  Anderson localization is a single particle localization phenomena in
disordered media that is accompanied by an absence of diffusion. Spin-orbit
coupling (SOC) describes an interaction between a particle's spin and its
momentum that directly affects its energy dispersion, for example creating
dispersion relations with gaps and multiple local minima. We show theoretically
that combining one-dimensional spin-orbit coupling with a transverse Zeeman
field suppresses the effects of disorder, thereby increasing the localization
length and conductivity. This increase results from a suppression of back
scattering between states in the gap of the SOC dispersion relation. Here, we
focus specifically on the interplay of disorder from an optical speckle
potential and SOC generated by two-photon Raman processes in quasi-1D
Bose-Einstein condensates. We first describe back-scattering using a Fermi's
golden rule approach, and then numerically confirm this picture by solving the
time-dependent 1D Gross Pitaevskii equation for a weakly interacting
Bose-Einstein condensate with SOC and disorder. We find that on the 10's of
millisecond time scale of typical cold atom experiments moving in harmonic
traps, initial states with momentum in the zero-momentum SOC gap evolve with
negligible back-scattering, while without SOC these same states rapidly
localize.
