{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T14:14:30Z","timestamp":1760364870918,"version":"build-2065373602"},"reference-count":45,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T00:00:00Z","timestamp":1578614400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We explore the geometric phase in a system of two non-interacting qubits embedded in two separated open cavities linked via an optical fiber and leaking photons to the external environment. The dynamical behavior of the generated geometric phase is investigated under the physical parameter effects of the coupling constants of both the qubit\u2013cavity and the fiber\u2013cavity interactions, the resonance\/off-resonance qubit\u2013field interactions, and the cavity dissipations. It is found that these the physical parameters lead to generating, disappearing and controlling the number and the shape (instantaneous\/rectangular) of the geometric phase oscillations.<\/jats:p>","DOI":"10.3390\/e22010085","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T04:06:51Z","timestamp":1578629211000},"page":"85","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Control of the Geometric Phase in Two Open Qubit\u2013Cavity Systems Linked by a Waveguide"],"prefix":"10.3390","volume":"22","author":[{"given":"Abdel-Baset A.","family":"Mohamed","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Al-Aflaj 710-11912, Saudi Arabia"},{"name":"Faculty of Science, Assiut University, Assiut 71516, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ibtisam","family":"Masmali","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Jazan University, Gizan 82785, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,10]]},"reference":[{"key":"ref_1","unstructured":"Louisell, W.H. (1973). Quantum Statistical Properties of Radiation, Wiley."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"5401","DOI":"10.1103\/PhysRevA.44.5401","article-title":"Intrinsic decoherence in quantum mechanics","volume":"44","author":"Milburn","year":"1991","journal-title":"Phys. Rev. A"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"2444","DOI":"10.1103\/PhysRevA.33.2444","article-title":"Dissipation in a fundamental model of quantum optical resonance","volume":"33","author":"Barnett","year":"1986","journal-title":"Phys. Rev. A"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3433","DOI":"10.1103\/PhysRevA.35.3433","article-title":"Finite-Q cavity electrodynamics: Dynamical and statistical aspects","volume":"35","author":"Puri","year":"1987","journal-title":"Phys. Rev. A"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2006.06.001","article-title":"Decoherence in atomfield interactions: A treatment using superoperator techniques","volume":"432","year":"2006","journal-title":"Phys. Rep."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"3699","DOI":"10.1016\/j.physleta.2008.02.046","article-title":"The effects of thermal photons on entanglement dynamics for a dispersive JaynesCummings model","volume":"372","author":"Obada","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Mohamed, A.-B.A., Hashem, M., and Eleuch, H. (2019). Enhancing the Generated Stable Correlation in a Dissipative System of Two Coupled Qubits inside a Coherent Cavity via Their Dipole-Dipole Interplay. Entropy, 21.","DOI":"10.3390\/e21070672"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"869","DOI":"10.1038\/35002528","article-title":"Geometric quantum computation using nuclear magnetic resonance","volume":"403","author":"Jones","year":"2000","journal-title":"Nature"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"398","DOI":"10.1007\/BF03046095","article-title":"Generalized theory of interference, and its applications","volume":"44","author":"Pancharatnam","year":"1956","journal-title":"Proc. Indian Acad. Sci. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1103\/PhysRevLett.78.755","article-title":"Experimental Separation of Geometric and Dynamical Phases Using Neutron Interferometry","volume":"78","author":"Wagh","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1992","DOI":"10.1103\/PhysRevLett.81.1992","article-title":"Neutron Interferometric Observation of Noncyclic Phase","volume":"81","author":"Wagh","year":"1998","journal-title":"Phys. Rev. Lett."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1098\/rspa.1984.0023","article-title":"Quantal phase factors accompanying adiabatic changes","volume":"392","author":"Berry","year":"1984","journal-title":"Proc. R. Soc. London A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1593","DOI":"10.1103\/PhysRevLett.58.1593","article-title":"Phase change during a cyclic quantum evolution","volume":"58","author":"Aharonov","year":"1987","journal-title":"Phys. Rev. Lett."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2339","DOI":"10.1103\/PhysRevLett.60.2339","article-title":"General Setting for Berry\u2019s Phase","volume":"60","author":"Samuel","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"260402","DOI":"10.1103\/PhysRevLett.93.260402","article-title":"Geometric Phase Distributions for Open Quantum Systems","volume":"93","author":"Marzlin","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1695","DOI":"10.1126\/science.1058835","article-title":"Geometric Manipulation of Trapped Ions for Quantum Computation","volume":"292","author":"Duan","year":"2001","journal-title":"Science"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"032309","DOI":"10.1103\/PhysRevA.66.032309","article-title":"Holonomic quantum computation with neutral atoms","volume":"66","author":"Recati","year":"2002","journal-title":"Phys. Rev. A"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"052321","DOI":"10.1103\/PhysRevA.74.052321","article-title":"Scalable superconducting qubit circuits using dressed states","volume":"74","author":"Liu","year":"2006","journal-title":"Phys. Rev. A"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1630","DOI":"10.1080\/09500340.2015.1058431","article-title":"Geometric phase in cavity QED containing a nonlinear optical medium and a quantum well","volume":"62","author":"Mohamed","year":"2015","journal-title":"J. Mod. Opt."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"2369","DOI":"10.1016\/j.aop.2011.06.005","article-title":"Asymptotic geometric phase and purity for phase qubit dispersively coupled to lossy LC circuit","volume":"326","author":"Mohamed","year":"2011","journal-title":"Ann. Phys."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"023409","DOI":"10.1103\/PhysRevA.82.023409","article-title":"Sensitivity of the population and the Pancharatnam phase for a trapped ion with Stark shift","volume":"82","author":"Bouchene","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1049\/el:19970427","article-title":"Interferometry with Faraday mirrors for quantum cryptography","volume":"33","author":"Zbinden","year":"1997","journal-title":"Electron Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4249","DOI":"10.1103\/PhysRevA.59.4249","article-title":"Distributed quantum computation over noisy channels","volume":"59","author":"Cirac","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1364\/JOSAB.35.000047","article-title":"Generation and robustness of bipartite non-classical correlations in two nonlinear microcavities coupled by an optical fiber","volume":"35","author":"Mohamed","year":"2018","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1178","DOI":"10.1364\/JOSAB.30.001178","article-title":"Implementing discrete quantum Fourier transform via superconducting qubits coupled to a superconducting cavity","volume":"30","author":"Obada","year":"2013","journal-title":"J. Opt. Soc. Am. B"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1007\/s11128-013-0664-z","article-title":"Efficient protocol of N-bit discrete quantum Fourier transform via transmon qubits coupled to a resonator","volume":"13","author":"Obada","year":"2014","journal-title":"Quantum Information Process."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"153602","DOI":"10.1103\/PhysRevLett.94.153602","article-title":"Spin-Dependent Forces on Trapped Ions for Phase-Stable Quantum Gates and Entangled States of Spin and Motion","volume":"94","author":"Haljan","year":"2005","journal-title":"Phys. Rev. Lett."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2659","DOI":"10.1103\/PhysRevA.59.2659","article-title":"Quantum communication with dark photons","volume":"59","author":"Kimble","year":"1999","journal-title":"Phys. Rev. A"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"010503","DOI":"10.1103\/PhysRevLett.96.010503","article-title":"Distributed Quantum Computation via Optical Fibers","volume":"96","author":"Serafini","year":"2006","journal-title":"Phys. Rev. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"042339","DOI":"10.1103\/PhysRevA.79.042339","article-title":"Quantum-information transfer in a coupled resonator waveguide","volume":"79","author":"Li","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"045003","DOI":"10.1088\/2058-9565\/aa868b","article-title":"Deterministic quantum state transfer between remote qubits in cavities","volume":"2","author":"Vogell","year":"2017","journal-title":"Quantum Sci. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1140\/epjd\/e2008-00173-4","article-title":"Noise spectra of microcavity-emitting field in the linear regime","volume":"49","author":"Eleuch","year":"2008","journal-title":"Eur. Phys. J. D"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1140\/epjd\/e2015-60198-0","article-title":"Non-classical effects in cavity QED containing a nonlinear optical medium and a quantum well: Entanglement and non-Gaussanity","volume":"69","author":"Mohamed","year":"2015","journal-title":"Eur. Phys. J. D"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"065101","DOI":"10.1088\/1402-4896\/aa6efb","article-title":"Quantum correlation control for two semiconductor microcavities connected by an optical fiber","volume":"92","author":"Mohamed","year":"2017","journal-title":"Phys. Scr."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"133601","DOI":"10.1103\/PhysRevLett.92.133601","article-title":"Maximally eentangled mixed states: Creation and concentration","volume":"92","author":"Peters","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"022302","DOI":"10.1103\/PhysRevA.97.022302","article-title":"Evolution of tripartite entangled states in a decohering environment and their experimental protection using dynamical decoupling","volume":"97","author":"Singh","year":"2018","journal-title":"Phys. Rev. A"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Cunha, M.M., Fonseca, A., and Silva, E.O. (2019). Tripartite entanglement: Foundations and applications. Universe, 5.","DOI":"10.3390\/universe5100209"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1016\/0034-4877(96)83640-8","article-title":"Geometric phases and related structures","volume":"36","author":"Uhlmann","year":"1995","journal-title":"Rep. Math. Phys."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"080405","DOI":"10.1103\/PhysRevLett.93.080405","article-title":"Kinematic approach to the mixed state geometric phase in nonunitary evolution","volume":"93","author":"Tong","year":"2004","journal-title":"Phys. Rev. Lett."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"023834","DOI":"10.1103\/PhysRevA.85.023834","article-title":"Single-photon absorption in coupled atom-cavity systems","volume":"85","author":"Dilley","year":"2012","journal-title":"Phys. Rev. A"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"033835","DOI":"10.1103\/PhysRevA.88.033835","article-title":"Single-photon storing in coupled non-Markovian atom-cavity system","volume":"88","author":"Shen","year":"2013","journal-title":"Phys. Rev. A"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1211","DOI":"10.1103\/PhysRevLett.60.1211","article-title":"Observation of topological phase by use of a laser interferometer","volume":"60","author":"Bhandari","year":"1988","journal-title":"Phys. Rev. Lett."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"012113","DOI":"10.1103\/PhysRevA.80.012113","article-title":"Measurement of Pancharatnam\u2019s phase by robust interferometric and polarimetric methods","volume":"80","author":"Loredo","year":"2009","journal-title":"Phys. Rev. A"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"034401","DOI":"10.1143\/JPSJ.80.034401","article-title":"Observation of Geometric Phases in Quantum Erasers","volume":"80","author":"Kobayashi","year":"2011","journal-title":"J. Phys. Soc. Jpn."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"5242","DOI":"10.1103\/PhysRevLett.79.5242","article-title":"Quantum Networking with Optical Fibres","volume":"79","author":"Pellizzari","year":"1997","journal-title":"Phys. Rev. Lett."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/85\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T13:29:14Z","timestamp":1760362154000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/1\/85"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,10]]},"references-count":45,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1]]}},"alternative-id":["e22010085"],"URL":"https:\/\/doi.org\/10.3390\/e22010085","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2020,1,10]]}}}