One-Dimensional Anderson Localization in Certain Correlated Random Potentials

@article{Lugan2009OneDimensionalAL,
  title={One-Dimensional Anderson Localization in Certain Correlated Random Potentials},
  author={Pierre Lugan and Alain Aspect and Laurent Sanchez-Palencia and Dominique Delande and Benoit Gr'emaud and Cord Axel Muller and Christian Miniatura},
  journal={Physical Review A},
  year={2009},
  volume={80},
  pages={023605}
}
We study Anderson localization of ultracold atoms in weak, one-dimensional speckle potentials, using perturbation theory beyond Born approximation. We show the existence of a series of sharp crossovers (effective mobility edges) between energy regions where localization lengths differ by orders of magnitude. We also point out that the correction to the Born term explicitly depends on the sign of the potential. Our results are in agreement with numerical calculations in a regime relevant for… 

Figures from this paper

Tailoring Anderson localization by disorder correlations in 1D speckle potentials
We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of
Many-body Anderson localization in one-dimensional systems
We show, using quasi-exact numerical simulations, that Anderson localization in a disordered one-dimensional potential survives in the presence of attractive interaction between particles. The
Localization of a matter wave packet in a disordered potential
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
Anderson Localization for Very Strong Speckle Disorder
We evaluate the localization length of the wave (or Schrödinger) equation in the presence of a disordered speckle potential. This is relevant for experiments on cold atoms in optical speckle
Topological insulator in the presence of spatially correlated disorder
We investigate the effect of spatially correlated disorder on two-dimensional topological insulators and on the quantum spin Hall effect which the helical edge states in these systems give rise to.
Ultracold Bose gases in random potentials: collective excitations and localization effects
In this thesis, we theoretically investigate the localization properties of weakly-interacting Bose gases in the presence of one-dimensional disorder. We focus on three aspects of those disordered
Three-Dimensional Anderson Localization of Ultracold Matter
TLDR
Three-dimensional Anderson localization of noninteracting ultracold matter is observed by allowing a spin-polarized atomic Fermi gas to expand into a disordered potential and a two-component density distribution emerges consisting of an expanding mobile component and a nondiffusing localized component.
Anderson localization of a weakly interacting one dimensional Bose gas
We consider the phase coherent transport of a quasi-one-dimensional beam of Bose-Einstein condensed particles through a disordered potential of length L. Among the possible different types of flow we
Quantum transport of atomic matter waves in anisotropic two-dimensional and three-dimensional disorder
The macroscopic transport properties in a disordered potential, namely diffusion and weak/strong localization, closely depend on the microscopic and statistical properties of the disorder itself.
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 48 REFERENCES
LOCALIZATION AND THE MOBILITY EDGE IN ONE-DIMENSIONAL POTENTIALS WITH CORRELATED DISORDER
We show that a mobility edge exists in 1D random potentials provided specific long-range correlations. Our approach is based on the relation between binary correlator of a site potential and the
Anderson localization and nonlinearity in one-dimensional disordered photonic lattices.
TLDR
An intermediate regime is found in which the ballistic and localized components coexist while diffusive dynamics is absent and evidence is found for a faster transition into localization under nonlinear conditions.
Delocalization phenomena in one-dimensional models with long-range correlated disorder: a perturbative approach
We study the nature of electronic states in one-dimensional continuous models with weak correlated disorder. Using a perturbative approach, we compute the inverse localization length (Lyapunov
Anderson localization of expanding Bose-Einstein condensates in random potentials.
TLDR
It is shown that the expansion of an initially confined interacting 1D Bose-Einstein condensate can exhibit Anderson localization in a weak random potential with correlation length sigma(R) and the localization is exponential.
Anderson localization of a non-interacting Bose–Einstein condensate
TLDR
This work uses a non-interacting Bose–Einstein condensate to study Anderson localization of waves in disordered media and describes the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice.
Transport and Anderson localization in disordered two-dimensional photonic lattices
TLDR
The experimental observation of Anderson localization in a perturbed periodic potential is reported: the transverse localization of light caused by random fluctuations on a two-dimensional photonic lattice, demonstrating how ballistic transport becomes diffusive in the presence of disorder, and that crossover to Anderson localization occurs at a higher level of disorder.
Electron transport in a disordered Luttinger liquid
We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. We demonstrate that the notion of weak localization is
Experimental observation of the Anderson metal-insulator transition with atomic matter waves.
TLDR
An atom-optics quantum-chaotic system, the quasiperiodic kicked rotor, is realized experimentally, which is equivalent to a 3D disordered system that allows us to demonstrate the Anderson metal-insulator transition.
Disorder-induced trapping versus Anderson localization in Bose–Einstein condensates expanding in disordered potentials
We theoretically investigate the localization of an expanding Bose–Einstein condensate (BEC) with repulsive atom–atom interactions in a disordered potential. We focus on the regime where the initial
Experimental study of the transport of coherent interacting matter-waves in a 1D random potential induced by laser speckle
We present a detailed analysis of the 1D expansion of a coherent interacting matterwave (a Bose–Einstein condensate (BEC)) in the presence of disorder. A 1D random potential is created via laser
...
1
2
3
4
5
...