Bogoliubov Excitations of Disordered Bose-Einstein Condensates

TL;DR

This paper develops a theoretical framework to analyze how spatially correlated disorder affects the excitation spectrum, condensate deformation, and localization properties of Bose-Einstein condensates across various dimensions.

Contribution

It introduces a method to compute the excitation dispersion and related properties in disordered Bose-Einstein condensates, extending previous models to correlated disorder and arbitrary dimensions.

Findings

Disorder deforms the mean-field condensate.

Quantum excitation spectrum is modified by disorder.

Localization lengths and mean free paths are characterized.

Abstract

We describe repulsively interacting Bose-Einstein condensates in spatially correlated disorder potentials of arbitrary dimension. The first effect of disorder is to deform the mean-field condensate. Secondly, the quantum excitation spectrum and condensate population are affected. By a saddle-point expansion of the many-body Hamiltonian around the deformed mean-field ground state, we derive the fundamental quadratic Hamiltonian of quantum fluctuations. Importantly, a basis is used such that excitations are orthogonal to the deformed condensate. Via Bogoliubov-Nambu perturbation theory, we compute the effective excitation dispersion, including mean free paths and localization lengths. Corrections to the speed of sound and average density of states are calculated, due to correlated disorder in arbitrary dimensions, extending to the case of weak lattice potentials.