title: Anderson localization and Mott insulator phase in the time domain.
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.
authors.affiliation: Instytut Fizyki imienia Mariana Smoluchowskiego, Uniwersytet Jagiellon'ski, ul. Prof. S. Łojasiewicza 11 PL-30-348 Kraków, Poland Mark Kac Complex Systems Research Center, Uniwersytet Jagiellon'ski, ul. Prof. S. Łojasiewicza 11 PL-30-348 Kraków, Poland.
authors.forename: Krzysztof
authors.initials: K
authors.lastname: Sacha