Localization of collisionally inhomogeneous condensates in a bichromatic optical lattice

Abstract

By direct numerical simulation and variational solution of the Gross-Pitaevskii equation, we studied the stationary and dynamic characteristics of a cigar-shaped, localized, collisionally inhomogeneous Bose-Einstein condensate trapped in a one-dimensional bichromatic quasiperiodic optical-lattice potential, as used in a recent experiment on the localization of a Bose-Einstein condensate [Roati et al., Nature (London) 453, 895 (2008)]. The effective potential characterizing the spatially modulated nonlinearity is obtained. It is found that the collisional inhomogeneity has influence not only on the central region but also on the tail of the Bose-Einstein condensate. The influence depends on the sign and value of the spatially modulated nonlinearity coefficient. We also demonstrate the stability of the stationary localized state by performing a standard linear stability analysis. Where possible, the numerical results are shown to be in good agreement with the variational results.

Localization of a Bose-Fermi mixture in a bichromatic optical lattice

“…4 the exponential fitting to density tails with ∼ exp(−|x|/L loc ), where L loc is the localization length. (Note that our definition of localization length [3] differs from that of Refs. [1,6] by a factor of 2.)…”

“…Now we consider the possibility of Anderson localization of the bosons with an exponential tail in density in the interacting Bose-Fermi mixture on the bichromatic OL [Eq. (3)] [1][2][3]6,31]. There are domains around region II of the phase diagram shown in Fig.…”

“…The original description of Anderson localization was based on the localization of noninteracting quantum waves in disorder potentials due to a cancellation of wave fronts coming from different locations of the disorder potential. However, superfluid atomic gases usually are interacting and the study of Anderson localization has also been extended to the case of localization of a single-component [3,4] or binary [5] BEC under repulsive effective interactions. Both a quasiperiodic OL in one [3,6] and three dimensions [7] and a random potential [8] were used in these studies.…”

“…However, superfluid atomic gases usually are interacting and the study of Anderson localization has also been extended to the case of localization of a single-component [3,4] or binary [5] BEC under repulsive effective interactions. Both a quasiperiodic OL in one [3,6] and three dimensions [7] and a random potential [8] were used in these studies. The effect of temperature on Anderson localization has also been investigated [9].…”

Matter-wave localization in a weakly perturbed optical lattice

“…Billy et al [2] observed the exponential tail of the spatial density distribution of a 87 Rb BEC after releasing it into a one-dimensional (1D) waveguide with a controlled disorder potential created by a laser speckle. Roati et al [3] observed the Anderson localization of a noninteracting 39 K BEC in a 1D quasiperiodic bichromatic optical lattice (OL). Recently, the experimental realizations of three-dimensional (3D) localization of ultracold gases of 40 K [4] and 87 Rb [5] atoms in a 3D speckle potential were also reported.…”