Anderson localization of a one-dimensional quantum walker

We study the evolution of a system performing a one-dimensional quantum walk in the presence of static phase disorder. The same model also describes the propagation of classical light pulses in photonic mesh lattices. We study the interplay between the coupling (i.e. the bias of the “quantum coin”) and disorder. We provide an exact analytical expression for the localization length for two limiting cases of strong and weak phase disorder. In all the cases of interest we supply numerical simulations for participation ratio, Lyapunov exponent and the return probability as functions of the coupling parameter.