  Quantum fluctuations in an ultrafast rotating Bose gas at zero temperature
are investigated. We calculate the condensate density perturbatively to show
that no condensate is present in the thermodynamic limit. The excitation from
Gaussian fluctuations around the mean field solution causes infrared
divergences in loop diagrams, nevertheless, in calculating the atom number
density, the correlation functions and the free energy, we find the sum of the
divergences in the same loop order vanishes and obtain finite physical
quantities. The long-range correlation is explored and the algebraic decay
exponent for the single-particle correlation function is obtained. The atom
number density distribution is obtained at the one-loop level, which
illustrates the quantum fluctuation effects to melt the mean field
vortex-lattice. By the non-perturbative Gaussian variational method, we locate
the spinodal point of the vortex-lattice state.
