Quantum Melting and Absence of Bose-Einstein Condensation in Two-Dimensional Vortex Matter

Abstract

We demonstrate that quantum fluctuations suppress Bose-Einstein condensation of quasi-two-dimensional bosons in a rapidly-rotating trap. Our conclusions rest in part on an effective-Lagrangian description of the triangular vortex lattice, and in part on microscopic Bogoliubov equations in the rapid-rotation limit. We obtain analytic expressions for the collective-excitation dispersion, which, in a rotating system, is quadratic rather than linear. Our estimates for the boson filling factor at which the vortex lattice melts at zero temperature due to quantum fluctuations are consistent with recent exact-diagonalization calculations.