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Based on two-photon exchange interaction between $n$ coupled optical cavitieseach of them containing a single three level atom, the $n$-qubit and$n$-photonic state transfer is investigated. In fact, following the approach ofRef.\cite{Alex1}, we consider $n$ coupled cavities instead of two cavities andgeneralize the discussions about quantum state transfer, photon transitionbetween cavities and entanglement generations between $n$ atoms. More clearly,by employing the consistency of number of photons (the symmetry ofHamiltonian), the hamiltonian of the system is reduced from $3^n$ dimensionalspace into 2n dimensional one. Moreover, by introducing suitable basis for theatom-cavity state space based on Fourier transform, the reduced Hamiltonian isblock-diagonalized, with 2 dimensional blocks. Then, the initial state of thesystem is evolved under the corresponding Hamiltonian and the suitable times$T$ at which the initially unentangled atoms, become maximally entangled, aredetermined in terms of the hopping strength $\xi$ between cavities.

Generation of quantum entanglement between three level atoms via $n$ coupled cavities