Quantum state transfer by electromagnetic fields initialized in vacuum states in a system comprised of two consecutive cavities connected by an optical fiber in the presence of an external classical field

The Hamiltonian of a system of two successive Jaynes-Cummings cells (JCCs) indirectly coupled through an optical fiber mode under the influence of an external classical field (ECF) is simplified. In the framework of unitary transformations of the atomic and bosonic delocalized operators, the simplification is carried out. Three dispersive regimes, namely, large optical fiber coupling strength (OFCS), large detuning, and comparable OFCS and detuning are considered. The analytical solutions of Schrödinger equation for the different Hamiltonians when the fields are initially in the vacuum states and initially the first and the second atoms are in the excited and the ground states, respectively, are presented. The exploitation of the atomic population inversion function (APIF) of a single atom to the track of the quantum state transfer (QST) between the distant atoms is considered. The temporal evolution of the APIF is investigated. Effects of the external classical fields couplings (ECFCs), and the OFCS on the APIF are analyzed. Analysis of the resulted features based on the difference between the ECFC and the localized and delocalized atomic frequencies is presented. The collapses-revivals phenomenon (CRP) is clearer in absence of the ECF. The behavior of both the APIF and the CRP follow those for the overlap of evanescent fields model while the rates of the QST in the two schemes are un equiv. The ECFs reformulate the initial quantum states and may augment the localized detuning. The ECFs either accelerate the transfer of the quantum state or delecerte it.