Fractional-Time Jaynes-Cummings Model: Unitary Description of its Quantum Dynamics, Inverse Problem and Photon Statistics

Quantum Physics [Submitted on 21 Apr 2026] Fractional-Time Jaynes-Cummings Model: Unitary Description of its Quantum Dynamics, Inverse Problem and Photon Statistics Thiago T. Tsutsui, Danilo Cius, Antonio S. M. de Castro, Fabiano M. Andrade We analyze the quantum dynamics of the fractional-time Jaynes-Cummings model using a recent unitary framework for the fractional-time Schrödinger equation. We examine how the fractional derivative order \alpha influences non-classical features under different initial conditions. For an initial Fock state, fractional evolution introduces transient dynamics and heightened sensitivity to coupling strength. Through an inverse problem approach, we interpret these effects as arising from an effective time-dependent coupling with a strong initial pulse. For an initial coherent state, the fractional order tunes the system between dynamical regimes, with a transition at \alpha = 0.50 where standard collapse-and-revival is replaced by stable, periodic evolution. This regime enhances non-classical field properties, including stronger sub-Poissonian statistics, periodic quadrature squeezing, and the formation of Schrödinger cat states. Comments: 13 pages, 12 figures, comments are welcome Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2604.20001 [quant-ph]   (or arXiv:2604.20001v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.20001 Focus to learn more Submission history From: Fabiano Andrade [view email] [v1] Tue, 21 Apr 2026 21:18:22 UTC (3,712 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)