Ultrastrong coupling effects in molecular cavity QED

The spectrum and energy dynamics for a system that comprises a molecule interacting with a cavity photon is analyzed, taking into account the effect of both molecular vibrations and counter-rotating terms (CR) in the dipole Hamiltonian. The CR terms do not have a strong effect on the spectrum even for moderately large values of the exciton-photon interaction. However, it is shown that the polariton subspace is governed by an effective Quantum-Rabi Hamiltonian, where polaritons act as a two-level system and the phonons play the role of cavity photons. The effect of the CR terms is amplified in the dynamics: as the vibrations reduce the effective photon-exciton coupling, small Bloch-Siegert energy shifts can bring the system out of resonance.