  We calculate the cavity-field distribution in the Wigner representation for
the two-photon resonance of the weakly driven Jaynes-Cummings (JC) oscillator
in its strong-coupling limit. Using an effective four-level system, we
analytically demonstrate the presence of steady-state and transient bimodality
which breaks azimuthal symmetry in phase space. The two steady-state peaks are
located at opposite positions and do not correspond to the two-photon amplitude
of the driven transition. The developing bimodality is portrayed in parallel
with the evolution of the intensity correlation function for the
forwards-scattered photons, before being finally contrasted to the few-photon
steady-state and transient phase-space profiles for the cavity mode in the JC
model driven on resonance.
