Photonic spectral density of coupled optical cavities

We study a pair of anharmonic optical cavities that is connected by an optical fiber. The photonic spectral density characterizes the evolution of the coupled cavities after the system has been prepared in a Fock or N00N state. We evaluate the photonic spectral density within the recursive projection method and find that the anharmonicity leads to a collapse of the low-energy spectrum. The level spacing of the remaining spectrum agrees quite well with that of the harmonic cavities, whereas the spectral weights are strongly affected by the anharmonicity.