  We propose a scheme for the detection of quantum phase transitions in the 1D
Bose-Hubbard (BH) and 1D Extended Bose-Hubbard (EBH) models, using the
non-demolition measurement technique of quantum polarization spectroscopy. We
use collective measurements of the effective total angular momentum of a
particular spatial mode to characterise the Mott insulator to superfluid phase
transition in the BH model, and the transition to a density wave state in the
EBH model. We extend the application of collective measurements to the ground
states at various deformations of a super-lattice potential.
