Fig. 4: Quantum simulations of the plasmon-QD coupling dynamics.

a Schematic level diagram describing the theoretical model. The plasmonic cavity is depicted on the left with an excited state of energy \(\omega _{pl}.\) The QD (right) is described as a three-level electronic system containing a ground state \(|{\mathrm{g}}\rangle\), a bright excitonic level, \(|{\mathrm{e}}_{\mathrm{B}}\rangle\), and a dark excitonic level, \(|{\mathrm{e}}_{\mathrm{D}}\rangle\). The bright (dark) excitonic transition occurs at energy \(\omega _{\mathrm{B}}\)(\(\omega _{\mathrm{D}}\)). For the PL spectrum. we assume that both the bright and the dark excitons are pumped incoherently. Plasmon–exciton coupling is described within the Jaynes–Cummings model with rates \(g_{\mathrm{B}}\) and \(g_{\mathrm{D}}\) (for coupling of the bright and dark exciton, respectively). A detailed description of the model terms is provided in the Methods section, and the parameters used are given in Table 1. b Emission (red), scattering (green), and absorption (blue) spectra calculated theoretically for parameters shown in Table 1. The dashed line marks the energy of the dark exciton, \(\hbar \omega _{\mathrm{D}}\). c A simulated g⁽²⁾(t) features a two-component decay. Inset shows a zoom of the fast (fs) decay of the system excitations that is not resolved on the ns time scale.