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Chinese Physics Letters

Phonon Spectrum and Modulational Instability in a Bose—Einstein Condensate Array

杨晓雪, 吴颖

Published Jan 1, 2002• 0 citations
OpenAlex

Abstract

We derive the phonon spectrum and the corresponding modulational instability conditions of an array of traps containing Bose-Einstein condensates with each trap linked to adjacent traps by tunnelling.It is shown that modulational instability regimes always exist regardless of the sign of the two-body interaction.

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We investigate theoretically an array of traps containing Bose-Einstein condensates, taking into account tunneling of atoms between adjacent traps and atom-atom interactions within each trap. After an expansion valid in the limit of a large number of atoms, we end up studying a variation of the problem of phonons in a one-dimensional lattice. Analysis of these fictitous phonons and their vacua shows that the fluctuations in atom numbers and phases of the condensates behave qualitatively as in the much-studied case of two traps.
We investigate analytically and numerically the modulational instability of a Bose-Einstein condensate with both two- and three-body interatomic interactions and trapped in an external parabolic potential. Analytical investigations performed lead us to establish an explicit time-dependent criterion for the modulational instability of the condensate. The effects of the potential as well as of the quintic nonlinear interaction are studied. Direct numerical simulations of the Gross-Pitaevskii equation with two- and three-body interactions describing the dynamics of the condensate agree with the analytical predictions.
We investigate the modulational instability (MI) of trapped Bose–Einstein condensates with three-body and higher-order interactions employing both semi-analytical and numerical methods. Using the time-dependent variational approach, we derive variational equations for the time evolution of the amplitude, phase of modulational perturbation, and effective potential of the system. By means of an effective potential, we retrieve the corresponding MI condition of the dynamical system under consideration. The interplay between three-body interaction and higher-order interaction is discussed in detail. The semi-analytical predictions are confirmed through numerical simulations.
By means of the time-dependent variational approach, we study the modulational instability of Bose–Einstein condensates (BECs), with both two- and three-body interatomic interactions, trapped in an external parabolic potential. Within this framework, we derive and analyse ordinary differential equations for the explicit time evolution of the amplitude and phase of modulational perturbation. The effect of the trapping coefficients as well as the quintic nonlinear interaction on the dynamics of the BEC are examined. Numerical simulations are carried out in order to support our theoretical findings.
A Bose-Einstein condensate in a modulated, one-dimensional, anharmonic potential can exhibit dynamical tunneling between islands of regular motion in phase space. With increasingly repulsive atomic interactions, dynamical tunneling is predicted to cease due to self-trapping [S. Wüster ]. This suppression of tunneling oscillations is related to the same phenomenon that occurs in the two-mode dynamics of a repulsively interacting Bose-Einstein condensate in a double-well potential. Here we present a two-mode model for dynamical tunneling based on nonlinear Floquet states and examine the range of validity of the approximation. We characterize nonlinear dynamical tunneling for different trap strengths, modulation amplitudes, and effective Planck constants. Using the linear Floquet states we derive an expression for the critical nonlinearity beyond which tunneling ceases. Finally we demonstrate the dynamical instability of selected nonlinear Floquet states and show how to initialize some Floquet states in experiments. Our detailed survey will enable experiments to target accessible parameter regimes for the study of nonlinear dynamical tunneling.