Quasiperiodic driving of Anderson localized waves in one dimension

TL;DR

This paper investigates how multi-frequency driving influences Anderson localized waves in a one-dimensional disordered lattice, revealing increased localization length under certain conditions while maintaining localization.

Contribution

It introduces a Floquet-based approach to analyze multi-frequency perturbations and identifies regimes where localization length is significantly enhanced.

Findings

Multi-frequency driving can increase localization length.

Two scaling regimes of weak and strong driving are identified.

Localization length remains finite with a finite number of frequencies.

Abstract

We consider a quantum particle in a one-dimensional disordered lattice with Anderson localization, in the presence of multi-frequency perturbations of the onsite energies. Using the Floquet representation, we transform the eigenvalue problem into a Wannier-Stark basis. Each frequency component contributes either to a single channel or a multi-channel connectivity along the lattice, depending on the control parameters. The single channel regime is essentially equivalent to the undriven case. The multi-channel driving substantially increases the localization length for slow driving, showing two different scaling regimes of weak and strong driving, yet the localization length stays finite for a finite number of frequency components.