# Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder

## Abstract

We study the Anderson localization of Bogoliubov quasiparticles (elementary many-body excitations) in a weakly interacting Bose gas of chemical potential {mu} subjected to a disordered potential V. We introduce a general mapping (valid for weak inhomogeneous potentials in any dimension) of the Bogoliubov-de Gennes equations onto a single-particle Schroedinger-like equation with an effective potential. For disordered potentials, the Schroedinger-like equation accounts for the scattering and localization properties of the Bogoliubov quasiparticles. We derive analytically the localization lengths for correlated disordered potentials in the one-dimensional geometry. Our approach relies on a perturbative expansion in V/{mu}, which we develop up to third order, and we discuss the impact of the various perturbation orders. Our predictions are shown to be in very good agreement with direct numerical calculations. We identify different localization regimes: For low energy, the effective disordered potential exhibits a strong screening by the quasicondensate density background, and localization is suppressed. For high-energy excitations, the effective disordered potential reduces to the bare disordered potential, and the localization properties of quasiparticles are the same as for free particles. The maximum of localization is found at intermediate energy when the quasicondensate healing length is of the order of the disorder correlation length. Possiblemore »

- Authors:

- Laboratoire Charles Fabry de l'Institut d'Optique, CNRS and Univ. Paris-Sud, Campus Polytechnique, RD 128, F-91127 Palaiseau cedex (France)
- (Germany)

- Publication Date:

- OSTI Identifier:
- 22058745

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. A

- Additional Journal Information:
- Journal Volume: 84; Journal Issue: 1; Other Information: (c) 2011 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; BOSE-EINSTEIN GAS; EXCITATION; HARTREE-FOCK-BOGOLYUBOV THEORY; MANY-BODY PROBLEM; ONE-DIMENSIONAL CALCULATIONS; PERTURBATION THEORY; QUASI PARTICLES; SCATTERING; SCHROEDINGER EQUATION

### Citation Formats

```
Lugan, P., Physikalisches Institut, Albert-Ludwigs-Universitaet, Hermann-Herder Strasse 3, D-79104 Freiburg, and Sanchez-Palencia, L.
```*Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder*. United States: N. p., 2011.
Web. doi:10.1103/PHYSREVA.84.013612.

```
Lugan, P., Physikalisches Institut, Albert-Ludwigs-Universitaet, Hermann-Herder Strasse 3, D-79104 Freiburg, & Sanchez-Palencia, L.
```*Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder*. United States. doi:10.1103/PHYSREVA.84.013612.

```
Lugan, P., Physikalisches Institut, Albert-Ludwigs-Universitaet, Hermann-Herder Strasse 3, D-79104 Freiburg, and Sanchez-Palencia, L. Fri .
"Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder". United States. doi:10.1103/PHYSREVA.84.013612.
```

```
@article{osti_22058745,
```

title = {Localization of Bogoliubov quasiparticles in interacting Bose gases with correlated disorder},

author = {Lugan, P. and Physikalisches Institut, Albert-Ludwigs-Universitaet, Hermann-Herder Strasse 3, D-79104 Freiburg and Sanchez-Palencia, L.},

abstractNote = {We study the Anderson localization of Bogoliubov quasiparticles (elementary many-body excitations) in a weakly interacting Bose gas of chemical potential {mu} subjected to a disordered potential V. We introduce a general mapping (valid for weak inhomogeneous potentials in any dimension) of the Bogoliubov-de Gennes equations onto a single-particle Schroedinger-like equation with an effective potential. For disordered potentials, the Schroedinger-like equation accounts for the scattering and localization properties of the Bogoliubov quasiparticles. We derive analytically the localization lengths for correlated disordered potentials in the one-dimensional geometry. Our approach relies on a perturbative expansion in V/{mu}, which we develop up to third order, and we discuss the impact of the various perturbation orders. Our predictions are shown to be in very good agreement with direct numerical calculations. We identify different localization regimes: For low energy, the effective disordered potential exhibits a strong screening by the quasicondensate density background, and localization is suppressed. For high-energy excitations, the effective disordered potential reduces to the bare disordered potential, and the localization properties of quasiparticles are the same as for free particles. The maximum of localization is found at intermediate energy when the quasicondensate healing length is of the order of the disorder correlation length. Possible extensions of our work to higher dimensions are also discussed.},

doi = {10.1103/PHYSREVA.84.013612},

journal = {Physical Review. A},

issn = {1050-2947},

number = 1,

volume = 84,

place = {United States},

year = {2011},

month = {7}

}