Influence of Geometric Configuration on Non-Markovian Dynamics and Quantum Speed Limits in a Quantum Emitter’s Spontaneous Emission Near a Multilayer Plasmonic Nanosphere

In this study, we investigate a hybrid system consisting of a Quantum Emitter (QE), or qubit, positioned in close proximity to a spherical, layered plasmonic nanostructure. Our primary focus is on the QE's spontaneous emission dynamics. Employing the dyadic Green tensor, we systematically analyze the influence of different geometries and materials on the system's behavior, with specific emphasis on the Quantum Speed Limit (QSL) and non-Markovian dynamics. Key geometrical parameters explored include the Core-Shell (CS) nanostructure's shell thickness, core radius, the nanosphere's radius, and the distance between the QE and the plasmonic nanostructures. Both Silver and Gold, two noble metals, are considered for the nanosphere and shell materials. Our findings show that as the distance between the QE and the plasmonic nanostructure increases, spontaneous emission dynamics shifts from non-Markovian to Markovian dynamics. Non-Markovian measures exhibit a rapid increase when the QE is positioned near the nanostructure, causing a reduction in the Quantum Speed Limit, making it shorter than the system's evolution time. Larger-radius nanospheres sustain non-Markovian dynamics over longer distances, and CS nanostructures with larger core radii exhibit non-Markovian behavior over extended distances. In addition to the geometrical parameters, the material of the plasmonic subsystem has a crucial influence on the dynamics. So both Gold and Silver shells induce significant Non-Markovian dynamics.