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

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Based on two-photon exchange interaction between n coupled optical cavities each of them containing a single three level atom, the n-qubit and n-photonic state transfer is investigated. In fact, following the approach of Ref.Alex1, we consider n coupled cavities instead of two cavities and generalize the discussions about quantum state transfer, photon transition between cavities and entanglement generations between n atoms. More clearly, by employing the consistency of number of photons (the symmetry of Hamiltonian), the hamiltonian of the system is reduced from 3ⁿ dimensional space into 2n dimensional one. Moreover, by introducing suitable basis for the atom-cavity state space based on Fourier transform, the reduced Hamiltonian is block-diagonalized, with 2 dimensional blocks. Then, the initial state of the system is evolved under the corresponding Hamiltonian and the suitable times T at which the initially unentangled atoms, become maximally entangled, are determined in terms of the hopping strength ξ between cavities.