  Considering the two-photon exchange interaction between n coupled cavities
each of them containing a two level atom, the atomic and photonic state
transfer is investigated. In fact, n atom-cavity systems are considered to be
distributed on the nodes of an uncolored Cayley network and interact with each
other via the adjacency matrix of the corresponding network. Then, by employing
the photon-excitation conservation and also the algebraic structure of the
networks, such as irreducible characters of the groups associated with the
networks, some suitable basis for the atom-cavity state space is introduced
based on the corresponding generalized Fourier transform, so that the
Hamiltonian of the whole system, is block diagonalized with two-dimensional
blocks. Then, by solving the corresponding Schrodinger equation exactly,
quantum state transfer and also entanglement generation between the atoms or
the photons are discussed. For instance, the probability amplitudes associated
with the photon transition between the cavities or excitation transition
between the atoms are obtained in terms of the irreducibles characters of the
corresponding network and the hopping parameter ? between the cavities.
