{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T22:56:47Z","timestamp":1740178607506,"version":"3.37.3"},"reference-count":31,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2022,7,14]],"date-time":"2022-07-14T00:00:00Z","timestamp":1657756800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003407","name":"MIUR","doi-asserted-by":"crossref","award":["PRIN Project 2017SRN-BRK QUSHIP"],"award-info":[{"award-number":["PRIN Project 2017SRN-BRK QUSHIP"]}],"id":[{"id":"10.13039\/501100003407","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"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.<\/jats:p>","DOI":"10.22331\/q-2022-07-14-764","type":"journal-article","created":{"date-parts":[[2022,7,14]],"date-time":"2022-07-14T13:20:11Z","timestamp":1657804811000},"page":"764","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":1,"title":["Statistical time-domain characterization of non-periodic optical clocks"],"prefix":"10.22331","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6862-0511","authenticated-orcid":false,"given":"Dario","family":"Cilluffo","sequence":"first","affiliation":[{"name":"Institute of Theoretical Physics & IQST, Ulm University, Albert-Einstein-Allee 11 89081, Ulm, Germany"},{"name":"Universit$\\grave{a}$ degli Studi di Palermo, Dipartimento di Fisica e Chimica - Emilio Segr\u00e8, via Archirafi 36, I-90123 Palermo, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2022,7,14]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"G. W. Ford. ``The fluctuation-dissipation theorem''. Contemporary Physics 58, 244\u2013252 (2017).","DOI":"10.1080\/00107514.2017.1298289"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Henry Reginald Arnulph Mallock. ``Pendulum clocks and their errors''. Proceeding of the Royal Society A 85 (1911).","DOI":"10.1098\/rspa.1911.0064"},{"key":"2","doi-asserted-by":"crossref","unstructured":"M Kesteven. ``On the mathematical theory of clock escapements''. American Journal of Physics 46, 125\u2013129 (1978).","DOI":"10.1119\/1.11369"},{"key":"3","doi-asserted-by":"publisher","unstructured":"Peter Hoyng. ``Dynamics and performance of clock pendulums''. American Journal of Physics 82, 1053\u20131061 (2014).","DOI":"10.1119\/1.4891667"},{"key":"4","doi-asserted-by":"publisher","unstructured":"S. Ghosh, F. Sthal, J. Imbaud, M. Devel, R. Bourquin, C. Vuillemin, A. Bakir, N. Cholley, P. Abbe, D. Vernier, and G. Cibiel. ``Theoretical and experimental investigations of 1\/f noise in quartz crystal resonators''. 2013 Joint European Frequency and Time Forum International Frequency Control Symposium (EFTF\/IFC)Pages 737\u2013740 (2013).","DOI":"10.1109\/EFTF-IFC.2013.6702262"},{"key":"5","doi-asserted-by":"publisher","unstructured":"G. J. Milburn. ``The thermodynamics of clocks''. Contemporary Physics 61, 69\u201395 (2020).","DOI":"10.1080\/00107514.2020.1837471"},{"key":"6","doi-asserted-by":"publisher","unstructured":"Paul Erker, Mark T. Mitchison, Ralph Silva, Mischa P. Woods, Nicolas Brunner, and Marcus Huber. ``Autonomous quantum clocks: Does thermodynamics limit our ability to measure time?''. Phys. Rev. X 7, 031022 (2017).","DOI":"10.1103\/PhysRevX.7.031022"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Mischa P. Woods. ``Autonomous ticking clocks from axiomatic principles''. Quantum 5, 381 (2021).","DOI":"10.22331\/q-2021-01-17-381"},{"key":"8","doi-asserted-by":"publisher","unstructured":"A. N. Pearson, Y. Guryanova, P. Erker, E. A. Laird, G. A. D. Briggs, M. Huber, and N. Ares. ``Measuring the thermodynamic cost of timekeeping''. Phys. Rev. X 11, 021029 (2021).","DOI":"10.1103\/PhysRevX.11.021029"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Heinz-Peter Breuer and Francesco Petruccione. ``The theory of open quantum systems''. Oxford University Press. (2007).","DOI":"10.1093\/acprof:oso\/9780199213900.001.0001"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Howard M. Wiseman and Gerard J. Milburn. ``Quantum measurement and control''. Volume 9780521804424, pages 1\u2013460. Cambridge university press. (2009).","DOI":"10.1017\/CBO9780511813948"},{"key":"11","doi-asserted-by":"publisher","unstructured":"Serge Haroche and Jean Michel Raimond. ``Exploring the Quantum: Atoms, Cavities, and Photons''. Oxford Univ. Press. Oxford (2006).","DOI":"10.1093\/acprof:oso\/9780198509141.001.0001"},{"key":"12","doi-asserted-by":"publisher","unstructured":"Crispin Gardiner, Peter Zoller, and Peter Zoller. ``Quantum noise: a handbook of markovian and non-markovian quantum stochastic methods with applications to quantum optics''. Springer Science & Business Media. (2004).","DOI":"10.48550\/ARXIV.QUANT-PH\/9702030"},{"key":"13","doi-asserted-by":"publisher","unstructured":"Todd A. Brun. ``Continuous measurements, quantum trajectories, and decoherent histories''. Physical Review A 61 (2000).","DOI":"10.1103\/physreva.61.042107"},{"key":"14","doi-asserted-by":"publisher","unstructured":"Todd A. Brun. ``A simple model of quantum trajectories''. American Journal of Physics 70, 719\u2013737 (2002).","DOI":"10.1119\/1.1475328"},{"key":"15","doi-asserted-by":"publisher","unstructured":"M. B. Plenio and P. L. Knight. ``The quantum-jump approach to dissipative dynamics in quantum optics''. Rev. Mod. Phys. 70, 101\u2013144 (1998).","DOI":"10.1103\/RevModPhys.70.101"},{"key":"16","doi-asserted-by":"publisher","unstructured":"Daniel Manzano and Pablo I Hurtado. ``Symmetry and the thermodynamics of currents in open quantum systems''. Phys. Rev. B 90, 125138 (2014).","DOI":"10.1103\/PhysRevB.90.125138"},{"key":"17","doi-asserted-by":"crossref","unstructured":"VV Belokurov, OA Khrustalev, VA Sadovnichy, and OD Timofeevskaya. ``Conditional density matrix: Systems and subsystems in quantum mechanics'' (2002). url: arxiv.org\/abs\/quant-ph\/0210149.","DOI":"10.1142\/9789812704634_0037"},{"key":"18","doi-asserted-by":"publisher","unstructured":"Vittorio Gorini, Andrzej Kossakowski, and Ennackal Chandy George Sudarshan. ``Completely positive dynamical semigroups of n-level systems''. Journal of Mathematical Physics 17, 821\u2013825 (1976).","DOI":"10.1063\/1.522979"},{"key":"19","doi-asserted-by":"publisher","unstructured":"Goran Lindblad. ``On the generators of quantum dynamical semigroups''. Communications in Mathematical Physics 48, 119\u2013130 (1976).","DOI":"10.1007\/BF01608499"},{"key":"20","doi-asserted-by":"publisher","unstructured":"RS Ellis. ``An overview of the theory of large deviations and applications to statistical mechanics.''. Insurance Mathematics and Economics 3, 232\u2013233 (1996).","DOI":"10.1080\/03461238.1995.10413952"},{"key":"21","doi-asserted-by":"publisher","unstructured":"Hugo Touchette. ``The large deviation approach to statistical mechanics''. Physics Reports 478, 1\u201369 (2009).","DOI":"10.1016\/j.physrep.2009.05.002"},{"key":"22","doi-asserted-by":"publisher","unstructured":"Angelo Vulpiani, Fabio Cecconi, Massimo Cencini, Andrea Puglisi, and Davide Vergni. ``Large deviations in physics''. The Legacy of the Law of Large Numbers (Berlin: Springer) (2014).","DOI":"10.1007\/978-3-642-54251-0"},{"key":"23","doi-asserted-by":"publisher","unstructured":"Juan P Garrahan and Igor Lesanovsky. ``Thermodynamics of quantum jump trajectories''. Phys. Rev. Lett. 104, 160601 (2010).","DOI":"10.1103\/physrevlett.104.160601"},{"key":"24","unstructured":"Charles Jordan and K\u00e1roly Jord\u00e1n. ``Calculus of finite differences''. Volume 33. American Mathematical Soc. (1965)."},{"key":"25","doi-asserted-by":"publisher","unstructured":"Bassano Vacchini. ``General structure of quantum collisional models''. International Journal of Quantum Information 12, 1461011 (2014).","DOI":"10.1142\/s0219749914610115"},{"key":"26","unstructured":"Howard Carmichael. ``An open systems approach to quantum optics: lectures presented at the universit\u00e9 libre de bruxelles, october 28 to november 4, 1991''. Volume 18. Springer Science & Business Media. (2009)."},{"key":"27","doi-asserted-by":"publisher","unstructured":"H. J. Carmichael, Surendra Singh, Reeta Vyas, and P. R. Rice. ``Photoelectron waiting times and atomic state reduction in resonance fluorescence''. Physical Review A 39, 1200\u20131218 (1989).","DOI":"10.1103\/PhysRevA.39.1200"},{"key":"28","unstructured":"A. A. Gangat and G. J. Milburn. ``Quantum clocks driven by measurement'' (2021). arXiv:2109.05390."},{"key":"29","doi-asserted-by":"publisher","unstructured":"James M. Hickey, Sam Genway, Igor Lesanovsky, and Juan P. Garrahan. ``Thermodynamics of quadrature trajectories in open quantum systems''. Physical Review A 86 (2012).","DOI":"10.1103\/physreva.86.063824"},{"key":"30","doi-asserted-by":"publisher","unstructured":"Dario Cilluffo, Salvatore Lorenzo, G Massimo Palma, and Francesco Ciccarello. ``Quantum jump statistics with a shifted jump operator in a chiral waveguide''. Journal of Statistical Mechanics: Theory and Experiment 2019, 104004 (2019).","DOI":"10.1088\/1742-5468\/ab371c"}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-07-14-764\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2022,7,18]],"date-time":"2022-07-18T12:11:39Z","timestamp":1658146299000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2022-07-14-764\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7,14]]},"references-count":31,"URL":"https:\/\/doi.org\/10.22331\/q-2022-07-14-764","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"type":"electronic","value":"2521-327X"}],"subject":[],"published":{"date-parts":[[2022,7,14]]},"article-number":"764"}}