Quenched dynamics of two-dimensional solitary waves and vortices in the Gross-Pitaevskii equation

摘要

We consider a two-dimensional (2D) counterpart of the experiment that led to the creation of quasi-1D bright solitons in Bose-Einstein condensates (BECs) (2002 Nature 417 150-3). We start by identifying the fundamental state of the 2D Gross-Pitaevskii equation for repulsive interactions, with a harmonic-oscillator (HO) trap, and with or without an optical lattice (OL). Subsequently, we switch the sign of the interaction to induce interatomic attraction and monitor the ensuing dynamics. Regions of stable self-trapping and a catastrophic collapse of 2D fundamental states are identified in the parameter plane of the OL strength and BEC norm. The increase of the OL strength expands the persistence domain for the solitary waves to larger norms. For single-charged solitary vortices, in addition to the survival and collapse regimes, an intermediate one is identified, where the vortex resists the collapse but loses its structure, transforming into a single-hump state. The same setting may also be implemented in the context of optical solitons and vortices, using photonic-crystal fibers.