Unusual vortex matter in rotating Bose-Einstein condensates with SU(2) broken symmetry*

We consider a Ginzburg-Landau model of a rotating two-component Bose-Einstein condensate with SU(2) broken symmetry through the use of numerical Monte Carlo techniques. We include the full spectrum of thermal amplitude- and phase-fluctuations. The model exhibits an unusual state of global phase coherence with no accompanying vortex line lattice. This state has no counterpart in single-component condensates. The conditions for such a state are experimentally realizable in, \textit{e.g.}, homonuclear mixes of atomic gases in separate hyperfine states, tuned to the SU(2) point with Feshbach resonance techniques.