Picocavity modal analysis: A multiple-scattering approach for picoscopic mode coupling

Picocavities serve as exceptional platforms for extreme atomic-scale field localization, enabling opportunities for light-matter interactions at subnanometer scales. Here we introduce a scattering-theory-based mode analysis approach to model the interaction between picocavity and nanocavity modes, providing insights into picoscopic field-field dynamics. By employing coupled-mode theory, we specifically investigate the coupling between multiple nanocavity quasinormal modes (QNMs) and a single picocavity QNM, highlighting the development of spectral correlations through mode hybridization. Our findings reveal that the induced hybridization can be controlled by adjusting the picocavity geometry and the frequency spacing of the excited modes. This strong field-field coupling at picoscopic scales leads to spectral mixing, which alters the optical density of states, facilitates the identification of Fano resonances, and produces spectrally stable picocavity modes with modified mode-mixing characteristics. Furthermore, the coupled-mode framework enables the modeling of quantum dynamics resembling the Jaynes-Cummings model, describing the interaction between a hybridized two-level system and a quantized picocavity field. These insights into picoscopic light-matter interactions pave the way for advancements in subnanometer photonic quantum dynamics.