We investigate the existence and especially the linear stability of single- and multiple-charge quantized vortex states of nonlinear Schrödinger equations in the presence of a periodic and a parabolic potential in two spatial dimensions. The study is motivated by an examination of pancake-shaped Bose-Einstein condensates in the presence of magnetic and optical confinement. A two-parameter space of the condensate's chemical potential versus the periodic potential's strength is scanned for both single- and double-quantized vortex states located at a local minimum or a local maximum of the lattice. Triple-charged vortices are also briefly discussed. Single-charged vortices are found to be stable for cosinusoidal potentials and unstable for sinusoidal ones above a critical strength. Higher-charge vortices are more unstable for both types of potentials, and their dynamical evolution leads to a breakup into single-charged vortices.
|Original language||English (US)|
|Journal||Physical Review A - Atomic, Molecular, and Optical Physics|
|State||Published - May 27 2008|
All Science Journal Classification (ASJC) codes
- Atomic and Molecular Physics, and Optics