Abstract
Vortices in a Bose-Einstein condensate are modelled as spontaneously symmetry breaking minimum energy solutions of the time dependent Gross-Pitaevskii equation, using the method of constrained optimization. In a non-rotating axially symmetric trap, the core of a single vortex precesses around the trap center and, at the same time, the phase of its wave function shifts at a constant rate. The precession velocity, the speed of phase shift, and the distance between the vortex core and the trap center, depend continuously on the value of the conserved angular momentum that is carried by the entire condensate. In the case of a symmetric pair of identical vortices, the precession engages an emergent gauge field in their relative coordinate, with a flux that is equal to the ratio between the precession and shift velocities.
Highlights
Vortices that appear in rotating cold atom Bose-Einstein condensates have been extensively studied, both experimentally and theoretically [16, 18, 19]
The time evolution amounts to a simple phase multiplication only when ψmin(x) is an eigenstate of the angular momentum operator; below we show that this can only occur for lz = 1, for all other values of lz = 0 the minimum energy solution always describes a precessing vortex configuration
Where {, } is the Poisson bracket. This is an example of spontaneous symmetry breaking, but the symmetry breaking minimum energy configuration is time dependent [30]
Summary
We consider a two dimensional single-component Bose-Einstein condensate on the xy-plane with an axially symmetric, non-rotating, harmonic trap. The condensate is described by a macroscopic wave function ψ(x, t) whose dynamics obeys the (dimensionless) time dependent Gross-Pitaevskii equation [14, 38]: i∂tψ. We search for solutions of the time dependent Gross-Pitaevskii equation (2.1), with fixed values of both the angular momentum Lz and the number of particles; in the following, with no loss of generality, we normalize the wave function so that N = 1 (see appendix A for details). The time evolution amounts to a simple phase multiplication only when ψmin(x) is an eigenstate of the angular momentum operator; below we show that this can only occur for lz = 1, for all other values of lz = 0 the minimum energy solution always describes a precessing vortex configuration. This is an example of spontaneous symmetry breaking, but the symmetry breaking minimum energy configuration is time dependent [30]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
