High-impedance microwave resonators with two-photon nonlinear effects

Nonlinear effects play a central role in photonics as they form the foundation for most of the device functionalities such as amplification and quantum state preparation and detection. Typically the nonlinear effects are weak and emerge only at high photon numbers with strong drive. Here we present an experimental study of a Josephson junction -based high-impedance resonator. We show that by taking the resonator to the limit of consisting effectively only of one junction, results in strong nonlinear effects already for the second photon while maintaining a high impedance of the resonance mode. Our experiment yields thus resonators with strong interactions both between individual resonator photons and from the resonator photons to other electric quantum systems. We also present an energy diagram technique which enables to measure, identify and analyse different multi-photon optics processes along their energy conservation lines.