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Journal of Physics A Mathematical and General

Exact Floquet states of a two-component Bose–Einstein condensate induced by a laser standing wave

Haiming Deng, Wenhua Hai, Qianquan Zhu

Published Nov 21, 2006• 12 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/39/49/001

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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 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.
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 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.
It is shown that by experimentally controlling a weak optical lattice potential to equilibrate the interatomic interactions, we can construct a set of exact solutions of the Gross-Pitaevskii equations (GPE) for a two-component Bose-Einstein condensate (BEC). The exact solutions describe some balance superfluid phases with different flow-density amplitudes that supply several different and useful sources of the atom lasers. In the definition of dynamical superfluid-insulator transition (DSIT), (see Smerzi A. et al. , Phys. Rev. Lett. 89 (2002) 170402), the DSITs from the balance superfluid phases to the balance insulator phases are studied. The DSITs can be detected experimentally by observing the deformation of the periodic structure and the losses of the interference pattern and stability.