Noise correlations of hard-core bosons: quantum coherence and symmetry breaking

Noise correlations, such as those observable in the time of flight images of a released cloud, are calculated for hard-core bosonic (HCBs) atoms. These second-order correlations are used to explore quantum coherence of strongly correlated bosons in the fermionized regime with and without external parabolic confinement. Our analysis points to distinctive new experimental signatures of the Mott phase. We also calculate noise correlations for the corresponding spin1/2 XY model onto which the HCB system is standardly mapped. Our study shows important differences between the two systems due to the contribution of multiply occupied virtual states in HCBs. Such states do not exist in spin models. An interesting manifestation of such states is the breaking of particle hole symmetry in HCB systems.