Strong coupling between a metallic nanoparticle and a single molecule

We theoretically investigate the strong coupling between a single molecule and a single metallic nanoparticle. A theory suited for the quantum-mechanical description of surface plasmon polaritons (SPPs) is developed. The coupling between these SPPs and a single molecule, and the modified molecular dynamics in the presence of the nanoparticle are described within a combined Drude and boundary-element-method approach. Our results show that strong coupling is possible for single molecules and metallic nanoparticles and can be observed in fluorescence spectroscopy through the splitting of emission peaks.

Figure 1

(Color online) (a) Spectrum of cigar-shaped Ag MNP. The height of the particle is $40\mathrm{nm}$ and the height-to-diameter ratio is 5:1. The solid and dashed lines show the calculated spectra for the dielectric function of Ref. 23 and the Drude form (Ref. 28), respectively. The triangles at the bottom indicate the energies of the plasmon modes (d) and (e), and the arrow at $\sim 1.7\mathrm{eV}$ indicates the energy of the molecular state $1$. (b) Nonradiative (solid line) and radiative (dashed-dotted line) decay rates for a molecule located at a certain distance from the MNP [see (c)] in units of the radiative free-space decay rate ${\gamma }_r^0$. The inset reports the level scheme used in our calculations. (c) Discretized particle surface as used in our calculations. [(d)–(f)] Surface charge distribution of SPP eigenmodes of lowest energy. Only mode (d) has a nonzero dipole moment.

Figure 2

(Color online) Simulation for molecule which is initially in state 1 [inset of Fig. 1b]. The solid and dashed lines show the population of the molecular state 1 and the SPP dipole mode [Fig. 1d], respectively, for two different molecule-MNP distances. We use a molecule dipole moment of $10\mathrm{a.u.}$, which corresponds to a free-space decay time $1∕{\gamma }_r^0$ of approximately $1\mathrm{ns}$. In weak coupling (corresponding to the $8\mathrm{nm}$ distance), the nonradiative decay rate can also be estimated from time-dependent perturbation theory, ${\gamma }_{nr}\approx {\mid g_{\lambda }\mid }^2∕{\gamma }_0$, where $g_{\lambda }$ is the coupling constant between the molecule and the resonant plasmon mode. The dotted line in the figure shows the resulting decay. In our simulations, we include the 40 plasmon modes of lowest energy.

Figure 3

(Color online) Fluorescence spectra of the molecule in the vicinity of the MNP for different molecular dipole moments, given in a.u. The moments correspond to free-space decay rates $1∕{\gamma }_r^0$ of approximately (a) $0.1\mu \mathrm{s}$, (b) $4\mathrm{ns}$, and (c) $1\mathrm{ns}$. In the weak-coupling regime of (a), the line broadens with decreasing distance but does not split. In the strong-coupling regime of (b) and (c), the line splits at a given distance into two lines.

Figure 4

(Color online) Line positions and oscillator strengths of polariton modes for cigar-shaped (two lines on left-hand side) and disk-shaped (two lines on right-hand side) nanoparticles and Ag and Au. In Au, the lines split at smaller distances because of the stronger plasmon damping (Ref. 28). We use $d=10\mathrm{a.u.}$.