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Journal of Hubei Normal University

Bose-einstein condensate solitons trapped in an optical lattice

Yongshan Cheng

Published Jan 1, 2005• 0 citations
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Abstract

The characteristics of the Bose-Einstein Condensate (BEC) bright soliton trapped in an optical lattice are investigated with direct numerical simulations of the Gross-Pitaevskii equation. It is found that the optical lattice can be controllably used as a symmetric matter-wave splitter. Its effect depends on the initial location of the BECs soliton, the lattice amplitude and wave vector and the number of atoms in the trap.

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The characteristics of the Bose-Einstein Condensate (BEC) bright soliton trapped in an optical lattice are investigated with direct numerical simulations of the Gross-Pitaevskii equation. It is found that the optical lattice can be controllably used as a symmetric matter-wave splitter. Its effect depends on the initial location of the BECs soliton, the lattice amplitude and wave vector and the number of atoms in the trap.
The characteristics of two coupled Bose-Einstein Condensate (BEC) bright solitons trapped in an optical lattice are investigated with the variational approach and direct numerical simulations of the Gross-Pitaevskii equation. It is found that the optical lattice can be controllably used to capture and drag the coupled BEC solitons. Its effect depends on the initial location of the BEC solitons, the lattice amplitude and wave-number, and the amplitude of the coupled BEC solitons. The effective interaction between the two coupled solitons is the attractive effect.
In the present paper, we analytically and numerically investigate the dynamics of Bose-Einstein condensates (BECs) loaded into deep optical lattices of one dimension (1D), 2D, and 3D. We focus on the self-trapped state and the effect of the lattice dimension. Under the tight-binding approximation, we obtain an analytical criterion for the self-trapped state of BEC using the time-dependent variational method. The phase diagram for self-trapping, soliton, breather, or diffusion of a BEC cloud is obtained accordingly and verified by directly solving a discrete Gross-Pitaevskii equation numerically. In particular, we find that the criterion and the phase diagrams are modified dramatically by the dimension of the optical lattices.
The evolution characteristics of the 2-dimension cake-shaped Bose-Einstein Condensate(BEC) soliton trapped in an anisotropy trap are investigated by solving the Gross-Pitaevskii equation with a variational approach.It is found that by introducing an optical lattice potential into certain direction in a columniform symmetrical magnetic trap,a BEC soliton can tend to be stable in that direction and its stability may increase due to the decrease of the soliton expansion in other directions as a result of the coupling effects on those directions.The effects depends on the number of atoms in the trap,the coefficient of the trap and the parameters of the optical lattice potential.
We present two families analytical solutions to the extended Gross-Pitaevskii equation (GPE), which describe the dynamics of bright and dark solitons in Bose-Einstein condensations(BECs) with varying coefficients of two and three-body interactions in a parabolic and complex potential. The properties of the dynamical evolutions of the bright and dark matter-wave solitons are investigated. It is interesting that the matter-wave can be controlled by applying the external magnetic field and a background.
The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose–Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross–Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.
Dynamics and stability of solitons in two-dimensional (2D) Bose-Einstein condensates (BEC), with one-dimensional (1D) conservative plus dissipative nonlinear optical lattices, are investigated. In the case of focusing media (with attractive atomic systems), the collapse of the wave packet is arrested by the dissipative periodic nonlinearity. The adiabatic variation of the background scattering length leads to metastable matter-wave solitons. When the atom feeding mechanism is used, a dissipative soliton can exist in focusing 2D media with 1D periodic nonlinearity. In the defocusing media (repulsive BEC case) with harmonic trap in one direction and nonlinear optical lattice in the other direction, the stable soliton can exist. Variational approach simulations are confirmed by full numerical results for the 2D Gross-Pitaevskii equation.