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An Analysis of the Stationary Operation of Atomic Clocks

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Abstract

We develop an abstract model of atomic clocks that fully describes the dynamics of repeated synchronization between a classical oscillator and a quantum reference. We prove existence of a stationary state of the model and study its dependence on the control scheme, the interrogation time and the stability of the oscillator. For unbiased atomic clocks, we derive a fundamental bound on atomic clocks long time stability for a given local oscillator noise. In particular, we show that for a local oscillator noise with integrated frequency variance scaling as \({T^\alpha}\) for short times T, the optimal clock time variance scales as \({F^{-(\alpha +1)/(\alpha +2)}}\) with respect to the quantum Fisher information, F, associated to the quantum reference. In an attempt to prove the bounds without the unbiasedness assumption, we derive a new Cramer-Rao type inequality.

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  1. 980 Ohlone Ave., Albany, CA, 94706, USA

    Martin Fraas

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  1. Martin Fraas
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Correspondence to Martin Fraas.

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Communicated by A. Winter

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Fraas, M. An Analysis of the Stationary Operation of Atomic Clocks. Commun. Math. Phys. 348, 363–393 (2016). https://doi.org/10.1007/s00220-016-2761-1

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  • DOI: https://doi.org/10.1007/s00220-016-2761-1

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