systems. This model rigorously incorporates the infinitely many degrees of freedom of the full
three-dimensional photonic scattering channels in the non-excitable ambient environment.
We show that the photon leakages to the scattering channels can be accounted for by a
reduced Hamiltonian and a restricted eigen-state, with a resultant atomic dissipation. This
model is valid for arbitrary photonic Fock and coherent states.