Rabi-vibronic resonance with large number of vibrational quanta

We study theoretically the Rabi oscillations of a resonantly driven two-level system linearly coupled to a harmonic oscillator (vibrational mode) with frequency, \omega_0. We show that for weak coupling, \omega_p \ll \omega_0, where \omega_p is the polaronic shift, Rabi oscillations are strongly modified in the vicinity of the Rabi-vibronic resonance \Omega_R = \omega_0, where \Omega_R is the Rabi frequency. The width of the resonance is (\Omega_R-\omega_0) \sim \omega_p^{2/3} \omega_0^{1/3} \gg \omega_p. Within this domain of \Omega_R the actual frequency of the Rabi oscillations exhibits a bistable behavior as a function of \Omega_R. Importantly, within the resonant domain, the oscillator is highly excited, which allows to treat it classically.