The underlying nonlinear dynamics of strong coupling via entangled dark states

The interplay between dark states and strong coupling remains a crucial aspect of quantum light-matter interactions, offering new pathways for harnessing collective quantum phenomena. A key challenge, however, is understanding the fundamental mechanisms that drive strong coupling and its connection to quantum correlations. Here, we show that strong coupling in a plasmonic system emerges from the entanglement of two dark states, one associated with the uncoupled plasmonic mode and the other a low-energy dark state whose precise nature remains undetermined. Our experiments reveal that this interaction produces hybrid light-matter states through sum- and difference-frequency generation, a nonlinear process known to encode quantum correlations. By applying this framework to prior studies, we recover key system parameters with high accuracy, demonstrating the model's broad applicability. These findings suggest a deeper connection between strong coupling and quantum entanglement, providing new insights into nonlinear optics and quantum coherence. By revealing how dark-state interactions shape hybrid polaritonic states, this work advances the understanding of light-matter interactions and offers a potential pathway toward quantum information technologies.