Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2201.07994 · Physical Review A

Localization of matter waves in lattice systems with moving disorder

Chenyue Guo, Wen-Hao Cui, Zi Cai

Published Mar 28, 2023• 7 citations
arXivHTMLPDF

Abstract

We study the localization phenomena in a one-dimensional lattice system with a uniformly moving disordered potential. At a low-moving velocity, we find a sliding localized phase in which the initially localized matter wave adiabatically follows the moving potential without diffusion, thus resulting in an initial state memory in the many-body dynamics. Such an intriguing localized phase distinguishes itself from the standard Anderson localization in two aspects: it is not robust against interaction, but persists in the presence of slowly varying perturbations. Such a sliding localized phase can be understood as a consequence of interference between the wave-packet paths under moving quasiperiodic potentials with various periods that are incommensurate with the lattice constant. The experimental realization and detection are also discussed.

DOI
10.1103/physreva.107.033330

Related papers

Anderson localization and Mott insulator phase in the time domain

Krzysztof Sacha

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.

arXiv:1502.02507•Scientific Reports•Jun 15, 2015•61 citations

Localization of a matter wave packet in a disordered potential

Marie Piraud, Pierre Lugan, Philippe Bouyer +2 more

We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening induced by the disorder. Our approach predicts a behavior of the localized density profile significantly more complex than a simple exponential decay. These results are confirmed by large-scale and long-time numerical calculations. They shed new light on recent experiments with ultracold atoms and may impact their analysis.

arXiv:1101.4467•Physical Review A•Mar 4, 2011•53 citations

Effects of interaction on the diffusion of atomic matter waves in one-dimensional quasiperiodic potentials

Marco Larcher, F. Dalfovo, Michele Modugno

We study the behavior of an ultracold atomic gas of bosons in a bichromatic lattice, where the weaker lattice is used as a source of disorder. We numerically solve a discretized mean-field equation, which generalizes the one-dimensional Aubry-Andr\`e model for particles in a quasiperiodic potential by including the interaction between atoms. We compare the results for commensurate and incommensurate lattices. We investigate the role of the initial shape of the wave packet as well as the interplay between two competing effects of the interaction, namely, self-trapping and delocalization. Our calculations show that, if the condensate initially occupies a single lattice site, the dynamics of the interacting gas is dominated by self-trapping in a wide range of parameters even for weak interaction. Conversely, if the diffusion starts from a Gaussian wave packet, self-trapping is significantly suppressed and the destruction of localization by interaction is more easily observable.

arXiv:0909.1714•Physical Review A•Nov 9, 2009•100 citations

Direct observation of Anderson localization of ultracold atoms in a quasiperiodic lattice

Wenbo Yan, Yuqing Li, Hongxing Zhao +7 more

Ultracold atoms in quasiperiodic lattices offer a versatile platform for studying many intriguingly disorder-driven phenomena. Here we study the quantum transport of noninteracting ultracold 133 Cs atoms in a one-dimensional quasiperiodic momentum lattice, which is formed by using the laser-coupled momentum states as synthetic dimensions. Through measurements of the site-resolved density distribution of atoms in the synthetic quasiperiodic lattice, we directly observe the transition from the atomic diffusive transport to Anderson localization in the initial injection site with increasing strength of the quasiperiodic modulation. We show the dependence of momentum width characterizing the atomic expansion degree on the quasiperiodic modulation strength, and our observation is in good agreement with the theoretical calculation. Our work provides significant insights for understanding the quantum spreading in disordered systems.

Optics Continuum•Sep 11, 2023•4 citations

Matter-Wave Localization in Disordered Cold Atom Lattices

Uri Gavish, Yvan Castin

We propose to observe Anderson localization of ultracold atoms in the presence of a random potential made of atoms of another species or spin state and trapped at the nodes of an optical lattice, with a filling factor less than unity. Such systems enable a nearly perfect experimental control of the disorder, while the possibility of modeling the scattering potentials by a set of pointlike ones allows an exact theoretical analysis. This is illustrated by a detailed analysis of the one-dimensional case.

arXiv:cond-mat/0412671•Physical Review Letters•Jul 5, 2005•197 citations

ANDERSON LOCALIZATION OF A NON-INTERACTING BOSE-EINSTEIN CONDENSATE

G. Roati, Chiara D’Errico, L. Fallani +6 more

Anderson localization of waves in disordered media was originally predicted[1] fifty years ago, in the context of transport of electrons in crystals[2]. The phenomenon is much more general[3] and has been observed in a variety of systems, including light waves[4, 5]. However, Anderson localization has not been observed directly for matter waves. Owing to the high degree of control over most of the system parameters (in particular the interaction strength), ultracold atoms offer opportunities for the study of disorder-induced localization[6]. Here we use a non-interacting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a one-dimensional quasi-periodic lattice - a system that features a crossover between extended and exponentially localized states, as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated through investigations of the transport properties and spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. This controllable system may be used to investigate the interplay of disorder and interaction (ref. 7 and references therein), and to explore exotic quantum phases[8, 9].

International Conference on Atomic Physics (ICAP)•Mar 1, 2009•62 citations
We study the localization phenomena in a one-dimensional lattice system with a uniformly moving disordered potential. At a low-moving velocity, we find a sliding localized phase in which the initially localized matter wave adiabatically follows the moving potential without diffusion, thus resulting in an initial state memory in the many-body dynamics. Such an intriguing localized phase distinguishes itself from the standard Anderson localization in two aspects: it is not robust against interaction, but persists in the presence of slowly varying perturbations. Such a sliding localized phase can be understood as a consequence of interference between the wave-packet paths under moving quasiperiodic potentials with various periods that are incommensurate with the lattice constant. The experimental realization and detection are also discussed.
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.
We theoretically study the Anderson localization of a matter wave packet in a one-dimensional disordered potential. We develop an analytical model which includes the initial phase-space density of the matter wave and the spectral broadening induced by the disorder. Our approach predicts a behavior of the localized density profile significantly more complex than a simple exponential decay. These results are confirmed by large-scale and long-time numerical calculations. They shed new light on recent experiments with ultracold atoms and may impact their analysis.
We study the behavior of an ultracold atomic gas of bosons in a bichromatic lattice, where the weaker lattice is used as a source of disorder. We numerically solve a discretized mean-field equation, which generalizes the one-dimensional Aubry-Andr\`e model for particles in a quasiperiodic potential by including the interaction between atoms. We compare the results for commensurate and incommensurate lattices. We investigate the role of the initial shape of the wave packet as well as the interplay between two competing effects of the interaction, namely, self-trapping and delocalization. Our calculations show that, if the condensate initially occupies a single lattice site, the dynamics of the interacting gas is dominated by self-trapping in a wide range of parameters even for weak interaction. Conversely, if the diffusion starts from a Gaussian wave packet, self-trapping is significantly suppressed and the destruction of localization by interaction is more easily observable.
Ultracold atoms in quasiperiodic lattices offer a versatile platform for studying many intriguingly disorder-driven phenomena. Here we study the quantum transport of noninteracting ultracold 133 Cs atoms in a one-dimensional quasiperiodic momentum lattice, which is formed by using the laser-coupled momentum states as synthetic dimensions. Through measurements of the site-resolved density distribution of atoms in the synthetic quasiperiodic lattice, we directly observe the transition from the atomic diffusive transport to Anderson localization in the initial injection site with increasing strength of the quasiperiodic modulation. We show the dependence of momentum width characterizing the atomic expansion degree on the quasiperiodic modulation strength, and our observation is in good agreement with the theoretical calculation. Our work provides significant insights for understanding the quantum spreading in disordered systems.
We propose to observe Anderson localization of ultracold atoms in the presence of a random potential made of atoms of another species or spin state and trapped at the nodes of an optical lattice, with a filling factor less than unity. Such systems enable a nearly perfect experimental control of the disorder, while the possibility of modeling the scattering potentials by a set of pointlike ones allows an exact theoretical analysis. This is illustrated by a detailed analysis of the one-dimensional case.
Anderson localization of waves in disordered media was originally predicted[1] fifty years ago, in the context of transport of electrons in crystals[2]. The phenomenon is much more general[3] and has been observed in a variety of systems, including light waves[4, 5]. However, Anderson localization has not been observed directly for matter waves. Owing to the high degree of control over most of the system parameters (in particular the interaction strength), ultracold atoms offer opportunities for the study of disorder-induced localization[6]. Here we use a non-interacting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a one-dimensional quasi-periodic lattice - a system that features a crossover between extended and exponentially localized states, as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated through investigations of the transport properties and spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. This controllable system may be used to investigate the interplay of disorder and interaction (ref. 7 and references therein), and to explore exotic quantum phases[8, 9].