Quantum Dynamics of molecular spontaneous emission process in a complex dielectric environment

Abstract

Molecular spontaneous emission altered by dielectric environments has attracted extensive attention in the area of chemical physics during 1970-1980. Recently, due to remarkable progress in nanotechnology, the spontaneous emission of a single molecule in nanocavities have been experimentally realized, and strong light-matter interactions between molecules and surface plasmon polaritons (SPPs) have been observed. However, in the traditional methods, the molecule is treated as a two-level system and the light field follows the classical Maxwell's Equations. Under such a strong couplings regime, one needs to use a full quantum method to study the dynamics of molecules strongly coupled with SPPs. Therefore, we adopt an advanced technique named macroscopic quantum electrodynamics (mQED) to explore the following subjects: (i) non-Markovian quantum dynamics of a molecule strongly coupled with SPPs. (ii) coherent-to-incoherent transition of molecular fluorescence controlled by the molecule-silver distance. (iii) molecular emission power spectrum in a complex dielectric environment.

When a molecular emitter is near a silver surface, the reabsorption of the emitted photon leads to the non-Markovian dynamics of the molecule. Based on mQED, we propose a theory including molecular vibrations, which is general for molecular fluorescence in the presence of arbitrary inhomogeneous, dispersive, and absorbing media.

Base on the first subject, we further study the quantum dynamics of molecular fluorescence with varying the metal-molecule distance. A clear coherent-to-incoherent transition is observed with increasing the distance. Moreover, in the incoherent regime, we prove that the exponential decay rate predicted by mQED is identical to the rate based on traditional methods. Additionally, we find that the coherent-to-incoherent transition can be controlled by the permittivity of the dielectric spacer.

In the third subject, we derive the formulae of molecular emission power spectra which reflect the quantum dynamics of molecular fluorescence. Furthermore, we prove that it can be divided into the electromagnetic environment factor and the line shape function. To demonstrate the validity of our theory, we obtain the analytical results of the line shape function in two limits. In the incoherent limit, the line shape function follows the Franck-Condon principle. In the coherent limit, the line shape function shows the Rabi splitting.