Time evolution of the signatures of coherent wave interference in two-dimensional spin-orbit coupled disordered systems

Spin-orbit coupling (SOC) breaks spin-rotation symmetry while preserving time-reversal symmetry, thus dramatically altering the interference effects for waves propagating in a disordered potential. Increasing SOC transforms the constructive interference between time-reversed processes into destructive interference. The crossover between these two limits is clearly visible in the time evolution of coherent backscattering (CBS) [M.K. and K.S., Phys. Rev. A 109, 033303 (2024)]. Moreover, for stronger disorder, the time evolution of the CBS width can be used to detect the Anderson transition [E. Arabahmadi et al., Phys. Rev. Res. 6, L012021 (2024)]. We investigate, both numerically and analytically, the time evolution of an initial plane-wave state as it is subject to elastic scattering in a two-dimensional disordered system with SOC. We track the time evolution of the CBS width in the diffusive regime and obtain the important time, energy, and momentum scales that govern the competition between constructive and destructive interference. This time evolution is expected to be accessible in cold atom experiments.