Theory of deterministic three-photon down-conversion in ultrastrong cavity QED*

In ultra- and deep-strong cavity quantum electrodynamics (QED) systems, in which the atom-cavity coupling strength is comparable or even larger than the bare transition frequencies of the atom and cavity, many intriguing phenomena that do not conserve the number of excitations are expected to occur. In this study, we theoretically analyze the optical response of an ultrastrong cavity QED system in which an atom is coupled to the fundamental and third harmonic modes of a cavity, and report the possibility of deterministic three-photon down-conversion, in which a single parent photon is converted into triplet photons by reflection from the cavity. In principle, such down-conversion may occur in the usual strong-coupling systems that does not reach the ultrastrong coupling regime. However, considering the required intrinsic loss rates, this phenomenon would be characteristic to the ultrastrong cavity QED.