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

Abstract

We study the nondemolition mapping of collective quantum coherence onto a cavity light field in a superradiant, cold-atom ${}^{87}$Rb 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, $\ensuremath{\Delta}\ensuremath{\phi}=1/\sqrt{N}$, where $N$ is the number of atoms. The associated characteristic measurement time scale ${\ensuremath{\tau}}_{W}\ensuremath{\propto}1/N$ 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 ${\ensuremath{\tau}}_{W}$. 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.