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Entanglement of a system of indirectly linked two-coupled-cavity through an optical fiber for single excitation atomic states in the presence of external classical fields.

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Abstract

The dynamics of the quantum entropies of a system of two cavities coupled by an optical fiber, each of which contains a two-level atom interacting with a single electromagnetic field in addition to an external classical field, is investigated. The entirely Hamiltonian is simplified within two canonical transformations. Effective Hamiltonians in three different limiting regimes approximations: namely large strength of the optical fiber coupling (SOFC), large detunig, and comparable detuning and SOFC are derived. The distant successive atoms are respectively prepared in the quantum and ground states while all fields are prepared in their vacuum states. The analytical expressions for the solution of the Schrödinger equation in all are derived. The degree of entanglement (DEM) is studied by von Neumann atomic entropies: atom-atom DEM, \(1^{st}\) atom-(the rest subsystems), and , \(2^{nd}\) atom-(the rest subsystems). The influences of both the SOFC and the detuning on the evolutions of the DEM are analyzed. General conclusions reached are illustrated by numerical results.

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Acknowledgements

 This research was supported by Taif University Researchers Supporting Project number (TURSP-2020/17), Taif University, Taif, Saudi Arabia.

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Authors and Affiliations

  1. Department of Basic Science, Faculty of Engineering, Sinai University, Al-Arish, Egypt

    S. A. Hanoura

  2. Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr, Cairo, 11884, Egypt

    M. M. A. Ahmed & A.-S. F. Obada

  3. Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia

    E. M. Khalil

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The dynamics of the DEM functions and the excitations of the different modes is analyzed. The time average effective Hamiltonians are formulated in the framework of the James’s theory. The rate of the energy transfer between the atomic subsystems is controlled by a certain factor which is differ from one dispersive to another.

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Hanoura, S.A., Ahmed, M.M.A., Khalil, E.M. et al. Entanglement of a system of indirectly linked two-coupled-cavity through an optical fiber for single excitation atomic states in the presence of external classical fields.. Opt Quant Electron 54, 823 (2022). https://doi.org/10.1007/s11082-022-03729-1

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