Plasmonic Cavity Quantum Dynamics under Linear Vibronic Coupling

Modeling the quantum dynamics of plasmonic excitations -- collective oscillations of free electrons interacting with light -- remains a significant theoretical challenge, particularly due to the need to accurately describe their quantum nature and the role of non-radiative decay channels. At the same time, a reliable theoretical framework is essential for advancing applications ranging from materials design to the development of new quantum optical platforms for quantum technologies. In this work, we address these challenges by introducing a Hermitian formalism based on the linear vibronic coupling (LVC) model for the description of plasmonic excitations in metallic nanostructures. This is parameterized through first-principles calculations -- including but not limited to, the full DFT ground state with tight-binding excited states -- and machine learning techniques using a newly implemented automated platform named Python Plasmonic Cavity (PyPC). The effectiveness of this workflow is demonstrated by successfully reproducing the experimental absorption spectra and vibronic broadening of plasmonic silver nanoparticles containing more than a hundred atoms. Additionally, the population dynamics of plasmonic states are investigated, showing that the LVC model accurately predicts ultrafast lifetimes for bright states and effectively captures the dynamics of dark states.