  The realization of strong nonlinear coupling between single photons has been
a long-standing goal in quantum optics and quantum information science,
promising wide impact applications, such as all-optical deterministic quantum
logic and single-photon frequency conversion. Here, we report an experimental
observation of the strong coupling between a single photon and a photon pair in
an ultrastrongly-coupled circuit-QED system. This strong nonlinear interaction
is realized by introducing a detuned flux qubit working as an effective coupler
between two modes of a superconducting coplanar waveguide resonator. The
ultrastrong light--matter interaction breaks the excitation number
conservation, and an external flux bias breaks the parity conservation. The
combined effect of the two enables the strong one--two-photon coupling. Quantum
Rabi-like avoided crossing is resolved when tuning the two-photon resonance
frequency of the first mode across the single-photon resonance frequency of the
second mode. Within this new photonic regime, we observe the second harmonic
generation for a mean photon number below one. Our results represent a key step
towards a new regime of quantum nonlinear optics, where individual photons can
deterministically and coherently interact with each other in the absence of any
stimulating fields.
