Self-interaction induced phase modulation for directed current, energy diffusion and quantum scrambling in a Floquet ratchet system

TL;DR

This paper explores how phase modulation in a Floquet ratchet system influences directed current, energy diffusion, and quantum scrambling, revealing control mechanisms via self-interaction and potential applications in quantum control.

Contribution

It demonstrates that phase modulation induced by self-interaction dominates energy growth and quantum scrambling, providing new insights into controlling quantum dynamics in Floquet systems.

Findings

Directed current controlled by ratchet phase, independent of self-interaction.

Self-interaction phase modulation dominates energy and OTOC growth.

Disorder suppresses current and induces dynamical localization.

Abstract

We investigate the wavepacket dynamics in an interacting Floquet system described by the Gross-Pitaevskii equation with a ratchet potential. Under quantum resonance conditions, we thoroughly examine the exotic dynamics of directed current, mean energy, and quantum scrambling, based on the exact expression of a time-evolving wavepacket. The directed current is controlled by the phase of the ratchet potential and remains independent of the self-interaction strength. Interestingly, the phase modulation induced by self-interaction dominates the quadratic growth of both mean energy and Out-of-Time-Ordered Correlators (OTOCs). In the quantum nonresonance condition, the disorder in momentum space, induced by the pseudorandom feature of the free evolution operator, suppresses the directed current at all times. Meanwhile, the disorder also leads to the dynamical localization of the mean energy and the freezing of quantum scrambling for initially finite time interval. The dynamical localization can be effectively manipulated by the phase, with underlying physics rooted in the different quasi-eigenenergy spectrum modulated by ratchet potential. Both the mean energy and OTOCs exponentially increase after long time evolution, which is governed by the classically chaotic dynamics dependent on the self-interaction. Possible applications of our findings on quantum control are discussed.