtain the semiclassical equations of motion. Taking the low-Berry-curvature limit results in equations that can be directly compared to previous results for the motion of wavepackets. Finally, we show that in the semiclassical regime, the effective mass of the equal Rashba-Dresselhaus spin-orbit coupled system can be viewed as a direct effect of the phase-space Berry curvature.

Spin Hall mode in a trapped thermal Rashba gas

“…Note that in this strong SOC regime, center-of-mass oscillations are qualitatively different from the dipole mode in the absence of SOC. In particular, here the center-of-mass position oscillates around the initial position x 0 and not the bottom of the trap [45] which is ultimately due to the physical momentum being substantially different from the canonical momentum [57]. Note further that the amplitude of the spin-dipole response is only one quarter of that of centerof-mass oscillations.…”