Circuit QED systems provide an ideal platform for exploring the strong-coupling regime of multimode cavity QED. Here we present two new phenomena from multimode strong coupling: a circuit Lagrangian analysis which captures beyond tight-binding effects of strong photon-photon coupling and experimental observation of strong wave-mixing resonances in the qubit response. Our circuit analysis reveals qualitatively new features such as emergent band gaps, lifted degeneracies, broadened flat bands, and frequency-dependent hopping. Within the multimode photon environment, strong qubit-photon coupling in turn gives rise to multiphoton processes involving multiple normal modes. We demonstrate a strong four-wave-mixing process involving excitation of a qubit and simultaneous frequency conversion between modes. Notably, this wave-mixing process is dominated by localized flat-band modes of the photonic lattice, which exhibit the strongest coupling to the transmon qubit.
@article{arxiv.2605.00983,
title = {Multimode Strong-Coupling Processes in Circuit QED Lattices},
author = {Won Chan Lee and Ali Fahimniya and Kellen O'Brien and Yu-Xin Wang and Alexandra Behne and Maya Amouzegar and Alexey V. Gorshkov and Alicia J. Kollár},
journal= {arXiv preprint arXiv:2605.00983},
year = {2026}
}