  We study theoretically the properties of a three-photon state prepared inside
a semiconductor cavity, due to the interaction between a quantum dot and an
electromagnetic field, and two consecutive spontaneous parametric
downconversion (SPDC) processes. Thus, we consider a scheme involving three
modes of the electromagnetic field, whose frequencies are given by the SPDC
processes: $\omega_0 \rightarrow \omega_1 + \omega_2$, and $\omega_2
\rightarrow \omega_1 + \omega_1$. Furthermore, we study the low excitation
regime, in which a three-photon state is accessible within the system's
dynamics.
