Non-Markovian Nature and Quantum Speed Limit in The Spontaneous Emission Dynamics of a Quantum Emitter in The Vicinity of a Plasmonic Core-shell Nanostructure

A hybrid system including a quantum emitter in the vicinity of a plasmonic core-shell nanostructure in the air is considered, and the spontaneous emission process of the emitter is investigated. The aim is to examine the effect of the plasmonic system on the quantum speed limit and the non-Markovian dynamics of the system. Using the dyadic Green's function of the system, the impact of geometric parameters such as the thickness of the plasmonic nanostructure shell and the distance between the emitter and the nanostructure on the evolution and physical behavior of the desired parameters has been investigated. According to the obtained results, by increasing the distance of the emitter from the nanostructure, the dynamics of spontaneous emission change from non-Markovian to Markovian, and the value of the non-Markovian measure tends to zero. In this condition, the quantum speed limit increases and becomes equal to the evolution time of the system. In addition, as the thickness of the shell increases, the mean value of the non-Markovian measure decreases.