Quantum dynamics and spectra of vibrational Raman-resonance fluorescence in a two-mode cavity

We study the classically driven two-level system with its center-of-mass motion vibrating in a harmonic trap and coupled to the photons in a two-mode cavity. The first mode is resonant to the driving field and an electronic transition. The second mode is off-resonant, forming a vibrational-assisted Raman transition. Using an exact numerical method, we investigate the quantum dynamics of the light emitted by the atom and the cavity modes. We analyze and compare the corresponding atomic and intracavity photon spectra for a range of the driving laser field and the cavity coupling strengths. The results provide better understanding of the effects of the laser field and atom-cavity coupling strengths on quantum interference effects and photon blockade, particularly the Mollow's triplet and the Autler-Townes splitting in the good and bad cavity limits