Distributed coherent manipulation of qutrits by virtual excitation processes

We propose a scheme for the deterministic coherent manipulation of two atomic qutrits, trapped in separate cavities coupled through a short optical fibre or optical resonator. We study such a system in the regime of dispersive atom-field interactions, where the dynamics of atoms, cavities and fibre operates through virtual population of both the atomic excited states and photonic states in the cavities and fibre. We show that the resulting effective dynamics allows for the creation of robust qutrit entanglement, and thoroughly investigate the influence of imperfections and dissipation, due to atomic spontaneous emission and photon leakage, on the entanglement of the two qutrits state.