Impact of Vibrational Modes in the Plasmonic Purcell Effect of Organic Molecules

By means of quantum tensor network calculations, we investigate the large Purcell effect experienced by an organic molecule placed in the vicinity of a plasmonic nanostructure. In particular, we consider a donor-π bridge-acceptor dye at the gap of two Ag nanospheres. Our theoretical approach allows for a realistic description of the continua of both molecular vibrations and optical nanocavity modes. We analyze both the ultrafast exciton dynamics in the large Purcell enhancement regime and the corresponding emission spectrum, showing that these magnitudes are not accurately represented by the simplified models used up to date. Specifically, both the two-level system model and the single vibrational mode model can only reproduce the dynamics over short time scales, whereas the Fermi's golden rule approach accounts only for the behavior at very long times. We demonstrate that including the whole set of vibrational modes is necessary to capture most of the dynamics and the corresponding spectrum. Moreover, by disentangling the coupling of the molecule to radiative and nonradiative plasmonic modes, we also shed light into the quenching phenomenology taking place in the system.