  We discuss the effects of quantum fluctuations on the properties of vortex
lattices in rapidly rotating ultracold atomic gases. We develop a variational
method that goes beyond the Bogoliubov theory by including the effects of
interactions between the quasiparticle excitations. These interactions are
found to have significant quantitative effects on physical properties even at
relatively large filling factors. We use our theory to predict the expected
experimental signatures of quantum fluctuations of vortices, and to assess the
competition of the triangular vortex lattice phase with other phases in
finite-sized systems.
