Bloch-like superoscillations and unidirectional motion of phase-driven quantum walkers

Abstract

We study the dynamics of a quantum walker simultaneously subjected to time-independent and -dependent phases. Such dynamics emulates a charged quantum particle in a lattice subjected to a superposition of static and harmonic electric fields. With proper settings, we investigate the possibility to induce Bloch-like superoscillations, resulting from a close tuning of the frequency of the harmonic phase $\ensuremath{\omega}$ and that associated with the regular Bloch-like oscillations ${\ensuremath{\omega}}_{B}$. By exploring the frequency spectra of the wave-packet centroid, we are able to distinguish the regimes on which regular and super-Bloch oscillations are predominant. Furthermore, we show that under exact resonant conditions $\ensuremath{\omega}={\ensuremath{\omega}}_{B}$ unidirectional motion is established with the wave-packet average velocity being a function of the quantum coin operator parameter, the relative strengths of the static and harmonic terms, as well as the own phase of the harmonic field. We show that the average drift velocity can be well described within a continuous-time analogous model.