title: Ground states and vortices of matter-wave condensates and optical guided waves.
abstract: We analyze the shape and stability of localized states in nonlinear cubic media with space-dependent potentials modeling an inhomogeneity. By means of a static variational approach, we describe the ground states and vortexlike stationary solutions, either in dilute atom gases or in optical cavities, with an emphasis on parabolic-type potentials. First, we determine the existence conditions for soliton and vortex structures for both focusing and defocusing nonlinearity. It is shown that, even for a defocusing medium, soliton modes can exist with a confining potential. Second, step potentials and boundedness effects in hollow capillaries are investigated, which both proceed from a similar analysis. Finally, we discuss applications of this procedure to charged vortices in dilute quantum gases and to Bose-Einstein condensates trapped in the presence of a light-induced Gaussian barrier.
authors.affiliation: Nonlinear Physics Group, Research School of Physical Sciences and Engineering, Australian National University, Canberra ACT 0200, Australia.
authors.forename: Tristram J
authors.initials: TJ
authors.lastname: Alexander
authors.forename: Luc
authors.initials: L
authors.lastname: Bergé