From Disordered Quantum Walk to Physics of Off-diagonal Disorder

Systems with purely off-diagonal disorder have peculiar features such as the localization-delocalization transition and long-range correlations in their wavefunctions. To motivate possible experimental studies of the physics of off-diagonal disorder, we study in detail disordered discrete-time quantum walk in a finite chain, where the diagonal disorder can be set to zero by construction. Starting from a transfer matrix approach, we show, both theoretically and computationally, that the dynamics of the quantum walk with disorder manifests all the main features of off-diagonal disorder. We also propose how to prepare a remarkable delocalized zero-mode from a localized and easy-to-prepare initial state using an adiabatic protocol that increases the disorder strength slowly. Numerical experiments are also performed with encouraging results.