# Statistical time-domain characterization of non-periodic optical clocks

Dario Cilluffo

Institute of Theoretical Physics & IQST, Ulm University, Albert-Einstein-Allee 11 89081, Ulm, Germany
Universit$\grave{a}$ degli Studi di Palermo, Dipartimento di Fisica e Chimica - Emilio Segrè, via Archirafi 36, I-90123 Palermo, Italy

### Abstract

Measuring time means counting the occurrence of periodic phenomena. Over the past centuries a major effort was put to make stable and precise oscillators to be used as clock regulators. Here we consider a different class of clocks based on stochastic clicking processes. We provide a rigorous statistical framework to study the performances of such devices and apply our results to a single coherently driven two-level atom under photodetection as an extreme example of non-periodic clock. Quantum Jump MonteCarlo simulations and photon counting waiting time distribution will provide independent checks on the main results.

Using a simplified optical model, we show that the large deviation formalism of quantum trajectories can be easily exploited to study the performances of a particular class of clocks relying on stochastic clicking processes. The proof of principle presented here provides a clear application of thermodynamics of quantum trajectories to practical problems and, at the same time, it suggests further connections with metrology.

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