From Disordered Quantum Walk to Physics of Off-diagonal Disorder

Systems with purely off-diagonal disorder may have peculiar features such as the localization-delocalization transition and long-range correlations in their wave functions. To motivate possible experimental studies of the physics of off-diagonal disorder (e.g., in systems with random nearest-neighbor hopping), we study in detail disordered discrete-time quantum walk in a finite chain. 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 systems with off-diagonal disorder. We also propose how to prepare a remarkable delocalized zero mode from a localized and easy-to-prepare initial zero mode using an adiabatic protocol that changes the disorder strength slowly. Numerical experiments are also performed with encouraging results.