Anderson localization of elementary excitations in a one-dimensional Bose-Einstein condensate

Abstract

Abstract. We study the elementary excitations of a transversely confined Bose-Einstein condensate in presence of a weak axial random potential. We determine the localization length (i) in the hydrodynamical low energy regime, for a domain of linear densities ranging from the Tonks-Girardeau to the transverse Thomas-Fermi regime, in the case of a white noise potential and (ii) for all the range of energies, in the "one-dimensional mean field regime", in the case where the randomness is induced by a series of randomly placed point-like impurities. We discuss our results in view of recent experiments in elongated BEC systems.

Mean-field phase diagram of the one-dimensional Bose gas in a disorder potential

“…The properties of the elementary Bogoliubov excitations stemming from the Gross-Pitaevskii state were studied analytically in the superfluid regime. Their localization length was shown to exhibit a power law behavior as a function of energy: E α , with α = 2 deep in the superfluid phase [13] and α = 1 at the phase transition [14]. Numerically we found that α < 1 in the Bose glass phase [15].…”

“…Thanks to the weak interaction limit, the theoretical description of these experiments can be performed in a first approximation with the Gross-Pitaevskii equation. The Gross-Pitaevskii equation in the presence of a disorder potential was recently studied by several groups [11][12][13][14]. For the condensate wave function, two different cases were identified: a connected density profile at weak and a fragmented one at strong disorder.…”

Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques

“…[495]). Another possibility is Anderson localization of elementary excitations in interacting BECs, as analyzed in the recent works [496,497]. Finally, it is worth also mentioning in passing parallel developments in this area, within the mathematically similar setting of photonic lattices, where Anderson localization and transition from ballistic to diffusive transport were recently observed in the presence of random fluctuations [498].…”

Coherent Backscattering of Bose-Einstein Condensates in Two-Dimensional Disorder Potentials

“…A central aim in this context is the realization and unambiguous identification of strong Anderson localization with Bose-Einstein condensates, which was attempted by several experimental groups [1][2][3] with recent success [4,5], and theoretically studied both from the perspective of the expansion process of the condensate [6,7] as well as from the scattering perspective [8,9]. Complementary studies were focused on localization properties of Bogoliubov quasiparticles [10,11], on dipole oscillations in the presence of disorder [12,13], as well as on the realization of Bose glass phases [14,15].The above-mentioned topics (apart from Ref.[7]) mainly refer to processes that are essentially one dimensional (1D) by nature. Qualitatively new phenomena, however, do arise in two or three spatial dimensions, due to the scenario of weak localization.…”

“…The past years have witnessed an increasing number of theoretical and experimental research activities on the behavior of ultracold atoms in magnetic or optical disorder potentials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. A central aim in this context is the realization and unambiguous identification of strong Anderson localization with Bose-Einstein condensates, which was attempted by several experimental groups [1][2][3] with recent success [4,5], and theoretically studied both from the perspective of the expansion process of the condensate [6,7] as well as from the scattering perspective [8,9].…”