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arXiv:cond-mat/0306281 · Physical Review A

Array of Bose-Einstein condensates under time-periodic Feshbach-resonance management

F. Kh. Abdullaev, E. N. Tsoy, Boris A. Malomed, R. A. Kraenkel

Published Nov 14, 2003• 55 citations
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Abstract

The dynamics of a discrete soliton in an array of Bose-Einstein condensates under the action of a periodically time-modulated atomic scattering length [Feshbach-resonance management (FRM)] is investigated. The cases of both slow and rapid modulations, in comparison with the tunneling frequency, are considered. We employ a discrete variational approach for the analysis of the system. The existence of nonlinear resonances and chaos is predicted at special values of the driving frequency. Soliton splitting is observed in numerical simulations. In the case of the rapid modulation, we derive an averaged equation, which is a generalized discrete nonlinear Schr\"odinger equation, including higher-order effective nonlinearities and intersite nonlinear interactions. Thus the predicted discrete FRM solitons are a direct matter-wave analog of recently investigated discrete diffraction-managed optical solitons.

DOI
10.1103/physreva.68.053606

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The dynamics of a discrete soliton in an array of Bose-Einstein condensates under the action of a periodically time-modulated atomic scattering length [Feshbach-resonance management (FRM)] is investigated. The cases of both slow and rapid modulations, in comparison with the tunneling frequency, are considered. We employ a discrete variational approach for the analysis of the system. The existence of nonlinear resonances and chaos is predicted at special values of the driving frequency. Soliton splitting is observed in numerical simulations. In the case of the rapid modulation, we derive an averaged equation, which is a generalized discrete nonlinear Schr"odinger equation, including higher-order effective nonlinearities and intersite nonlinear interactions. Thus the predicted discrete FRM solitons are a direct matter-wave analog of recently investigated discrete diffraction-managed optical solitons.
Compacton matter waves are considered in Bose-Einstein condensates (BEC) and in binary BEC mixtures, trapped in deep optical lattices in the presence of strong and rapid periodic time modulations of the atomic scattering length, are considered.For this, we derive vector averaged discrete nonlinear Schrödinger equations (DNLSE) and show that compacton solutions of different types can exist as stable excitations.Stability properties are studied by linear analysis and by direct numerical integrations of the DNLSE system.
The dynamics of matter waves in the atomic to molecular condensate transition with a time-modulated atomic scattering length is investigated. Both the cases of rapid and slow modulations are studied. In the case of rapid modulations, the average over oscillations for the system is derived. The corresponding conditions for dynamical suppression of the association of atoms into the molecular field, or of second-harmonic generation in nonlinear optical systems, are obtained. For the case of slow modulations, we find resonant enhancement in the molecular field. We then illustrate chaos in the atomic-molecular BEC system. We suggest a sequential application of the two types of modulations, slow and rapid, when producing molecules.
An experimentally realizable scheme of periodic sign-changing modulation of the scattering length is proposed for Bose-Einstein condensates similar to dispersion-management schemes in fiber optics. Because of controlling the scattering length via the Feshbach resonance, the scheme is named Feshbach-resonance management. The modulational-instability analysis of the quasiuniform condensate driven by this scheme leads to an analog of the Kronig-Penney model. The ensuing stable localized structures are found. These include breathers, which oscillate between the Thomas-Fermi and Gaussian configuration, or may be similar to the 2-soliton state of the nonlinear Schrödinger equation, and a nearly static state ("odd soliton") with a nested dark soliton. An overall phase diagram for breathers is constructed, and full stability of the odd solitons is numerically established.
The mean-field dynamics of Bose-Einstein condensates loaded in an optical lattice, confined by a parabolic potential, and subjected to a change of scattering length by means of the Feshbach resonance is considered. The system is described by the Gross-Pitaevskii (GP) equation with varying nonlinearity, which in a number of cases is reduced to one-dimensional (1D) perturbed nonlinear Schr\"odinger (NLS) equations, the particular form of which depends on the relation among the parameters of the problem. We analytically describe the adiabatic dynamics of periodic solutions of the respective NLS equations, provide a numerical study of 1D models confined by a parabolic trap, and carry out numerical simulations of the matter-wave dynamics within the framework of the radially symmetric 3D GP equation. Special attention is paid to processes of generation of trains of bright and dark matter solitons from initially periodic waves. The results of the 1D approximation are compared with direct numerical simulation of the original 3D GP eqation, showing remarkable coincidence for definite regions of parameters.
We investigate the modulational instability of nonlinear Schrödinger equations with periodic variation of their coefficients. In particular, we focus on the case of the recently proposed, experimentally realizable protocol of Feshbach Resonance Management for Bose–Einstein condensates. We derive the corresponding linear stability equation analytically and we show that it can be reduced to a Kronig–Penney model, which allows the determination of the windows of instability. The results are tested numerically in the absence, as well as in the presence of the magnetic trapping potential.