Relaxation dynamics of a quantum emitter resonantly coupled to a coherent state of a localized surface plasmon

We investigate the relaxation dynamics of a quantum dipole emitter (QDE),e.g., a molecule or quantum dot, located near a metal nanoparticle (MNP) exhibiting a dipolar localized surface plasmon (LSP) resonance at the frequency of the QDE radiative transition. A generic three-level QDE, which is pumped with an external laser pulse and thereby brought into an optically active excited state, is considered to be weakly coupled to the resonant LSP described by a coherent state. It is shown that, under the condition of the QDE–MNP characteristic relaxation time being much shorter than that of the QDE in free space but much longer than the LSP lifetime, the QDE relaxation dynamics can be described analytically and feature, in general, non-exponential decay with complicated transient behaviour. The main physical consequence of this relaxation process is that the emission, being largely determined by the MNP, comes out with a substantial delay. It is also shown that energy dissipation in the QDE–MNP system is relatively weak with the probability of the photon emission being ∼0.75, a number which, rather surprisingly, does not explicitly depend on the metal absorption characteristics. A large number of QDE–MNP system parameters in our analytical description open new possibilities for controlling quantum emitter dynamics.