Dynamically controlled superradiant laser for hybrid sensing of collective atomic coherence

We implement dynamic control of a superradiant, cold atom $^{87}$Rb Raman laser to realize the equivalent of conditional Ramsey spectroscopy for sensing atomic phase shifts. Our method uses the non-demolition mapping of the collective quantum phase of an ensemble of two-level atoms onto the phase of a detected cavity light field. We show that the fundamental precision of the non-demolition measurement can theoretically approach the standard quantum limit on phase estimation for a coherent spin state, the traditional benchmark for Ramsey spectroscopy. Finally, we propose a hybrid optical lattice clock based on this method that combines continuous and discrete measurements to realize both high precision and accuracy.