The dynamics of bright matter wave solitons in a quasi one-dimensionalBose–Einstein condensate with a rapidly varying trap

Abstract

The dynamics of a bright matter wave soliton in a quasi one-dimensionalBose–Einstein condensate (BEC) with a periodically rapidly varying time trap isconsidered. The governing equation is based on averaging the fast modulations ofthe Gross–Pitaevskii (GP) equation. This equation has the form of a GP equationwith an effective potential of a more complicated structure than an unperturbedtrap. In the case of an inverted (expulsive) quadratic trap corresponding to anunstable GP equation, the effective potential can be stable. For the boundedspace trap potential it is showed that bifurcation exists, i.e. the single-wellpotential bifurcates to the triple-well effective potential. The stabilization of aBEC cloud on-site state in the temporary modulated optical lattice is found. Thisphenomenon is analogous to the Kapitza stabilization of an inverted pendulum.The analytical predictions of the averaged GP equation are confirmed bynumerical simulations of the full GP equation with rapid perturbations.