Initializing a quantum register from Mott-insulator states in optical lattices

We propose a technique to measure multi-spin correlation functions of arbitrary range as determined by the ground states of spinful cold atoms in optical lattices. We show that an observation of the atomic version of the Stokes parameters, using focused lasers and microwave pulsing, can be related to \$n\$-spin correlators. We discuss the possibility of detecting not only ground state static spin correlations, but also time-dependent spin wave dynamics as a demonstrative example using our proposed technique.