Coupling, lifetimes and "strong coupling" maps for single molecules at plasmonic interfaces.

The interaction between excited states of a molecule and excited states of metal nanostructure (e.g. plasmons) leads to hybrid states with modified optical properties. When plasmon resonance is swept through molecular transition frequency an avoided crossing may be observed, which is often regarded as a signature of strong coupling between plasmons and molecules. Such strong coupling is expected to be realized when $2|U|/{\hbar\Gamma}>1$, where $U$ and ${\Gamma}$ are the molecule-plasmon coupling and the spectral width of the optical transition respectively. Because both $U$ and ${\Gamma}$ strongly increase with decreasing distance between a molecule and a plasmonic structure it is not obvious that this condition can be satisfied for any molecule-metal surface distance. In this work we investigate the behavior of $U$ and ${\Gamma}$ for several geometries. Surprisingly, we find that if the only contributions to ${\Gamma}$ are lifetime broadenings associated with the radiative and nonradiative relaxation of a single molecular vibronic transition, including effects on molecular radiative and nonradiative lifetimes induced by the metal, the criterion $2|U|/{\hbar\Gamma}>1$ is easily satisfied by many configurations irrespective of the metal-molecule distance. This implies that the Rabi splitting can be observed in such structures if other sources of broadening are suppressed. Additionally, when the molecule-metal surface distance is varied keeping all other molecular and metal parameters constant, this behavior is mitigated due to the spectral shift associated with the same molecule-plasmon interaction, making the observation of Rabi splitting more challenging.