Abstract
Detection of radiation signals is at the heart of precision metrology and sensing. In this article we show how the fluctuations in photon-counting signals can be exploited to optimally extract information about the physical parameters that govern the dynamics of the emitter. For a simple two-level emitter subject to photon counting, we show that the Fisher information and the Cram\'er-Rao sensitivity bound based on the full detection record can be evaluated from the waiting-time distribution in the fluorescence signal which can, in turn, be calculated for both perfect and imperfect detectors by a quantum trajectory analysis. We provide an optimal estimator achieving that bound.
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