Dissipative dynamics of a solid-state qubit coupled to surface plasmons: from non-Markov to Markov regimes

We theoretically study the dissipative dynamics of a quantum emitter placed near the planar surface of a metal supporting surface plasmon excitations. The emitter-metal coupling regime can be tuned by varying some control parameters such as the qubit-surface separation and/or the detuning between characteristic frequencies. By using a Green's function approach jointly with a time-convolutionless master equation, we analyze the non-Markovian dissipative features on the qubit time evolution in two cases of interest: i) an undriven qubit initially prepared in its excited state and ii) the evolution towards a steady-state for a system driven by a laser field. For weak to moderate qubit-metal coupling strength, and on timescales large compared to the surface plasmon oscillation time, a Markovian approximation for the master equation results to be adequate to describe the qubit main optical properties: surface enhancements of rate emission, optical spectra and time-dependent photon-photon correlation functions. The qubit decay shows a crossover passing from being purely dissipative for small qubit-surface distances to plasmon emission for larger separations.