Considerable improvement of entanglement swapping by considering multiphoton transitions via cavity quantum electrodynamics method

Recently we studied the effect of photon addition in the initial coherent field on the entanglement swapping which causes some improvements in the process [Soltani et al., Int. J. Mod. Phys. B 31, 1750198 (2017)]. In this paper, we investigate the influence of multiphoton transitions in the atom field interaction based on the cavity quantum electrodynamics on the entanglement swapping and show its considerable constructive effect on this process. The presented model consists of two two-level atoms namely A(1) and A(2) and two distinct cavity fields F-1 and F-2. Initially, the atoms are prepared in a maximally entangled state and the fields in the cavities are prepared in hybrid entangled state of number and coherent states, separately. Making the atom A(2) to interact with the field F-1 (via the generalized Jaynes-Cummings model which allows m-photon transitions between atomic levels in the emission and absorption processes) followed by their detection allows us to arrive at the entanglement swapping from the two atoms A(1), A(2) and the two fields F-1, F-2 to the atom field A(1)-F-2 system. Then, we pay our attention to the time evolution of success probability of detecting processes and fidelity. Also, to determine the amount of entanglement of the generated entangled state in the swapping process, the linear entropy is evaluated and the effect of parameter m concerning the multiphoton transitions on these quantities is investigated, numerically. It is observed that, by increasing the number of photons in the transition process, one may obtain considerable improvement in the relevant quantities of the entanglement swapping. In detail, the satisfactorily acceptable values 1 and 0.5 corresponding to success probability and fidelity are obtained for most of the times during observing of the above-mentioned procedure. We concluded that the presented formalism in this paper is much more advantageous than our presentation model in our earlier work mentioned above.