Entanglement of a System of an Indirectly Linked Two-Coupled-Cavity through an Optical Fiber Cable for Single Excitation Atomic States in the Presence of an External Field

The dynamics of the quantum entropies of a system of two cavities coupled by an optical fiber cable, each cavity contains a two-level atom interacting with a single electromagnetic field in addition to an external classical field, is investigated. Under canonical transformations, the considered Hamiltonian is diagonalized. Effective Hamiltonians in three different limiting regimes: namely large optical fiber cable coupling bstrength, large detunig, and comparable detuning and optical fiber cable coupling strength, are derived. The ith ¯ -tom are respectively prepared in the superposition coherent and the ground states while the fields are prepared in the vacuum states. An analytical expression for the solution of the Schr¨odinger equation for each dispersive is derived. The degree of entanglement (DEM) is studied by using von Neumann atomic entropies. The influences of both the optical fiber cable coupling strength and the detuning on the evolution of the DEM ”their values are closely chosen to be compatible with the imposed restrictions for the applications of the different regimes” are analyzed. General conclusions reached are illustrated by numerical results.