Steering random walks with kicked ultracold atoms

A kicking sequence of the atom opticskicked rotor at quantum resonance can be interpreted as a quantum random walkin momentumspace. We show how to steer such a random walkby applying a random sequenceof intensities and phases of the kicking lattice chosen according to a probability distribution. This distribution converts on average into the final momentumdistribution of the kicked atoms. In particular, it is shown that a power-lawdistribution for the kicking strengths results in a L\'evy walk in momentumspace and in a power-lawwith the same exponent in the averaged momentumdistribution. Furthermore, we investigate the stability of our predictions in the context of a realistic experiment with Bose-Einstein condensates.