  The optical emission spectrum of a quantum dot in strong coupling with the
single mode of a microcavity is obtained in the nonlinear regime. We study how
exciton-exciton interactions alter the emission spectrum of the system,
bringing the linear Rabi doublet into a multiplet structure that is strongly
dependent on the cavity-exciton energy detuning. We emphasise how nonlinearity
can be used to evidence the genuine quantum nature of the coupling by producing
satellites peaks of the Rabi doublet that originate from the quantized energy
levels of the interactions.
