  We study a pair of anharmonic microwave 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 has no substantial effect on the spectral
properties. In all cases the photonic spectral density has a Gaussian envelope
for large photon numbers.
