Large deviations, central limit, and dynamical phase transitions in the atom maser

Girotti, Federico; Van Horssen, Merlijn; Carbone, Raffaella; Guţa, Madalin

Abstract

The theory of quantum jump trajectories provides a new framework for understanding dynamical phase transitions in open systems. A candidate for such transitions is the atom maser, which for certain parameters exhibits strong intermittency in the atom detection counts and has a bistable stationary state. Although previous numerical results suggested that the "free energy"may not be a smooth function, we show that the atom detection counts satisfy a large deviations principle and, therefore, we deal with a phase crossover rather than a genuine phase transition. We argue, however, that the latter occurs in the limit of an infinite pumping rate. As a corollary, we obtain the central limit theorem for the counting process. The proof relies on the analysis of a certain deformed generator whose spectral bound is the limiting cumulant generating function. The latter is shown to be smooth so that a large deviations principle holds by the Gärtner-Ellis theorem. One of the main ingredients is the Krein-Rutman theory, which extends the Perron-Frobenius theorem to a general class of positive compact semigroups.

Citation

Girotti, F., Van Horssen, M., Carbone, R., & Guţa, M. (2022). Large deviations, central limit, and dynamical phase transitions in the atom maser. Journal of Mathematical Physics, 63(6), Article 062202. https://doi.org/10.1063/5.0078916

• Journal Article Type: Article
• Acceptance Date: May 15, 2022
• Online Publication Date: Jun 8, 2022
• Publication Date: Jun 1, 2022
• Deposit Date: Jun 13, 2022
• Publicly Available Date: Jun 14, 2022
• Journal: Journal of Mathematical Physics
• Print ISSN: 0022-2488
• Electronic ISSN: 1089-7658
• Publisher: American Institute of Physics
• Peer Reviewed: Peer Reviewed
• Volume: 63
• Issue: 6
• Article Number: 062202
• DOI: https://doi.org/10.1063/5.0078916
• Keywords: Mathematical Physics; Statistical and Nonlinear Physics
• Public URL: https://nottingham-repository.worktribe.com/output/8493273
• Publisher URL: https://aip.scitation.org/doi/10.1063/5.0078916