  We study the dynamics of a system composed of two coupled cavities, each
containing a single Rydberg atom. The interplay between Rydberg-Rydberg
interaction and photon hopping enables the transition of the atoms from the
collective ground state to the double Rydberg excitation state by individually
interacting with the hybrid cavity modes and suppressing the up conversion
process between them. The atomic transition is accompanied by the two-photon
absorption and emission of the hybrid modes. Since the energy level structure
of the atom-cavity system is photon number dependent, there is only a pair of
states being in the two-photon resonance. Therefore, the system can act as a
quantum nonlinear absorption filter through the nonclassical quantum process,
converting coherent light field into a non-classical state. Meanwhile, the
vacuum field in the cavity inspires the Rydberg atoms to simultaneously emit
two photons into the hybrid mode, resulting in obvious emission enhancement of
the mode.
