  We present a study of the strong coupling between radiation and matter,
considering a system of two quantum dots, which are in mutual interaction and
interacting with a single mode of light confined in a semiconductor nanocavity.
We take into account dissipative mechanisms such as the escape of the cavity
photons, decay of the quantum dot excitons by spontaneous emission, and
independent exciton pumping. It is shown that the mutual interaction between
the dots can be measured off-resonance, only if the strong coupling condition
is reached. Using the quantum regression theorem, a reasonable definition of
the dynamical coupling regimes is introduced in terms of the complex Rabi
frequency. Finally, the emission spectrum for relevant conditions is presented
and compared with the above definition, demonstrating that the interaction
between the excitons does not affect the Strong Coupling.
