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Thermal fluctuations and melting transitions for rotating single-componentsuperfluids have been intensively studied and are well understood. In contrast,the thermal effects on vortex states for two-component superfluids withdensity-density interaction, which have a much richer variety of vortex groundstates, have been much less studied. Here, we investigate the thermal effectson vortex matter in superfluids with $\mathrm{U(1)}\times \mathrm{U(1)}$ brokensymmetries and intercomponent density-density interactions, as well as the casewith a larger $\mathrm{SU(2)}$ broken symmetry obtainable from the$\mathrm{U(1)}\times \mathrm{U(1)}$-symmetric case by tuning scatteringlengths. In the former case we find that, in addition to first-order meltingtransitions, the system exhibits thermally driven phase transitions betweensquare and hexagonal lattices. Our main result, however, concerns the casewhere the condensate exhibits $\mathrm{SU(2)}$-symmetry, and where vortices arenot topological. At finite temperature, the system exhibits effects which donot have a counter-part in single component systems. Namely, it has a statewhere thermally averaged quantities show no regular vortex lattice, yet thesystem retains superfluid coherence along the axis of rotation. In such astate, the thermal fluctuations result in transitions between different(nearly)-degenerate vortex states without undergoing a melting transition. Ourresults apply to multi-component Bose-Einstein condensates, and we suggest howto experimentally detect some of these unusual effects in such systems.

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Fluctuation effects in rotating Bose-Einstein condensates with broken  $\mathrm{SU}(2)$ and $\mathrm{U}(1)\times \mathrm{U}(1)$ symmetries in the  presence of intercomponent density-density interactions