Quantum random walks using quantum accelerator modes
  We discuss the use of high-order quantum accelerator modes to achieve an atom optical realization of a biased quantum random walk. We first discuss how one can create co-existent quantum accelerator modes, and hence how momentum transfer that depends on the atoms' internal state can be achieved. When combined with microwave driving of the transition between the states, a new type of atomic beam splitter results. This permits the realization of a biased quantum random walk through quantum accelerator modes. 
Z.-Y Ma, K. Burnett, M. B. d'Arcy, S. A. Gardiner