  We propose an implementation for quantum information processing based on
coherent manipulations of nuclear spins I=3/2 in GaAs semiconductors. We
describe theoretically an NMR method which involves multiphoton transitions and
which exploits the non-equidistance of nuclear spin levels due to quadrupolar
splittings. Starting from known spin anisotropies we derive effective
Hamiltonians in a generalized rotating frame, valid for arbitrary I, which
allow us to describe the non-perturbative time evolution of spin states
generated by magnetic rf fields. We identify an experimentally accessible
regime where multiphoton Rabi oscillations are observable. In the nonlinear
regime, we find Berry phase interference effects.
