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Physica Scripta

Influence of geometric configuration on non-Markovian dynamics and quantum speed limits in a quantum emitter’s spontaneous emission near a multilayer plasmonic nanosphere

Narges Imani, M. Bagheri Harouni

Published Jul 30, 2025• 0 citations
Publisher

Abstract

Abstract In this study, we investigate a hybrid system consisting of a Quantum Emitter (QE) positioned in close proximity to a spherical, Multilayer plasmonic nanostructure (PNS). 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 shell thickness of Core/Shell nanostructure (CSNS), core radius, the nanosphere radius, and the QE-PNS spatial separation distance. Both Silver and Gold, two noble metals, are considered for the nanosphere and shell materials. Our findings show that as the QE-PNS separation distance increases, spontaneous emission dynamics shifts from non-Markovian to Markovian regime. Non-Markovian measures exhibit a rapid increase when the QE is positioned near the PNS, causing a reduction in the QSL, making it shorter than the system’s evolution time. Larger-radius nanospheres sustain non-Markovian dynamics over longer distances, and CSNSs 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.

DOI
10.1088/1402-4896/adf5f3

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Abstract In this study, we investigate a hybrid system consisting of a Quantum Emitter (QE) positioned in close proximity to a spherical, Multilayer plasmonic nanostructure (PNS). 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 shell thickness of Core/Shell nanostructure (CSNS), core radius, the nanosphere radius, and the QE-PNS spatial separation distance. Both Silver and Gold, two noble metals, are considered for the nanosphere and shell materials. Our findings show that as the QE-PNS separation distance increases, spontaneous emission dynamics shifts from non-Markovian to Markovian regime. Non-Markovian measures exhibit a rapid increase when the QE is positioned near the PNS, causing a reduction in the QSL, making it shorter than the system’s evolution time. Larger-radius nanospheres sustain non-Markovian dynamics over longer distances, and CSNSs 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.
Plasmons in nanostructured metals are widely utilized to trigger strong light-matter interactions with quantum light sources. While the nonclassical behavior of such quantum emitters (QEs) is well understood in this context, the role of quantum and surface effects in the plasmonic resonator is usually neglected. Here, we combine the Green's tensor approach with the Feibelman ddd-parameter formalism to theoretically explore the influence of quantum surface effects in metal-dielectric layered nanostructures on the relaxation dynamics of a proximal two-level QE. Having identified electron spill-out as the dominant source of quantum effects in jellium-like metals, we focus our study on sodium. Our results reveal a clear splitting in the emission spectrum, indicative of having reached the strong coupling regime, and, more importantly, non-Markovian relaxation dynamics of the emitter. Our findings establish that strong light-matter coupling is not suppressed by the emergence of nonclassical surface effects in the optical response of the metal.
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.
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 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.
We analyze the spontaneous emission dynamics of a quantum emitter near a topological insulator Bi2Te3 nanosphere, using a combination of electromagnetic calculations and quantum dynamics simulations. For the study of the quantum system dynamics, besides the excited state population dynamics, different non-Markovianity measures are used. We also estimate the quantum speed limit in the system. For large free-space decay rates, the dynamics has strong non-Markovian features, which correlate directly with large values of non-Markovianity measures and possible significant quantum speedup of the dynamics. The dynamical features become gradually Markovian as the free-space decay times become long, while the corresponding non- Markovianity measures tend to zero and the quantum speedup diminishes.
We study theoretically the effects of the presence of a plasmonic nanostructure on free-space spontaneous emission in a four-level quantum system, where one V\mathsf{V}V-type transition is influenced by the interaction with surface plasmons and the other V\mathsf{V}V-type transition occurs in free space. The plasmonic nanostructure that we consider is a two-dimensional array of metal-coated dielectric nanospheres. We show that the spectrum of spontaneous emission in the free-space modes is strongly influenced by the presence of the plasmonic nanostructure, and we explore the dependence of the spectrum on different initial conditions of the quantum system and on the distance from the nanostructure.