The authors investigated the exact non-stationary solutions for a two-component BEC system confined in an external potential constructed by a optical lattice potential and a optical standing wave.The cases of the interaction strengths are considered.The authors find that the two-component BEC has different properties for the two cases.
Coupled nonlinear Schrödinger (CNLS) equations with an external elliptic function potential model with high accuracy a quasi-one-dimensional interacting two-component Bose-Einstein condensate (BEC) trapped in a standing wave generated by a few laser beams. The construction of stationary solutions of the two-component CNLS equation with a periodic potential is detailed and their stability properties are studied by direct numerical simulations. Some of these solutions allow reduction to the Manakov system. From a physical point of view the trivial phase solutions can be interpreted as exact Bloch states at the edge of the Brillouin zone. Some of them are stable while others are found to be unstable against weak modulations of long wavelength. By numerical simulations it is shown that the modulationally unstable solutions lead to the formation of localized ground states of the coupled BEC system.
Coupled nonlinear Schrodinger equations (CNLS) with an external elliptic function potential model a quasi one--dimensional interacting two-component Bose-Einstein condensate trapped in a standing light wave. New families of stationary solutions of the CNLS with a periodic potential are presented and their stability studied by direct numerical simulations. Some of these solutions allow reduction to Manakov system. From a physical point of view these solutions can be interpreted as exact Bloch states at the edge of the Brillouin zone. Some of them are stable while others are found to be unstable against modulations of long wavelength. The solutions which are modulationally unstable are shown to lead to the formation of localized ground states of the coupled BEC system.
Based on the idea of balance between the internal and external potentials, it is shown that for a two-component Bose–Einstein condensate (BEC) confined in an optical lattice the presence of a spacetime periodic laser field can induce a family of exact Floquet states (EFSs). The atomic-number densities of the EFSs are illustrated and the atomic current, phase blowing-up and the quantum reflection are investigated. The balance conditions and blowing-up region on parameter space are found, and the influences of phase blowing-up to the velocity fields, flow densities are revealed. It is demonstrated that the BEC motions can be controlled by adjusting the laser frequency, wave vector and amplitude.
The cubic vector nonlinear Schrödinger equation with an external trigonometric potential models a quasi-one-dimensional multi-component Bose–Einstein condensate trapped in a standing light wave. We construct families of exact stationary solutions for the more general case of an elliptic function potential. Some of these solutions degenerate to zero as the effect of the external potential disappears, whereas others limit to solutions of the free vector nonlinear Schrödinger equation. The stability of these solutions is examined both analytically and numerically. The stability results depend on the nature of the atomic interactions not only within the components but also between components. As in the scalar case (one component) with repulsive interaction, all linearly stable solutions are deformations of the ground state of the linear Schrödinger equation. Unlike the scalar case with attractive interaction, no solutions are found to be stable if there is any attractive interaction present.
The ground state solutions of two-component Bose-Einstein condensates (BECs) in Bessel optical lattices (BLs) are studied by means of the balance condition between BLs strength and inter-atomic interactions. We consider a quasi-two-dimensional (2D) BECs system,strongly confined in longitudinal direction and weakly trapped in the radial direction in the transverse plane,which obeys 2D Gross-Pitaevskii equation (GPE) derived from its 3D counterpart. Analytically we obtained the atom number distribution,atom number and energy of ground state and give the parameter ranges. Compared to single-component BEC,two-component BECs exhibit a rich variety of ground state structures. These structures depend upon various parameters,in particular the inter-atomic interactions and the BLs strength. Neglecting the inter-component atomic interaction,the corresponding results of single-component situation are given.