Multimode cavity-QED systems can be leveraged to explore a wide range of physical phenomena; however, a complex multimode environment makes systematic characterization of light-matter interactions challenging. Here we present a general measurement protocol, applicable to both atomic and synthetic cavity-QED systems, that enables the determination of coupling to individual photonic modes. The method leverages measurements of the AC-Stark and Kerr effects, along with known detuning dependencies, to eliminate the need for single-photon resolution, independent photon-number calibration, or insertion-loss calibration. We demonstrate the method using a superconducting transmon qubit coupled to a one-dimensional microwave resonator lattice. We validate the consistency of the extracted light-matter couplings g determined at multiple qubit detunings, and from the self-Kerr and cross-Kerr shifts for three photon modes, which provide separate measurements of g for each of the three modes.
@article{arxiv.2603.05583,
title = {In-situ Characterization of Light-Matter Coupling in Multimode Circuit-QED Systems},
author = {Kellen O'Brien and Won Chan Lee and Alexandra Behne and Ali Fahimniya and Yu-Xin Wang and Maya Amouzegar and Alexey V. Gorshkov and Alicia J. Kollár},
journal= {arXiv preprint arXiv:2603.05583},
year = {2026}
}