{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:01:34Z","timestamp":1760058094982,"version":"build-2065373602"},"reference-count":67,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T00:00:00Z","timestamp":1741824000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia","award":["PNURSP2025R225"],"award-info":[{"award-number":["PNURSP2025R225"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We introduce a framework presenting the interaction between a four-level atom (F-LA) and a field mode that begins in a coherent state within the para-Bose field (P-BF). The F-LA is considered in a cascade configuration and initially prepared in the upper level. We display the system dynamics by solving the motion equation. We discuss various dynamical behaviors of fundamental quantum resources used in quantum optics and information tasks, including atomic population inversion, quantum entanglement (QE), and the statistical properties of the P-BF based on the parameters of the quantum model. In this context, we demonstrate the impact of various system parameters on these quantum resources. Finally, we illustrate the dynamic relationships among the quantum resources within the model.<\/jats:p>","DOI":"10.3390\/axioms14030211","type":"journal-article","created":{"date-parts":[[2025,3,13]],"date-time":"2025-03-13T06:53:00Z","timestamp":1741848780000},"page":"211","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Interaction of a Four-Level Atom with a Deformed Quantum Field: Mathematical Model and Quantum Resources"],"prefix":"10.3390","volume":"14","author":[{"given":"Mariam","family":"Algarni","sequence":"first","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sayed","family":"Abdel-Khalek","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kamal","family":"Berrada","sequence":"additional","affiliation":[{"name":"Department of Physics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), P.O. Box 90950, Riyadh 11432, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,3,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1063\/1.522937","article-title":"Hilbert spaces of analytic functions and generalized coherent states","volume":"17","author":"Arik","year":"1976","journal-title":"J. Math. 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