Continuum Theory of Tkachenko Modes in Rapidly Rotating Bose-Einstein Condensate

摘要

The continuum theory of Tkachenko modes in a rotating 2D Bose-Einstein condensate (BEC) is considered taking into account density inhomogeneity and compressibility of the condensate. Two regimes of rotation are discussed: (i) the Vortex Line Lattice (VLL) regime, in which the vortex array consists of thin vortex lines with the core size much less than the intervortex distance; (ii) the Lowest-Landau Level (LLL) regime, in which vortex cores overlap and the BEC wave function is a superposition of states at the lowest Landau level. The theory is in good agreement with experimental observation of Tkachenko modes in the VLL regime. But theoretical frequencies in the LLL regime are essentially higher than those observed for very rapidly rotating BEC. This provides evidence that the experiment has not yet reached the LLL regime.