Active and passive sensing of collective atomic coherence in a superradiant laser

We study the nondemolition mapping of collective quantum coherence onto a cavity light field in a superradiant, cold-atom ⁸⁷Rb Raman laser. We show theoretically that the fundamental precision of the mapping is near the standard quantum limit on phase estimation for a coherent spin state, Δφ=1/√N, where N is the number of atoms. The associated characteristic measurement time scale τW∝1/N is collectively enhanced. The nondemolition nature of the measurement is characterized by only 0.5 photon recoils deposited per atom due to optical repumping in a time τW. We experimentally realize conditional Ramsey spectroscopy in our superradiant Raman laser, compare the results to the predicted precision, and study the mapping in the presence of decoherence, far from the steady-state conditions previously considered. Finally, we demonstrate a hybrid mode of operation in which the laser is repeatedly toggled between active and passive sensing.