Dynamical stabilization of matter-wave solitons revisited

TL;DR

This paper revisits the dynamical stabilization of Bose-Einstein condensates using time-dependent scattering length modulation, revealing that stable solutions are not clearly evidenced and metastable states dominate the dynamics.

Contribution

It compares various theoretical methods for stabilization, finds discrepancies with numerical results, and explores non-Gaussian trial functions to better predict metastability thresholds.

Findings

Numerical solutions show metastability, not true stabilization.

The phase of the wavefunction differs from theoretical assumptions.

Non-Gaussian trial functions improve predictions of critical nonlinearity.

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.