Large two-atom two-photon vacuum Rabi oscillations in a high quality cavity

We predict large cooperative effect involving two atom two photon vacuum Rabi oscillations in a high quality cavity. The two photon emission occurs as a result of simultaneous de-excitation of both atoms with two photon resonance condition $\omega_1+\omega_2\approx \omega_a+\omega_b$, where $\omega_1$, $\omega_2$ are the atomic transition frequencies and $\omega_a$, $\omega_b$ are the frequencies of the emitted photons. The actual resonance condition depends on the vacuum Rabi couplings. The effect can be realized either with identical atoms in a bimodal cavity or with nonidentical atoms in a single mode cavity.