Quantum metrology with spin ensembles and collective superradiant decay

Spin ensembles are among the most ubiquitous and versatile kinds of quantum sensors. A standard approach to readout is to couple the ensemble to a detuned cavity and make a dispersive readout. Here we analyze an alternate approach: couple the ensemble resonantly to a cavity, and perform readout by analyzing the output light generated by the resulting superradiant decay. The output light is a complex multi-mode, non-classical field. While previous works have focused on the photon-number content of the emitted temporal modes, here we ask about the information content of the modes. Our work reveals several surprises. In particular, the temporal mode with the most information has a vanishingly small fraction of the total photons emitted. Further, despite the complex multi-mode entanglement of the output photons, quantum-entangled or collective measurements on the light are not required to recover (up to a prefactor) the quantum Fisher information of the initial spin state. We also show how this approach to readout can be used to with standard spin squeezing techniques to perform entanglement-assisted metrology and achieve Heisenberg-limited scaling. Our work has relevance both to quantum sensing experiments in cavity QED setups, as well as those using ensembles of solid-state spins.