# 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…

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## References

SHOWING 1-10 OF 48 REFERENCES

LOCALIZATION AND THE MOBILITY EDGE IN ONE-DIMENSIONAL POTENTIALS WITH CORRELATED DISORDER

- Physics
- 1999

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.

- PhysicsPhysical review letters
- 2008

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

- Physics
- 2002

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.

- Physics, MathematicsPhysical review letters
- 2007

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

- PhysicsNature
- 2008

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

- PhysicsNature
- 2007

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

- Physics
- 2007

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.

- PhysicsPhysical review letters
- 2008

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

- Physics
- 2008

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

- Physics
- 2006

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…