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Continuous measurement of a quantum phase transition in a collective atomic system weakly coupled to a single optical mode

Robert Cook, University of New Mexico

(Session 7 : Saturday from 2:30-3:00)

Abstract. We consider an atomic ensemble that is dispersively coupled to a high finesse optical cavity. The application of cavity assisted Raman transitions generate two body interactions that are symmetrically distributed across the entire ensemble. If the cavity mode rapidly decays to an external field, adiabatic elimination of the cavity produces effective atomic dynamics that are equivalent to a dissipative Lipkin-Meshkov-Glick model, which exhibits a zero temperature quantum phase transition. In the framework of quantum stochastic calculus, we derive the propagator that describes the effective coupling between the collective atomic spin and the external field. We then derive a filter that describes the atomic state conditioned on a continuous measurement of the external field. Finally, we simulate this measurement as the system is tuned though its critical parameter range.