Anderson localization and Mott insulator phase in the time domain

TL;DR

This paper demonstrates that phenomena like Anderson localization and Mott insulator phases, traditionally observed in space, can also manifest in the time domain using periodically driven quantum systems, revealing new temporal crystal-like behaviors.

Contribution

It introduces the concept of realizing solid state phenomena such as Anderson localization and Mott insulators in the time domain through driven quantum systems, a novel perspective in condensed matter physics.

Findings

Wave-packets localized on classical trajectories lead to Anderson localization in time.

Disorder in time induces Anderson localization effects.

Stationary states can be Bose-Einstein condensates or Fock states depending on interactions.

Abstract

Particles in space periodic potentials constitute standard models for investigation of crystalline phenomena in solid state physics. Time periodicity of periodically driven systems is a close analogue of space periodicity of solid state crystals. There is an intriguing question if solid state phenomena can be observed in the time domain. Here we show that wave-packets localized on resonant classical trajectories of periodically driven systems are ideal elements to realize Anderson localization or Mott insulator phase in the time domain. Uniform superpositions of the wave-packets form stationary states of a periodically driven particle. However, an additional perturbation that fluctuates in time results in disorder in time and Anderson localization effects emerge. Switching to many-particle systems we observe that depending on how strong particle interactions are, stationary states can be Bose-Einstein condensates or single Fock states where definite numbers of particles occupy the periodically evolving wave-packets. Our study shows that non-trivial crystal-like phenomena can be observed in the time domain.