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Journal of Liaocheng University

Exact Floquet States of Bose-Einstein Condensates in a Three-modeLaser-driven Optical Lattice

Wen Ling-Hua

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

We investigate the exact nonstationary states of three-component Bose-Einstein condensates(BECs) in a three-mode laser-driven optical lattice by using the mean-field theory.Starting with a set of coupled Gross-Pitaevskii(GP) equations describing one-dimensional(1D) three-component BECs,we obtain a set of equivalent uncoupled GP equations via three introduced interaction constants and the balance condition between the mean-field interaction and the external potential.It is shown that for appropriate parameter regions the system surports exact Floquet states which evolve periodically in spatiotemporal domain.In addition,the evolution properties of the particle denstiy,the phase,the velocity and the current density are analyzed and discussed.

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We investigate the Gross-Pitaevskii equation for a classically chaotic system, which describes an atomic Bose-Einstein condensate confined in an optical lattice and driven by a spatiotemporal periodic laser field. It is demonstrated that the exact Floquet states appear when the external time-dependent potential is balanced by the nonlinear mean-field interaction. The balance region of parameters is divided into a phase-continuing region and a phase-jumping one. In the latter region, the Floquet states are spatiotemporal vortices of nontrivial phase structures and zero-density cores. Due to the velocity singularities of vortex cores and the blowing-up of perturbed solutions, the spatiotemporal vortices are unstable periodic states embedded in chaos. The stability and instability of these Floquet states are numerically explored by the time evolution of fidelity between the exact and numerical solutions. It is numerically illustrated that the stable Floquet states could be prepared from the uniformly initial states by slow growth of the external potential.
We investigate the Gross–Pitaevskii equation which describes an atomic Bose–Einstein condensate confined in an optical lattice and driven by a spatiotemporal periodic laser field. It is demonstrated that the exact Floquet states appear when the external time-dependent potential is balanced by the nonlinear mean-field interaction. The balance region of parameters is divided into a phase-continuing region and a phase-jumping one. In the latter region, the Floquet states are spatiotemporal vortices of nontrivial phase structures and zero-density cores. Due to the velocity singularities of vortex cores and the blowing-up of perturbed solutions, the spatiotemporal vortices are unstable periodic states embedded into chaos. The stability and instability of these Floquet states are numerically explored by the time evolution of fidelity between the exact and numerical solutions. It is numerically illustrated that the stable Floquet states in the phase-continuing region could be prepared from the uniformly initial states by slow growth of the external potential. 1.
We investigate the Gross-Pitaevskii equation for a classically chaotic system, which describes an atomic Bose-Einstein condensate confined in an optical lattice and driven by a spatiotemporal periodic laser field. It is demonstrated that the exact Floquet states appear when the external time-dependent potential is balanced by the nonlinear mean-field interaction. The balance region of parameters is divided into a phase-continuing region and a phase-jumping one. In the latter region, the Floquet states are spatiotemporal vortices of nontrivial phase structures and zero-density cores. Due to the velocity singularities of vortex cores and the blowing-up of perturbed solutions, the spatiotemporal vortices are unstable periodic states embedded in chaos. The stability and instability of these Floquet states are numerically explored by the time evolution of fidelity between the exact and numerical solutions. It is numerically illustrated that the stable Floquet states could be prepared from the uniformly initial states by slow growth of the external potential.
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.
We study the spatiotemporal dynamics of Bose-Einstein condensates (BECs) with spatiotemporally varying two- and three-body interactions and without an external trapping potential. The cubic and quintic terms in the Gross-Pitaevskii (GP) equation play the roles of external trapping potentials. Spatiotemporal modulation of the two- and three-body interactions can be of great importance in BEC field. But it is the subject of relatively fewer studies. Through theoretical analyses we obtain the equilibrium points (centers and saddles in phase space) of the unperturbed repulsive and attractive cases. With the heteroclinic solution of the unperturbed repulsive system, we theoretically construct the general solution of the 1st-order perturbed equation of the system. By using the boundedness conditions of the general solution we obtain the Melnikov chaos criterion predicting the existence of Smale-horseshoe chaos in the system. With a set of system parameters satisfied the Melnikov chaos criterion, numerical simulations show that the system is in a chaotic state. For BECs that do not satisfy the Melnikov chaos criterion, numerical simulations demonstrate that the modulating frequency can be an effective controlling parameter for the spatiotemporal dynamics of the BECs.
We study the existence of modulated amplitude waves with non-trivial phase of a quasi-1D multicomponent Bose–Einstein condensate (BEC) in the presence of an external periodic potential. Mathematically, such coherent structures are doubly periodic solutions, in space and time, of a coupled system of Gross–Pitaevskii equations. For a binary BEC, the weak interaction regime is tackled by means of the averaging method and regular perturbation theory. The case of strong particle interaction is covered by a simple rescaling argument. One of the components is stationary, while the second component has non-trivial phase, meaning that there is circulation of matter only of the second component. The case of three components is briefly discussed as well.