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arXiv:0904.0480 · Physical Review A

Application of the Feshbach-resonance management to a tightly confined Bose-Einstein condensate

Giovanni Filatrella, Boris A. Malomed, Luca Salasnich

Published Apr 27, 2009• 8 citations
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Abstract

We study suppression of the collapse and stabilization of matter-wave solitons by means of time-periodic modulation of the effective nonlinearity, using the nonpolynomial Schr\"odinger equation for Bose-Einstein condensate trapped in a tight cigar-shaped potential. By means of systematic simulations, a stability region is identified in the plane of the modulation amplitude and frequency. In the low-frequency regime, solitons feature chaotic evolution, although they remain robust objects.

DOI
10.1103/physreva.79.045602

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We study suppression of the collapse and stabilization of matter-wave solitons by means of time-periodic modulation of the effective nonlinearity, using the nonpolynomial Schr"odinger equation for Bose-Einstein condensate trapped in a tight cigar-shaped potential. By means of systematic simulations, a stability region is identified in the plane of the modulation amplitude and frequency. In the low-frequency regime, solitons feature chaotic evolution, although they remain robust objects.
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By means of the variational approximation (VA) and systematic simulations, we study dynamics and stability boundaries for solitons in a two-dimensional (2D) self-attracting Bose-Einstein condensate (BEC), trapped in an optical lattice (OL) whose amplitude is subjected to periodic time modulation (the modulation frequency $\ensuremath{\omega}$ may be in the range of several kHz). Regions of stability of the solitons against the collapse and decay are identified in the space of the model's parameters. A noteworthy result is that the stability limit may reach the largest (100%) modulation depth, and the collapse threshold may exceed its classical value in the static lattice (which corresponds to the norm of Townes soliton). The minimum norm Nmin{N}_{\text{min}}Nmin​ necessary for the stability of the solitons is identified too. It features a strong dependence on $\ensuremath{\omega}$ at low frequencies, due to a resonant decay of the soliton. Predictions of the VA are reasonably close to results of the simulations. In particular, the VA helps understand salient resonant features in the shape of the stability boundaries observed with the variation of $\ensuremath{\omega}$.
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.
We derive an effective nonpolynomial Schr\"odinger equation (NPSE) for self-repulsive or attractive BEC in the nearly one-dimensional cigar-shaped trap, with the transverse confining frequency periodically modulated along the axial direction. In addition to the usual linear cigar-shaped trap, where the periodic modulation emulates the action of an optical lattice (OL), the model may be also relevant to toroidal traps, where an ordinary OL cannot be created. For either sign of the nonlinearity, extended and localized states are found, in the numerical form [using both the effective NPSE and the full three-dimensional (3D) Gross-Pitaevskii equation] and by means of the variational approximation (VA). The latter is applied to construct ground-state solitons and predict the collapse threshold in the case of self-attraction. It is shown that numerical solutions provided by the one-dimensional NPSE are always very close to full 3D solutions, and the VA yields quite reasonable results too. The transition from delocalized states to gap solitons, in the first finite bandgap of the linear spectrum, is examined in detail, for the repulsive and attractive nonlinearities alike.
We study the tunnelling properties of a cigar-shaped Bose-Einstein condensate by using an effective 1D nonpolynomial nonlinear Schrödinger equation (NPSE). First we investigate a mechanism to generate periodic pulses of coherent matter by means of a Bose condensate confined in a potential well with an oscillating height of the energy barrier. We show that it is possible to control the periodic emission of matter waves and the tunnelling fraction of the Bose condensate. We find that the number of emitted particles strongly increases if the period of oscillation of the height of the energy barrier is in parametric resonance with the period of oscillation of the centre of mass of the condensate inside the potential well. Then we use NPSE to analyse the periodic tunnelling of a Bose-Einstein condensate in a double-well potential which has an oscillating energy barrier. We show that the dynamics of the Bose condensate critically depends on the frequency of the oscillating energy barrier. The macroscopic quantum self-trapping (MQST) of the condensate can be suppressed under the condition of parametric resonance between the frequency of the energy barrier and the frequency of oscillation through the barrier of the very small fraction of particles which remain untrapped during MQST.
We observe the breakup dynamics of an elongated cloud of condensed 85Rb^{85}\mathrm{Rb}85Rb atoms placed in an optical waveguide. The number of localized spatial components observed in the breakup is compared with the number of solitons predicted by a plane-wave stability analysis of the nonpolynomial nonlinear Schr\"odinger equation, an effective one-dimensional approximation of the Gross-Pitaevskii equation for cigar-shaped condensates. It is shown that the numbers predicted from the fastest growing sidebands are consistent with the experimental data, suggesting that modulational instability is the key underlying physical mechanism driving the breakup.