Disordered ensembles of strongly coupled single-molecule plasmonic picocavities as nonlinear optical metamaterials

We propose to use molecular picocavity ensembles as macroscopic coherent nonlinear optical devices enabled by nanoscale strong coupling. For a generic picocavity model that includes molecular and photonic disorder, we derive theoretical performance bounds for coherent cross-phase modulation signals using weak classical fields of different frequencies. We show that strong coupling of the picocavity {\it vacua} with a specific vibronic sideband in the molecular emission spectrum results in a significant variation of the effective refractive index of the metamaterial relative to a molecule-free scenario, due to a vacuum-induced Autler-Townes effect. For a realistic molecular disorder model, we demonstrate that cross-phase modulation of optical fields as weak as 10 kW/cm$^2$ is feasible using dilute ensembles of molecular picocavities at room temperature, provided that the confined vacuum is not resonantly driven by the external probe field}. Our work paves the way for the development of plasmonic metamaterials that exploit strong coupling for optical state preparation and quantum control.