Quantum Noise Analysis of Spin Systems Realized with Cold Atoms

We consider the use of quantum noise to characterize many-body states of spin systems realized with ultracold atomic systems. These systems offer a wealth of experimental techniques for realizing strongly interacting many-body states in a regime with a large but not macroscropic number of atoms where fluctuations of an observable such as the magnetization are discernable compared to the mean value. The full distribution function is experimentally relevant and encodes high order correlation functions that may distinguish various many-body states. We apply quantum noise analysis to the Ising model in a transverse field and find a distinctive even versus odd splitting in the distribution function for the transverse magnetization that distinguishes between the ordered, critical, and disordered phases. We also discuss experimental issues relevant for applying quantum noise analysis for general spin systems and the specific results obtained for the Ising model.