Dynamical stabilization of matter-wave solitons revisited

Abstract

We consider dynamical stabilization of Bose-Einstein condensates (BEC) by time-dependent modulation of the scattering length. The problem has been studied before by several methods: Gaussian variational approximation, the method of moments, method of modulated Townes soliton, and the direct averaging of the Gross-Pitaevskii (GP) equation. We summarize these methods and find that the numerically obtained stabilized solution has different configuration than that assumed by the theoretical methods (in particular a phase of the wavefunction is not quadratic with $r$). We show that there is presently no clear evidence for stabilization in a strict sense, because in the numerical experiments only metastable (slowly decaying) solutions have been obtained. In other words, neither numerical nor mathematical evidence for a new kind of soliton solutions have been revealed so far. The existence of the metastable solutions is nevertheless an interesting and complicated phenomenon on its own. We try some non-Gaussian variational trial functions to obtain better predictions for the critical nonlinearity $g_{cr}$ for metastabilization but other dynamical properties of the solutions remain difficult to predict.

References in corpus (4)

• Stabilization of bright solitons and vortex solitons in a trapless three-dimensional Bose-Einstein condensate by temporal modulation of the scattering length
• Fully three dimensional breather solitons can be created using Feshbach resonance
• Stabilization of a (3+1)D soliton in a Kerr medium by a rapidly oscillating dispersion coefficient
• n-body dynamics of stabilized vector solitons

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