Quantum dynamics of two quantum dots coupled through localized plasmons: An intuitive and accurate quantum optics approach using quasinormal modes

We study the quantum dynamics of two quantum dots (QDs) or artificial atoms coupled through the fundamental localized plasmon of a gold nanorod resonator. We derive an intuitive and efficient time-local master equation, in which the effect of the metal nanorod is taken into consideration self-consistently using a quasinormal mode (QNM) expansion technique of the photon Green function. Our efficient QNM technique offers an alternative and more powerful approach over the standard Jaynes-Cummings model, where the radiative decay, nonradiative decay, and spectral reshaping effect of the electromagnetic environment is rigorously included in a clear and transparent way. We also show how one can use our approach to compliment the approximate Jaynes-Cummings model in certain spatial regimes where it is deemed to be valid. We then present a study of the quantum dynamics and photoluminescence spectra of the two plasmon-coupled QDs. We first explore the non-Markovian regime, which is found to be important only on the ultrashort time scale of the plasmon mode which is about 40 fs. For the field free evolution case of excited QDs near the nanorod, we demonstrate how spatially separated QDs can be effectively coupled through the plasmon resonance and we show how frequencies away from the plasmon resonance can be more effective for coherently coupling the QDs. Despite the strong inherent dissipation of gold nanoresonators, we show that qubit entanglements as large as 0.7 can be achieved from an initially separate state, which has been limited to less than 0.5 in previous work for weakly coupled reservoirs. We also study the superradiance and subradiance decay dynamics of the QD pair. Finally, we investigate the rich quantum dynamics of QDs that are incoherently pumped, and study the polarization dependent behavior of the emitted photoluminescence spectrum where a double-resonance structure is observed due to the strong photon exchange interactions. Our general quantum plasmonics formalism can easily be extended to include multiple QDs interacting through the QNMs of metallic resonator structures, fully accounting for radiative and nonradiative coupling, as well as nonlinear light-matter interaction processes.