  We propose how to achieve strong photon antibunching effect in a cavity-QED
system coupled with two Rydberg-Rydberg interaction atoms. Via calculating the
equal time second order correlation function g(2)(0), we find that the
unconventional photon blockade and the conventional photon blockade appear in
the atom-driven scheme, and they are both significantly affected by the
Rydberg-Rydberg interaction. We also find that under appropriate parameters,
the photon antibunching and the mean photon number can be significantly
enhanced by combining the conventional photon blockade and the unconventional
photon blockade. In the cavity-driven scheme, the existence of the
Rydberg-Rydberg interaction severely destroys the photon antibunching under the
unconventional photon blockade mechanism. These results will help to guide the
implementation of the single photon emitter in the Rydberg atoms-cavity system.
