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:cond-mat/0007202 · Physical Review A

Quasiperiodic versus irreversible dynamics of an optically confined Bose-Einstein condensate

Pierre Villain, Patrik Öhberg, Maciej Lewenstein

Published Feb 12, 2001• 6 citations
arXivHTMLPDF

Abstract

We consider the evolution of a dilute Bose-Einstein condensate in an optical trap formed by a doughnut laser mode. By solving a one-dimensional Gross-Pitaevskii equation and looking at the variance and the statistical entropy associated with the position of the system, we can study the dynamical behavior of the system. It is shown that for small condensates nonlinear revivals of the macroscopic wave function are expected. For sufficiently large and dense condensates irreversible dynamics takes place for which revivals of regular dynamics appear as predicted in P. Villain and M. Lewenstein, Phys. Rev. A 62, 043601 (2000). These results are confirmed by a two-dimensional simulation in which the scales of energy associated with the two different directions mimic the experimental situation.

DOI
10.1103/physreva.63.033607

Related papers

Localization of a Bose-Einstein condensate in a bichromatic optical lattice

Sadhan K. Adhikari, Luca Salasnich

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC [Roati et al., Nature (London) 453, 895 (2008)], can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential [Billy et al., Nature (London) 453, 891 (2008)]. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms.

arXiv:0907.3498•Physical Review A•Aug 11, 2009•80 citations

Loss and revival of phase coherence in a Bose–Einstein condensate moving through an optical lattice

Francesco Nesi, Michele Modugno

We investigate the phase coherence of a trapped Bose–Einstein condensate that undergoes a dynamical superfluid–insulator transition in the presence of a one-dimensional optical lattice. We study the evolution of the condensate after a sudden displacement of the harmonic trapping potential by solving the Gross–Pitaevskii equation, and comparing the results with the prediction of two effective 1D models. We show that, owing to the 3D nature of the system, the breakdown of the superfluid current above a critical displacement is not associated with a sharp transition, but there exists a range of displacements for which the condensate can recover a certain degree of coherence. We also discuss the implications on the interference pattern after the ballistic expansion as measured in recent experiments at LENS.

arXiv:cond-mat/0310659•Journal of Physics B Atomic Molecular and Optical Physics•Mar 24, 2004•18 citations

Chaotic self-trapping of a weakly irreversible double Bose condensate

P. Coullet, Nicolas Vandenberghe

We analyze the dynamics of a weakly open Bose-Einstein condensate trapped in a double-well potential. Close to the self-trapping bifurcation, numerical simulations of the weakly irreversible one-dimensional Gross Pitaevskii equation reveal chaotic behaviors. A two-mode model is used to derive amplitude equations describing the complex dynamic of the condensate.

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics•Jul 19, 2001•49 citations

Collapse of a Bose-Einstein condensate induced by fluctuations of the laser intensity

Josselin C. Garnier, F. Kh. Abdullaev, Bakhtiyor B. Baizakov

The dynamics of a metastable attractive Bose-Einstein condensate trapped by a system of laser beams is analyzed in the presence of small fluctuations of the laser intensity. It is shown that the condensate will eventually collapse. The expected collapse time is inversely proportional to the integrated covariance of the time autocorrelation function of the laser intensity and it decays logarithmically with the number of atoms. Numerical simulations of the stochastic three-dimensional Gross-Pitaevskii equation confirm analytical predictions for small and moderate values of mean-field interaction.

arXiv:cond-mat/0405223•Physical Review A•May 10, 2004•19 citations

Dynamics of Bose-Einstein condensates: Variational solutions of the Gross-Pitaevskii equations

Víctor M. Pérez‐García, Humberto Michinel, J. I. Cirac +2 more

A variational technique is applied to solve the time-dependent nonlinear Schr\"odinger equation (Gross-Pitaevskii equation) with the goal to model the dynamics of dilute ultracold atom clouds in the Bose-Einstein condensed phase. We derive analytical predictions for the collapse, equilibrium widths, and evolution laws of the condensate parameters and find them to be in very good agreement with our numerical simulations of the nonlinear Schr\"odinger equation. It is found that not only the number of particles, but also both the initial width of the condensate and the effect of different perturbations to the condensate may play a crucial role in the collapse dynamics. The results are applicable when the shape of the condensate is sufficiently simple.

Physical Review A•Aug 1, 1997•406 citations

Quasi one-dimensional Bose–Einstein condensate in a gravito-optical surface trap

Javed Akram, Benjamin Girodias, Axel Pelster

Abstract We study both static and dynamic properties of a weakly interacting Bose–Einstein condensate (BEC) in a quasi one-dimensional gravito-optical surface trap, where the downward pull of gravity is compensated by the exponentially decaying potential of an evanescent wave. First, we work out approximate solutions of the Gross–Pitaevskii equation for both a small number of atoms using a Gaussian ansatz and a larger number of atoms using the Thomas–Fermi limit. Then we confirm the accuracy of these analytical solutions by comparing them to numerical results. From there, we numerically analyze how the BEC cloud expands non-ballistically, when the confining evanescent laser beam is shut off, showing agreement between our theoretical and previous experimental results. Furthermore, we analyze how the BEC cloud expands non-ballistically due to gravity after switching off the evanescent laser field in the presence of a hard-wall mirror which we model by using a blue-detuned far-off-resonant sheet of light. There we find that the BEC shows significant self-interference patterns for a large number of atoms, whereas for a small number of atoms, a revival of the BEC wave packet with few matter-wave interference patterns is observed.

arXiv:1509.05987•Journal of Physics B Atomic Molecular and Optical Physics•Mar 17, 2016•7 citations
We consider the evolution of a dilute Bose-Einstein condensate in an optical trap formed by a doughnut laser mode. By solving a one-dimensional Gross-Pitaevskii equation and looking at the variance and the statistical entropy associated with the position of the system, we can study the dynamical behavior of the system. It is shown that for small condensates nonlinear revivals of the macroscopic wave function are expected. For sufficiently large and dense condensates irreversible dynamics takes place for which revivals of regular dynamics appear as predicted in P. Villain and M. Lewenstein, Phys. Rev. A 62, 043601 (2000). These results are confirmed by a two-dimensional simulation in which the scales of energy associated with the two different directions mimic the experimental situation.
By direct numerical simulation of the time-dependent Gross-Pitaevskii equation, we study different aspects of the localization of a noninteracting ideal Bose-Einstein condensate (BEC) in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Such a quasiperiodic potential, used in a recent experiment on the localization of a BEC [Roati et al., Nature (London) 453, 895 (2008)], can be formed by the superposition of two standing-wave polarized laser beams with different wavelengths. We investigate the effect of the variation of optical amplitudes and wavelengths on the localization of a noninteracting BEC. We also simulate the nonlinear dynamics when a harmonically trapped BEC is suddenly released into a quasiperiodic potential, as done experimentally in a laser speckle potential [Billy et al., Nature (London) 453, 891 (2008)]. We finally study the destruction of the localization in an interacting BEC due to the repulsion generated by a positive scattering length between the bosonic atoms.
We investigate the phase coherence of a trapped Bose–Einstein condensate that undergoes a dynamical superfluid–insulator transition in the presence of a one-dimensional optical lattice. We study the evolution of the condensate after a sudden displacement of the harmonic trapping potential by solving the Gross–Pitaevskii equation, and comparing the results with the prediction of two effective 1D models. We show that, owing to the 3D nature of the system, the breakdown of the superfluid current above a critical displacement is not associated with a sharp transition, but there exists a range of displacements for which the condensate can recover a certain degree of coherence. We also discuss the implications on the interference pattern after the ballistic expansion as measured in recent experiments at LENS.
The dynamics of a metastable attractive Bose-Einstein condensate trapped by a system of laser beams is analyzed in the presence of small fluctuations of the laser intensity. It is shown that the condensate will eventually collapse. The expected collapse time is inversely proportional to the integrated covariance of the time autocorrelation function of the laser intensity and it decays logarithmically with the number of atoms. Numerical simulations of the stochastic three-dimensional Gross-Pitaevskii equation confirm analytical predictions for small and moderate values of mean-field interaction.
A variational technique is applied to solve the time-dependent nonlinear Schr\"odinger equation (Gross-Pitaevskii equation) with the goal to model the dynamics of dilute ultracold atom clouds in the Bose-Einstein condensed phase. We derive analytical predictions for the collapse, equilibrium widths, and evolution laws of the condensate parameters and find them to be in very good agreement with our numerical simulations of the nonlinear Schr\"odinger equation. It is found that not only the number of particles, but also both the initial width of the condensate and the effect of different perturbations to the condensate may play a crucial role in the collapse dynamics. The results are applicable when the shape of the condensate is sufficiently simple.
Abstract We study both static and dynamic properties of a weakly interacting Bose–Einstein condensate (BEC) in a quasi one-dimensional gravito-optical surface trap, where the downward pull of gravity is compensated by the exponentially decaying potential of an evanescent wave. First, we work out approximate solutions of the Gross–Pitaevskii equation for both a small number of atoms using a Gaussian ansatz and a larger number of atoms using the Thomas–Fermi limit. Then we confirm the accuracy of these analytical solutions by comparing them to numerical results. From there, we numerically analyze how the BEC cloud expands non-ballistically, when the confining evanescent laser beam is shut off, showing agreement between our theoretical and previous experimental results. Furthermore, we analyze how the BEC cloud expands non-ballistically due to gravity after switching off the evanescent laser field in the presence of a hard-wall mirror which we model by using a blue-detuned far-off-resonant sheet of light. There we find that the BEC shows significant self-interference patterns for a large number of atoms, whereas for a small number of atoms, a revival of the BEC wave packet with few matter-wave interference patterns is observed.