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

TL;DR

This paper explores how phase-driven quantum walks can exhibit Bloch-like super-oscillations and unidirectional motion, revealing conditions for controlled wavepacket dynamics influenced by static and harmonic electric fields.

Contribution

It introduces a novel analysis of quantum walk dynamics under combined static and harmonic phases, demonstrating the emergence of super-oscillations and unidirectional motion under resonant conditions.

Findings

Super-oscillations occur when harmonic and Bloch frequencies are tuned close.

Unidirectional wavepacket motion is achieved at resonance $\,\omega=\omega_B$.

Average drift velocity depends on coin parameters and phase settings.

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 super-oscillations, resulting from a close tuning of the frequency of the harmonic phase $\omega$ and that associated with the regular Bloch-like oscillations $\omega_B$ . By exploring the frequency spectra of the wavepacket 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 $\omega=\omega_B$ unidirectional motion is established with the wavepacket average velocity being a function of the quantum walk coin operator parameter, the relative strengths of the static and harmonic terms, as well as the own phase of the harmonic phase. We show that the average drift velocity can be well described within a continuous-time analogous model.