Characterization of Bose-Hubbard Models with Quantum Non-demolition   Measurements
  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. 
B. Rogers, M. Paternostro, J. F. Sherson and G. De Chiara
cond-mat.quant-gas quant-ph