Bloch-like energy oscillations

TL;DR

This paper introduces a new type of periodic energy oscillation in driven quantum systems, mapping them to tilted lattice models and demonstrating the phenomenon through two models, with effects disrupted by disorder.

Contribution

The paper reveals a novel energy oscillation mechanism in driven quantum systems and establishes a mapping to lattice models, providing a new perspective on quantum dynamics.

Findings

Demonstrates energy Bloch oscillations in two models

Shows oscillations break down with disorder

Confirms the mapping to lattice models accurately describes the dynamics

Abstract

We identify a new type of periodic evolution that appears in driven quantum systems. Provided that the instantaneous (adiabatic) energies are equidistant we show how such systems can be mapped to (time-dependent) tilted single-band lattice models. Having established this mapping, the dynamics can be understood in terms of Bloch oscillations in the instantaneous energy basis. In our lattice model the site-localized states are the adiabatic ones, and the Bloch oscillations manifest as a periodic repopulation among these states, or equivalently a periodic change in the system's instantaneous energy. Our predictions are confirmed by considering two different models: a driven harmonic oscillator and a Landau-Zener grid model. Both models indeed show convincing, or even perfect, oscillations. To strengthen the link between our energy Bloch oscillations and the original spatial Bloch oscillations we add a random disorder that breaks the translational invariance of the spectrum. This verifies that the oscillating evolution breaks down and instead turns into a ballistic spreading.