Anderson localization in the time domain

TL;DR

This paper demonstrates that temporally disordered potentials can induce Anderson localization in the time domain, leading to localized quantum wave-packets in contrast with classical delocalization, exemplifying a time crystal phenomenon.

Contribution

It introduces the concept of Anderson localization in the time domain through one-dimensional models with temporally disordered potentials, highlighting a novel form of time crystal behavior.

Findings

Quantum wave-packets become localized in time due to disorder.

Classical dynamics remain fully delocalized despite temporal disorder.

The phenomenon exemplifies a new type of time crystal behavior.

Abstract

In analogy with usual Anderson localization taking place in time-independent disordered quantum systems where the disorder acts in configuration space, systems exposed to temporally disordered potentials can display Anderson localization in the time domain. We demonstrate this phenomenon with one-dimensional examples where a temporally disordered potential induces localization during the quantum evolution of wave-packets, in contrast with a fully delocalized classical dynamics. This is an example of a time crystal phenomenon, i.e., a crystalline behavior in the time domain.