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The localization of a Bose-Einstein condensate in one-dimensional, two-dimensional and three-dimensional bichromatic optical lattices

Hai-jun Chen

Published Jan 1, 2016• 0 citations
OpenAlex

Abstract

We investigate the stability of the localization of a Bose-Einstein condensate in one-dimensional, two-dimensional and three-dimensional bichromatic optical lattices using a time-dependent variational approach. We derive the effective potential for the stability analysis of the system using the Gauss type trial wave function and give the stable criteria through this effective potential. It is demonstrated that the bichromatic optical lattice's intensities, two-body, three-body and high-order interactions play different roles in the stability of the system. The two-body and high-order have an important influence to the stability but the others play a regulatory role on the stability.

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We investigate the stability of the localization of a Bose-Einstein condensate in one-dimensional, two-dimensional and three-dimensional bichromatic optical lattices using a time-dependent variational approach. We derive the effective potential for the stability analysis of the system using the Gauss type trial wave function and give the stable criteria through this effective potential. It is demonstrated that the bichromatic optical lattice's intensities, two-body, three-body and high-order interactions play different roles in the stability of the system. The two-body and high-order have an important influence to the stability but the others play a regulatory role on the stability.
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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.
By numerical simulation of the time-dependent Gross-Pitaevskii equation we show that a weakly interacting or noninteracting Bose-Einstein condensate (BEC) vortex can be localized in a three-dimensional bichromatic quasiperiodic optical-lattice (OL) potential generated by the superposition of two standing-wave polarized laser beams with incommensurate wavelengths. We also study the localization of a (nonrotating) BEC in two and three dimensions by bichromatic OL potentials along orthogonal directions. This is a generalization of the localization of a BEC in a one-dimensional bichromatic OL as studied in a recent experiment [Roati et al., Nature 453, 895 (2008)]. We demonstrate the stability of the localized state by considering its time evolution in the form of a stable breathing oscillation in a slightly altered potential for a large period of time. Finally, we consider the localization of a BEC in a random one-dimensional potential in the form of several identical repulsive spikes arbitrarily distributed in space.
In order to investigate the stability and dynamics properties of a cold atom Bose-Einstein Condensate (BEC) in two-dimensional Bessel optical lattices, the stability condition of the system is analyzed and the corresponding Gross-pitaevskii equation (GPE) is solved in this paper by time-dependent variational method and numerical simulation. Firstly, the Euler-Lagrange equation containing the parameters describing the system stability and the effective potential energy needed by the variational analysis method to analyze the system stability is obtained by using the adjustable exponent Gaussian trial wave function. Secondly, according to the analytical solution of Euler-Lagrange equation and the local minimum value of potential energy, the stability condition of the system is further illuminated. Finally, the influence mechanism of these parameters on the local dynamics is revealed by solving the corresponding GPE with numerical method.
By numerical simulation and variational analysis of the Gross–Pitaevskii equation we study the localization, with an exponential tail, of a dipolar Bose–Einstein condensate (DBEC) of 52 Cr atoms in a three-dimensional bichromatic optical lattice (OL) generated by two monochromatic OLs of incommensurate wavelengths along three orthogonal directions. For a fixed dipole–dipole interaction, a localized state of a small number of atoms (∼1000) could be obtained when the short-range interaction is not too attractive or not too repulsive. A phase diagram showing the region of stability of a DBEC with a short-range interaction and dipole–dipole interaction is given.