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We study the dynamics of a quantum walker simultaneously subjected totime-independent and -dependent phases. Such dynamics emulates a chargedquantum particle in a lattice subjected to a superposition of static andharmonic electric fields. With proper settings, we investigate the possibilityto induce Bloch-like super-oscillations, resulting from a close tuning of thefrequency of the harmonic phase $\omega$ and that associated with the regularBloch-like oscillations $\omega_B$ . By exploring the frequency spectra of thewavepacket centroid, we are able to distinguish the regimes on which regularand super-Bloch oscillations are predominant. Furthermore, we show that underexact resonant conditions $\omega=\omega_B$ unidirectional motion isestablished with the wavepacket average velocity being a function of thequantum walk coin operator parameter, the relative strengths of the static andharmonic terms, as well as the own phase of the harmonic phase. We show thatthe average drift velocity can be well described within a continuous-timeanalogous model.

Bloch-like super-oscillations and unidirectional motion of phase driven quantum walkers