Article ID Journal Published Year Pages File Type
1897898 Physica D: Nonlinear Phenomena 2009 10 Pages PDF
Abstract

In this paper, we consider the existence, stability and dynamical evolution of dark vortex states in the two-dimensional defocusing discrete nonlinear Schrödinger model, a model of interest both to atomic physics and to nonlinear optics. Our considerations are chiefly based on initializing such vortex configurations at the anti-continuum limit of zero coupling between adjacent sites, and continuing them to finite values of the coupling. Systematic tools are developed for such continuations based on amplitude-phase decompositions and explicit solvability conditions enforcing the vortex phase structure. Regarding the linear stability of such nonlinear waves, we find that in a way reminiscent of their 1d analogs, i.e., of discrete dark solitons, the discrete defocusing vortices become unstable past a critical coupling strength and, subsequently feature a cascade of alternating stabilization–destabilization windows for any finite lattice. Although the results are mainly geared towards the uniform case, we also consider the effect of harmonic trapping potentials often present in experimental atomic physics settings.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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