  We study the localization of a noninteracting and weakly interacting
Bose-Einstein condensate with spin-orbit coupling loaded in a quasiperiodic
bichromatic optical lattice potential using the numerical solution and
variational approximation of a binary mean-field Gross-Pitaevskii equation with
two pseudo-spin components. We confirm the existence of the stationary
localized states in the presence of the spin-orbit and Rabi couplings for an
equal distribution of atoms in the two components. We find that the interaction
between the spin-orbit and Rabi couplings favors the localization or
delocalization of the BEC depending on the the phase difference between the
components. We also studied the oscillation dynamics of the localized states
for an initial population imbalance between the two components.
