Resonant states reveal strong light-matter coupling in nanophotonic cavities

Photonic resonances are a powerful tool for controlling light-matter interactions. However, unlocking many of the most scientifically intriguing and technologically promising phenomena requires entering the strong coupling regime, where light and matter fully mix, unlocking emergent properties of the coupled states. Nowadays, distinguishing between weak and strong coupling primarily relies on studying the optical response of the hybrid system at real frequencies, which only provides indirect estimates of the underlying resonant dynamics. In contrast, the actual resonances live at complex frequencies. Resolving this contradiction, we show that photonic resonant states provide the framework to unambiguously quantify the strength of light-matter interaction, enabling a rigorous distinction between weak and strong coupling regimes. Assuming a single dominant resonant state of the bare photonic resonator, we derive an effective Hamiltonian that captures the interaction between the photonic resonator and an arbitrary number of material resonances. Our analysis reveals that, unlike most coupled-oscillator models commonly employed in the literature, hybridization not only introduces off-diagonal coupling but also shifts the bare eigenfrequency of the photonic mode. We demonstrate the accuracy of this approach by studying planar and spherical silver resonators filled with a molecular material whose properties were extracted from quantum-chemical simulations. Our work paves the way towards a unified description of light-matter coupling in open photonic environments.