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

Abstract

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.[1], 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 3 n 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.