Atomic clocks and the continuous-time random-walk

Valerio Formichella (), James Camparo and Patrizia Tavella
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Valerio Formichella: Istituto Nazionale di Ricerca Metrologica
James Camparo: The Aerospace Corporation
Patrizia Tavella: Istituto Nazionale di Ricerca Metrologica

The European Physical Journal B: Condensed Matter and Complex Systems, 2017, vol. 90, issue 11, 1-9

Abstract: Abstract Atomic clocks play a fundamental role in many fields, most notably they generate Universal Coordinated Time and are at the heart of all global navigation satellite systems. Notwithstanding their excellent timekeeping performance, their output frequency does vary: it can display deterministic frequency drift; diverse continuous noise processes result in nonstationary clock noise (e.g., random-walk frequency noise, modelled as a Wiener process), and the clock frequency may display sudden changes (i.e., “jumps”). Typically, the clock’s frequency instability is evaluated by the Allan or Hadamard variances, whose functional forms can identify the different operative noise processes. Here, we show that the Allan and Hadamard variances of a particular continuous-time random-walk, the compound Poisson process, have the same functional form as for a Wiener process with drift. The compound Poisson process, introduced as a model for observed frequency jumps, is an alternative to the Wiener process for modelling random walk frequency noise. This alternate model fits well the behavior of the rubidium clocks flying on GPS Block-IIR satellites. Further, starting from jump statistics, the model can be improved by considering a more general form of continuous-time random-walk, and this could bring new insights into the physics of atomic clocks.

Date: 2017
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DOI: 10.1140/epjb/e2017-80272-7

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