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arXiv:1701.04440 · Physical review. B./Physical review. B

Non-Markovian dynamics in plasmon-induced spontaneous emission interference

Ioannis Thanopulos, Vassilios Yannopapas, Emmanuel Paspalakis

Published Feb 9, 2017• 67 citations
arXivHTMLPDF

Abstract

We investigate theoretically the non-Markovian dynamics of a degenerate V-type quantum emitter in the vicinity of a metallic nanosphere, a system that exhibits quantum interference in spontaneous emission due to the anisotropic Purcell effect. We calculate numerically the electromagnetic Green's tensor and employ the effective modes differential equation method for calculating the quantum dynamics of the emitter population, with respect to the resonance frequency and the initial state of the emitter, as well as its distance from the nanosphere. We find that the emitter population evolution varies between a gradual total decay and a partial decay combined with oscillatory population dynamics, depending strongly on the specific values of the above three parameters. Under strong-coupling conditions, coherent population trapping can be observed in this system. We compare our exact results with results when the flat continuum approximation for the vacuum modified by the metallic nanosphere is applied. We conclude that the flat continuum approximation is an excellent approximation only when the spectral density of the system under study is characterized by nonoverlapping plasmonic resonances.

DOI
10.1103/physrevb.95.075412

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Optics Letters•Jul 9, 2019•24 citations
We investigate theoretically the non-Markovian dynamics of a degenerate V-type quantum emitter in the vicinity of a metallic nanosphere, a system that exhibits quantum interference in spontaneous emission due to the anisotropic Purcell effect. We calculate numerically the electromagnetic Green's tensor and employ the effective modes differential equation method for calculating the quantum dynamics of the emitter population, with respect to the resonance frequency and the initial state of the emitter, as well as its distance from the nanosphere. We find that the emitter population evolution varies between a gradual total decay and a partial decay combined with oscillatory population dynamics, depending strongly on the specific values of the above three parameters. Under strong-coupling conditions, coherent population trapping can be observed in this system. We compare our exact results with results when the flat continuum approximation for the vacuum modified by the metallic nanosphere is applied. We conclude that the flat continuum approximation is an excellent approximation only when the spectral density of the system under study is characterized by nonoverlapping plasmonic resonances.
We study theoretically the emergence of an anisotropic Purcell factor in random two-dimensional fractal aggregates of nanoparticles. These nanoparticles can either be metallic nanoparticles made of silver, which exhibit surface plasmon resonances, or high-index dielectric nanoparticles like silicon, which possess optical Mie resonances. To calculate the spontaneous emission rates of a quantum emitter, we utilize the electromagnetic Green’s tensor within the framework of the coupled-dipole method. Our findings reveal that the Purcell factor exhibits spatial variations, with certain regions, referred to as hot spots, displaying high values for dipoles oriented within the plane of the fractal aggregate, while dipoles oriented vertically to the aggregate have values close to unity. This anisotropy in the Purcell factor leads to significant quantum interference effects in the spontaneous emission paths of multi-level quantum emitters. As a consequence of this quantum interference, we demonstrate the occurrence of population trapping in a V-type quantum emitter embedded within a fractal aggregate of nanoparticles which cannot otherwise take place if the emitter is placed in vacuum.
A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the excited QE will not relax completely to its ground state and is partially stabilized in its excited state after a long time. We develop some theoretical methods for investigating this problem and show how to form such a bound state and its effect on the non-Markovian decay dynamics. We put forward an efficient numerical approach for calculating the analytical part of the self-energy for frequency below the lower energy threshold. We also propose an efficient formalism for obtaining the long-time value of the excited-state population without calculating the eigenfrequency of the bound state or performing a time evolution of the system, in which the probability amplitude for the excited state in the steady limit is equal to one minus the integral of the evolution spectrum over the positive frequency range. With the above two quantities obtained, we show that the non-Markovian decay dynamics of an initially excited QE can be efficiently obtained by the method based on the Green's function expression for the evolution operator when a bound state exists. A general criterion for identifying the existence of a bound state is presented. The performances of the above methods are numerically demonstrated for a QE located around a metal nanosphere and in a gap plasmonic nanocavity. Numerical results show that these methods work well and the QE becomes partially stabilized in its excited state at a long time for the transition dipole moment beyond its critical value. In addition, it is also found that this critical value is heavily dependent on the distance between the QE and the metal surface, but nearly independent on the size of the nanosphere or the rod. Our methods can be utilized to understand the suppressed decay dynamics for a QE in an open quantum system and provide a general picture on how to form such a bound state.
It has been recently shown that the placement of a three-level V\mathsf{V}V-type quantum emitter in the proximity of metallic nanostructures can create dynamics similar to that of quantum interference in spontaneous emission. Here we continue this work and present results on the population dynamics of a three-level V-type quantum emitter for various initial conditions in the presence of a two-dimensional array of metal-coated dielectric nanospheres.
We study the spontaneous emission of a two-level quantum emitter next to a plasmonic nanoparticle beyond the Markovian approximation and the rotating-wave approximation (RWA) by combining quantum dynamics and classical electromagnetic calculations. For emitters with decay times in the picosecond to nanosecond time regime, as well as located at distances from the nanoparticle up to its radius, the dynamics with and without the RWA and the transition from the non-Markovian to the Markovian regime are investigated. For emitters with longer decay times, the Markov approximation proves to be adequate for distances larger than half the nanoparticle radius. However, the RWA is correct for all distances of the emitter from the nanoparticle. For short decay time emitters, the Markov approximation and RWA are both inadequate, with only the RWA becoming valid again at a distance larger than half the nanoparticle radius. We also show that the entanglement dynamics of two initially entangled qubits interacting independently with the nanoparticle may have a strong non-Markovian character when counter-rotating effects are included. Interesting effects such as entanglement sudden death, periodic entanglement revival, entanglement oscillations, and entanglement trapping are further observed when different initial two-qubit states and different distances between the qubit and the nanoparticle are considered.
Abstract In this work, we analyze the spontaneous emission dynamics of a V‐type quantum emitter near a graphene nanodisk based on the combination of electromagnetic and quantum dynamical calculations. The presence of the graphene nanodisk gives strong anisotropy to the Purcell factors of the quantum emitter, leading to interference effects in spontaneous emission appearing as coupling between the emitter’s upper levels. This effect is further enhanced by the strong light–matter interaction of the quantum emitter with the modified electromagnetic mode continuum, which induces non‐Markovian spontaneous emission dynamics. We have studied the population dynamics of the quantum emitter at a specific distance from the center of the graphene nanodisk for various free‐space decay widths and different quantum emitter’s initial conditions and have shown weak coupling results appearing with Markovian decay dynamics, obtained for quantum emitters with small free‐space decay widths, and population dynamics that exhibits distinctly non‐Markovian features, such as prominent decaying Rabi oscillations in the population evolution of the quantum emitter’s excited states and energy exchange between them during the overall population decay into the photonic mode continuum for largest free‐space decay widths. Also, for the largest value of the free‐space decay width, we obtain significant population trapping effects in the excited states of the quantum emitter. Furthermore, we find that the population dynamics for specific light–matter interaction strength conditions between the quantum emitter and the graphene nanodisk depend distinctively on the initial state of the quantum emitter, whether it is a single state or a superposition state.
We propose a nanophotonic structure that gives high-degree quantum interference (QI) in the spontaneous emission (SE) of a quantum emitter (QE) in conjunction with strong light-matter coupling and non-Markovian dynamics. Specifically, we study the SE dynamics of a three-level V-type QE close to a MoS2 nanodisk (ND). We combine quantum dynamics calculations with electromagnetic calculations and find reversible population dynamics in the QE, together with high-degree QI created by the ND. A rich population dynamics is obtained, depending on the energy of the QE with respect to the energies of the exciton-polariton resonances of the MoS2 ND, the distance of the QE from the ND, and the initial state of the QE. Our results have potential applications in emergent quantum technologies.