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arXiv:1411.3474 · Physical Review A

Parameter estimation by multichannel photon counting

Alexander Holm Kiilerich, Klaus Mølmer

Published Jan 29, 2015• 18 citations
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Abstract

The physical parameters governing the dynamics of a light-emitting quantum system can be estimated from the photon counting signal. The information available in the full detection record can be analyzed by means of the distribution of waiting times between detection events. Our theory allows calculation of the asymptotic, long-time behavior of the sensitivity limit, and it applies to emission processes with branching towards different final states accompanied by the emission of distinguishable photons. We illustrate the theory by application to a laser-driven $\ensuremath{\Lambda}$-type atom.

DOI
10.1103/physreva.91.012119

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The physical parameters governing the dynamics of a light-emitting quantum system can be estimated from the photon counting signal. The information available in the full detection record can be analyzed by means of the distribution of waiting times between detection events. Our theory allows calculation of the asymptotic, long-time behavior of the sensitivity limit, and it applies to emission processes with branching towards different final states accompanied by the emission of distinguishable photons. We illustrate the theory by application to a laser-driven \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ-type atom.
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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The quantum Cramer-Rao bound relates estimation sensitivity in quantum precision measurements to the distinguishability of different quantum states. We show that the theoretical sensitivity limit to parameters that govern the dynamics of an open quantum system coupled to a fully quantized environment can be evaluated from the reduced system master equation. We provide the bound for a laser driven two-state atom, where photon counting and homodyne detection of the fluorescence signal yield different sensitivity to the atomic and field parameters, while none of them exceed our general sensitivity limit.