Vortices, Rings, and Spherical Shells in Bose-Einstein Condensates. I. Case of Repulsive Nonlinearity
L D. Carr, Charles W. Clark
The stationary behavior of axisymmetric vortex and vortex-like states of a Bose-Einstein condensate are described numerically and analytically. Both extended and con?ned condensates are considered in the context of the nonlinear Schrodinger equation, which models the mean ?eld. The assumption of azimuthal symmetry and integer winding number leads to three physical solution types. Vortex solutions have no nodes anda regular singular pointat the origin, approacha nonzero constant density as the radial coordinate approaches in?nity, and present a boundary between non-divergent and divergent solutions. Ring solutions have a central vortex which may be surrounded by concentric nodal rings, and take the same asymptotic form as the Coulomb function to leading order. Spherical shell solutions are the three-dimensional generalization of ring solutions but have a winding number of zero, and consist of spherical layers of alternating positive and negative phase of the order parameter. These solutions include the ground state for extended and con?ned condensates in both two and three dimensions.
Physical Review A (Atomic, Molecular and Optical Physics)
and Clark, C.
Vortices, Rings, and Spherical Shells in Bose-Einstein Condensates. I. Case of Repulsive Nonlinearity, Physical Review A (Atomic, Molecular and Optical Physics)
(Accessed December 9, 2021)