Atomic and Photonic Entanglement Generation in n Coupled Atom-Cavity Systems

Abstract

Based on two-photon Jaynes-Cummings Hamiltonian for the n coupled optical cavities each of them containing a single three level atom, the n-qubit and n-photonic state transfer between the corresponding atoms and cavities is investigated. In fact, we consider that the cavities are located at the nodes (vertices) of the complete network (graph) K n at which all of the nodes are connected, so that the cavities are interact with each other (via two photon exchange) completely. Then, quantum state transfer, photon transition between cavities and entanglement generations between n atoms are discussed. More clearly, by employing the consistency of number of photons and atomic excitations (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.