Spectral magnetization ratchets with discrete-time quantum walks

Abstract

© 2020 American Physical Society. We predict and theoretically study in detail the ratchet effect for the spectral magnetization of periodic discrete-time quantum walks (DTQWs)-a repetition of a sequence of m different DTQWs. These generalized DTQWs are achieved by varying the corresponding coin operator parameters periodically with discrete time. We consider periods m = 1, 2, and 3. The dynamics of m-periodic DTQWs is characterized by a two-band dispersion relation omega((m))(+/-)(k), where k is the wave vector. We identify a generalized parity symmetry of m-periodic DTQWs. The symmetry can be broken for m = 2 and 3 by proper choices of the coin operator parameters. The obtained symmetry breaking results in a ratchet effect, i.e., the appearance of a nonzero spectral magnetization M-s(omega). This ratchet effect can be observed in the framework of continuous quantum measurements of a time-dependent correlation function of periodic DTQWs