{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T02:30:23Z","timestamp":1760149823625,"version":"build-2065373602"},"reference-count":60,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T00:00:00Z","timestamp":1694736000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we present a theoretical scheme for the generation and manipulation of bipartite atom\u2013atom entanglement in a dissipative optomechanical system containing two atoms in the presence of linear and nonlinear (quadratic) couplings. To achieve the goal of paper, we first obtain the interaction Hamiltonian in the interaction picture, and then, by considering some resonance conditions and applying the rotating wave approximation, the effective Hamiltonian, which is independent of time, is derived. In the continuation, the system solution was obtained via solving the Lindblad master equation, which includes atomic, optical and mechanical dissipation effects. Finally, bipartite atom\u2013atom entanglement is quantitatively discussed, by evaluating the negativity, which is a well-known measure of entanglement. Our numerical simulations show that a significant degree of entanglement can be reached via adjusting the system parameters. It is noticeable that the optical and mechanical decay rates play an important role in the quasi-stability and even stability of the obtained atom\u2013atom entanglement.<\/jats:p>","DOI":"10.3390\/sym15091770","type":"journal-article","created":{"date-parts":[[2023,9,17]],"date-time":"2023-09-17T06:36:45Z","timestamp":1694932605000},"page":"1770","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Generation of Stable Entanglement in an Optomechanical System with Dissipative Environment: Linear-and-Quadratic Couplings"],"prefix":"10.3390","volume":"15","author":[{"given":"Mehran","family":"Rafeie","sequence":"first","affiliation":[{"name":"Optics and Laser Group, Faculty of Physics, Yazd University, Yazd P.O. Box 89195-741, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9373-1416","authenticated-orcid":false,"given":"Mohammad Kazem","family":"Tavassoly","sequence":"additional","affiliation":[{"name":"Optics and Laser Group, Faculty of Physics, Yazd University, Yazd P.O. Box 89195-741, Iran"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,9,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1131","DOI":"10.1126\/science.272.5265.1131","article-title":"A \u201cSchr\u00f6dinger Cat\u201d Superposition State of an Atom","volume":"272","author":"Christopher","year":"1996","journal-title":"Science"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"680","DOI":"10.1038\/44348","article-title":"Wave\u2013particle duality of C60 molecules","volume":"401","author":"Nairz","year":"1999","journal-title":"Nature"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1038\/ncomms1263","article-title":"Quantum interference of large organic molecules","volume":"2","author":"Gerlich","year":"2011","journal-title":"Nat. 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