Quantum information processing with large nuclear spins in GaAs semiconductors

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.