Plasmon-plasmon interactions supported by a one-dimensional plasmonic crystal: Rabi phase and generalized Rabi frequency

Plasmon-plasmon interactions are key in controlling light at the nanoscale and in the development of high-performance plasmonic devices. Sophisticated design and efficient dynamic control of such devices requires a precise description of both spectral responses and ultrafast temporal dynamics in plasmon-plasmon coupling systems. Here, a microscopic model based on the Heisenberg-Langevin formalism is developed for generic plasmon-plasmon interacting systems. The validity of the model was experimentally supported by precisely reproducing the output spectra of interacting plasmons in a one-dimensional plasmonic crystal. We discussed the inheritance from an initial phase to the Rabi phase, which is accompanied by the vacuum fluctuations dephasing the incoherent coupling channel. We further derived the generalized Rabi frequency between two coupled plasmonic modes. We demonstrate that the interplay between the Rabi phase and the coupling-induced incoherent damping process modulates the ultrafast dynamics of the polariton modes, resulting in distinctly different spectral responses including the degeneracy and reversing in the polariton branches. Our model can be readily extended to any other bosonic coupling systems such as interacting nanoparticles and photonic/plasmonic cavities, thus holding great promise and potential applications in nanocircuits and cavity QED.