Coherent wave propagation in spin-orbit coupled disordered systems

Interaction-tunable cold atomic gases provide an ideal platform for simulating coherent propagation in disordered systems that permits the direct monitoring of the time evolution of particle motion, e.g. the observation of coherent backscattering in a random potential created by a laser speckle (F. Jendrzejewski et al (2012), PRL 109, 195302), which is challenging in solid state experiments. We investigate the time evolution of the momentum-space particle density distribution in disordered systems with spin-orbit coupling (SOC). The importance of SOC is that it breaks spin rotation symmetry while preserving time reversal symmetry, with a dramatic effect on the interference between time reversed processes, changing it from constructive to destructive. As an initial step in investigating time-dependent momentum signatures in SOC systems, we performed analytic and numerical calculations using a solid-state model with an uncorrelated random potential. The analytic calculation is non-perturbative in SOC strength and perturbative in disorder, using the Diffuson and Cooperon. We explore the crossover from weak to strong SOC and the corresponding crossover from D'yakonov-Perel' to Elliot-Yafet like spin relaxation. Synthetic SOC in cold atoms has the potential to confirm our results.