Exact dissipation model for arbitrary photonic Fock state transport in waveguide QED systems

We present an exact dissipation model for correlated photon transport in waveguide QED 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.