Inducing interactions between individual photons is key for photonic quantum information and studying many-body photon states. Superconducting circuits are well suited to combine strong interactions with low losses. Typically, microwave photons are stored in an LC oscillator shunted by a Josephson junction, where the zero-point phase fluctuations across the junction determine the strength and order of photon interactions. Most superconducting nonlinear oscillators operate with small phase fluctuations, where two-photon Kerr interactions dominate. In our experiment, we shunt a high-impedance LC oscillator with a dipole element favoring the tunneling of paired Cooper pairs. This leads to large phase fluctuations of 3.4, accessing a regime where transition frequencies shift non-monotonically with excitation number. From spectroscopy, we extract two-, three-, and four-photon interaction energies, all of similar strength and exceeding the photon loss rate. Our results open a new regime of high-order photon interactions in microwave quantum optics.
@article{arxiv.2312.15075,
title = {Spectral signature of high-order photon processes enhanced by Cooper-pair pairing},
author = {W. C. Smith and A. Borgognoni and M. Villiers and E. Roverc'h and J. Palomo and M. R. Delbecq and T. Kontos and P. Campagne-Ibarcq and B. Douçot and Z. Leghtas},
journal= {arXiv preprint arXiv:2312.15075},
year = {2026}
}