Single vortex dynamics in binary Bose-Einstein condensates

We study the phases of a binary system of Bose-Einstein condensates, with their dynamical wave functions modeled by a set of coupled, time-dependent Gross-Pitaevskii equations. Beginning with an effective two-dimensional system, we identify phases characterized by the relationship between inter- and intra-atomic interactions and the initial configuration of the system. We then consider a binary system of mixing Bose-Einstein condensates placed in a rotating harmonic trap and study the single vortex dynamics in this system. We derive an approximate form for the energy due to a single vortex at the center of this binary system and a critical angular velocity for the global stability of a vortex at the center. We also compute the metastability onset angular velocity for the local stability of a vortex at the center of the trap. Our numerical solutions to the Gross-Pitaevskii equations support these results. We use these analyses to map out the behavior of vortices in the mixing phase of the rotating binary system. These results demonstrate that non-trivial behavior and vortex dynamics may exist in binary Bose-Einstein condensates as a result of their non-linear interactions, and we hope that such effects may be observable in suitable laboratory environments.