From Anderson to anomalous localization in cold atomic gases with effective spin-orbit coupling

We study the dynamics of a spin-orbit (SO)-coupled Schrodinger particle with two internal degrees of freedom moving in a one-dimensional random potential. Numerical calculation of the density of states reveals the emergence of a Dyson-like singularity at zero energy when the system approaches the quasi-relativistic limit of the random-mass Dirac model for large SO coupling. Simulations of the expansion of an initially localized wave-packet show a crossover from an exponential (Anderson) localization to an anomalous power-law behavior reminiscent of the zero-energy (mid-gap) state of the random-mass Dirac model. We discuss conditions under which the crossover is observable in an experiment and derive the zero-energy state, thus proving its existence under proper conditions. Finally we describe a possible experimental realization using an ensemble of cold Rb-87-atoms interacting with external control lasers and speckle fields.