  We present an approach to induce localization of a Bose-Einstein condensate
in a one-dimensional lattice under the influence of unitary quantum walk
evolution using disordered quantum coin operation. We introduce a discrete-time
quantum walk model in which the interference effect is modified to diffuse or
strongly localize the probability distribution of the particle by assigning a
different set of coin parameters picked randomly for each step of the walk,
respectively. Spatial localization of the particle/state is explained by
comparing the variance of the probability distribution of the quantum walk in
position space using disordered coin operation to that of the walk using an
identical coin operation for each step. Due to the high degree of control over
quantum coin operation and most of the system parameters, ultracold atoms in an
optical lattice offer opportunities to implement a disordered quantum walk that
is unitary and induces localization. Here we present a scheme to use a
Bose-Einstein condensate that can be evolved to the superposition of its
internal states in an optical lattice and control the dynamics of atoms to
observe localization. This approach can be adopted to any other physical system
in which controlled disordered quantum walk can be implemented.
