Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:0711.1896 · Physical Review A

Exact dynamics of multicomponent Bose-Einstein condensates in optical lattices in one, two, and three dimensions

R. Mark Bradley, James E. Bernard, Lincoln D. Carr

Published Mar 20, 2008• 10 citations
arXivHTMLPDF

Abstract

Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one-, two-, and three-dimensional optical lattices. We find both stationary and nonstationary solutions, which are given in closed form. Among these solutions are a vortex-antivortex array on the square optical lattice and modes in which two or more components slosh back and forth between neighboring potential wells. We obtain a variety of solutions for multicomponent condensates on the simple cubic lattice, including a solution in which one condensate is at rest and the other flows in a complex three-dimensional array of intersecting vortex lines. A number of physically important solutions are stable for a range of parameter values, as we show by direct numerical integration of the equations of motion.

DOI
10.1103/physreva.77.033622

Related papers

Exact nonstationary solutions to the mean-field equations of motion for two-component Bose–Einstein condensates in periodic potentials

R. Mark Bradley, Bernard Deconinck, J Nathan Kutz

We study the dynamics of two-component Bose–Einstein condensates in periodic potentials in one dimension. Elliptic potentials which have the sinusoidal optical potential as a special case are considered. We construct exact nonstationary solutions to the mean-field equations of motion. Among the solutions are two types of temporally periodic solutions—in one type there are condensate oscillations between neighbouring potential wells, while in the other the condensates oscillate from side to side within the wells. Our numerical studies of the stability of these solutions suggest the existence of one-parameter families of stable nonstationary solutions.

arXiv:nlin/0403043•Journal of Physics A Mathematical and General•Feb 16, 2005•22 citations

Dynamics and Stability of Bose-Einstein Condensates: the Nonlinear Schrodinger Equation with Periodic Potential

Bernard Deconinck, Béla A. Frigyik, J. Nathan Kutz

The cubic nonlinear Schrodinger equation with a lattice potential is used to model a periodic dilute gas Bose-Einstein condensate. Both two- and three-dimensional condensates are considered, for atomic species with either repulsive or attractive interactions. A family of exact solutions and corresponding potential is presented in terms of elliptic functions. The dynamical stability of these exact solutions is examined using both analytical and numerical methods. For condensates with repulsive atomic interactions, all stable, trivial-phase solutions are off-set from the zero level. For condensates with attractive atomic interactions, no stable solutions are found, in contrast to the one-dimensional case.

arXiv:cond-mat/0106231•Jun 12, 2001•0 citations

Dynamics of periodic multi-component Bose–Einstein condensates

Bernard Deconinck, J. Nathan Kutz, Matthew S Patterson +1 more

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.

Journal of Physics A Mathematical and General•May 8, 2003•49 citations

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

Wen Ling-Hua

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.

Journal of Liaocheng University•Jan 1, 2011•0 citations

Stationary Classical Chaos of Trapped Two-Component Bose–Einstein Condensates in 1-D Optical Lattice Potentials

Jianshu Fang, Wing‐Ki Liu, Zhu Shan-Hua

We study the nonlinear dynamics of two-component Bose–Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross–Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.

Communications in Theoretical Physics•Jul 1, 2007•2 citations

Stability Diagrams of a Bose–Einstein Condensate in a Periodic Array of Quantum Wells

Xue Rui, Liang Zhao-Xin, Weidong Li

With the help of a set of exact closed-form solutions to the stationary Gross–Pitaevskii equation, we comprehensively investigate Landau and dynamical instabilities of a Bose–Einstein condensate in a periodic array of quantum wells. In the tight-binding limit, the analytical expressions for both Landau and dynamical instabilities are obtained in terms of the compressibility and effective mass of the BEC system. Then the stability phase diagrams are shown to be similar to the one in the case of the sinusoidal optical lattice.

Chinese Physics Letters•Jul 1, 2009•2 citations
Numerous exact solutions to the nonlinear mean-field equations of motion are constructed for multicomponent Bose-Einstein condensates on one-, two-, and three-dimensional optical lattices. We find both stationary and nonstationary solutions, which are given in closed form. Among these solutions are a vortex-antivortex array on the square optical lattice and modes in which two or more components slosh back and forth between neighboring potential wells. We obtain a variety of solutions for multicomponent condensates on the simple cubic lattice, including a solution in which one condensate is at rest and the other flows in a complex three-dimensional array of intersecting vortex lines. A number of physically important solutions are stable for a range of parameter values, as we show by direct numerical integration of the equations of motion.
We study the dynamics of two-component Bose–Einstein condensates in periodic potentials in one dimension. Elliptic potentials which have the sinusoidal optical potential as a special case are considered. We construct exact nonstationary solutions to the mean-field equations of motion. Among the solutions are two types of temporally periodic solutions—in one type there are condensate oscillations between neighbouring potential wells, while in the other the condensates oscillate from side to side within the wells. Our numerical studies of the stability of these solutions suggest the existence of one-parameter families of stable nonstationary solutions.
The cubic nonlinear Schrodinger equation with a lattice potential is used to model a periodic dilute gas Bose-Einstein condensate. Both two- and three-dimensional condensates are considered, for atomic species with either repulsive or attractive interactions. A family of exact solutions and corresponding potential is presented in terms of elliptic functions. The dynamical stability of these exact solutions is examined using both analytical and numerical methods. For condensates with repulsive atomic interactions, all stable, trivial-phase solutions are off-set from the zero level. For condensates with attractive atomic interactions, no stable solutions are found, in contrast to the one-dimensional case.
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.
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.
We study the nonlinear dynamics of two-component Bose–Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross–Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.
With the help of a set of exact closed-form solutions to the stationary Gross–Pitaevskii equation, we comprehensively investigate Landau and dynamical instabilities of a Bose–Einstein condensate in a periodic array of quantum wells. In the tight-binding limit, the analytical expressions for both Landau and dynamical instabilities are obtained in terms of the compressibility and effective mass of the BEC system. Then the stability phase diagrams are shown to be similar to the one in the case of the sinusoidal optical lattice.