Phase transitions in rotating Bose-Einstein condensates.

Phase transitions, or abrupt changes of state under a smooth variation of external conditions, are of great interest in natural sciences. A remarkable property of a Bose-Einstein superfluid in a rotating bucket is its change to a vortex state once the bucket's rotational velocity exceeds a critical value. This transition to the Abrikosov state has been observed in cold atomic gases [1]. Such critical behavior is very sensitive to the interaction between the particles in the condensate [2,3]. We give an analytic description [4] of the first phase-transition point and classify the types of the corresponding instabilities that depend on the interaction. This toy model of a continuous phase transition predicts the same behavior patterns for all systems governed by a similar energy functional. [1] V. Schweikhard, I. Coddington, P. Engels, V. P. Mogendorff, and E. A. Cornell, Phys. Rev. Lett. {\bf 92}, 040404 (2004). [2] O. K. Vorov, P. Van Isacker, M. S. Hussein and K. Bartschat, Phys. Rev. Lett. {\bf 95}, 230406 (2005). [3] O. K. Vorov, M. S. Hussein and P. Van Isacker, Phys. Rev. Lett. {\bf 90}, 200402 (2003). [4] O. K. Vorov, P. Van Isacker, M. S. Hussein and K. Bartschat, submitted to Nature (2006).