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Physical Review A

Radiative coupling and decay dynamics of two two-level quantum emitters in arbitrary dielectric nanostructures

Gengyan Chen, Jingfeng Liu, Renming Liu, Guanghui Liu, Yongzhu Chen, Zhanxu Chen, Xuehua Wang

Published Jan 27, 2020• 4 citations
Publisher

Abstract

Photon-mediated coherent interaction determines the decay dynamics of quantum emitters and facilitates on-chip quantum manipulation for quantum information processing. We derive a general formalism to efficiently and flexibly simulate the radiative coupling between two two-level quantum emitters in arbitrary dielectric nanostructures, based on which, the decay dynamics of the two quantum emitters can be obtained. We demonstrate this formalism to investigate the two quantum dots embedded in the photonic crystal L3 cavity. The anticrossing behavior in the evolution spectrum and the vacuum Rabi oscillation in the populations of the two quantum dots can be simulated in both zero and small dot-dot detuning case. Our formalism can serve as a flexible and efficient theoretical tool and may be further developed to handle the cases for different initial states, multiple quantum emitters, and arbitrary metallic nanostructures.

DOI
10.1103/physreva.101.013828

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Photon-mediated coherent interaction determines the decay dynamics of quantum emitters and facilitates on-chip quantum manipulation for quantum information processing. We derive a general formalism to efficiently and flexibly simulate the radiative coupling between two two-level quantum emitters in arbitrary dielectric nanostructures, based on which, the decay dynamics of the two quantum emitters can be obtained. We demonstrate this formalism to investigate the two quantum dots embedded in the photonic crystal L3 cavity. The anticrossing behavior in the evolution spectrum and the vacuum Rabi oscillation in the populations of the two quantum dots can be simulated in both zero and small dot-dot detuning case. Our formalism can serve as a flexible and efficient theoretical tool and may be further developed to handle the cases for different initial states, multiple quantum emitters, and arbitrary metallic nanostructures.
We propose a general formalism beyond Weisskopf-Wigner approximation to efficiently calculate the coupling matrix element, evolution spectrum and population evolution of two quantum emitters in arbitrary metallic nanostructures. We demonstrate this formalism to investigate the radiative coupling and decay dynamics of two quantum emitters embedded in the two hot spots of three silver nano-spheroids. The vacuum Rabi oscillation in population evolution and the anti-crossing behavior in evolution spectrum show strong radiative coupling is realized in this metallic nanostructure despite its strong plasmon damping. Our formalism can serve as a flexible and efficient calculation tool to investigate the distant coherent interaction in a large variety of metallic nanostructures, and may be further developed to handle the cases for multiple quantum emitters and arbitrary dielectric-metallic hybrid nanostructures.
Abstract Understanding the photon number statistics of a quantum emitter (QE) interacting with complex photonic environments is fundamental to advances in quantum optics and nanophotonics. We introduce a general theoretical framework for calculating the modal photon number density spectrum (MPNDS) in arbitrary dielectric structures with an embedded two-level QE. We validate our approach by investigating a system composed of a two-level QE and a photonic crystal (PhC) slab with an L3 cavity and a waveguide, finding that the MPNDS exhibits significant changes in both waveguide and background radiative channels as the interaction between the QE and modal field transitions from weak coupling to strong coupling. We observe that the number of photons guided along the waveguide shows a strong dependence on the QE’s transition frequency and transition dipole moment, but demonstrates robustness to the transition dipole moment when the transition frequency approaches the waveguide cutoff frequency. Our work allows for the determination and tailoring of light emission characteristics across diverse radiative channels in complex photonic environments.
In recent years, Born-Markov master equations based on tracing out the electromagnetic degrees of freedom have been extensively employed in the description of quantum optical phenomena originating from photon-mediated interactions in quantum emitter ensembles. The breakdown of these effective models, built upon assumptions such as ensemble spectral homogeneity, an unstructured photonic density of states, and weak light-matter coupling, has also recently attracted considerable attention. Here, we investigate the accuracy of this well-established framework beyond the most conventional, and extensively explored, spontaneous emission configuration. Specifically, we consider a system comprising two coherently driven and detuned quantum emitters, embedded within a hybrid photonic-plasmonic cavity, formed by a metallic nanorod integrated into a high-refractive-index dielectric microresonator. The local density of photonic states in this structure exhibits a complex frequency dependence, making it a compelling platform for exploring photon-mediated interactions beyond the assumptions above. We benchmark this modeling approach for the quantum dynamics of the emitter pair against exact calculations based on a macroscopic field quantization formalism, providing an illustrative assessment of its validity in significantly structured and dispersive photonic environments. Our analysis reveals four distinct regimes of laser driving and frequency splitting that lead to markedly different levels of accuracy in the effective model.
The control of interactions among quantum emitters through nanophotonic structures offers significant opportunities for quantum technologies. However, a rigorous theoretical description of the interaction of multiple quantum emitters with complex, dispersive dielectric objects remains challenging. Here, we introduce an approach based on the modified Langevin noise formalism that unveils the roles of both the noise polarization currents of the dielectrics and the vacuum fluctuations of the electromagnetic field scattered by the dielectrics. This work extends Refs. \cite{miano_quantum_2025} and \cite{miano_spectral_2025} to the general case of an arbitrary number of emitters. The proposed approach allows us to describe the dynamics of the quantum emitters for arbitrary initial quantum states of the electromagnetic environment, consisting of two independent bosonic reservoirs, a medium-assisted reservoir and a scattering-assisted reservoir, each characterized by its own spectral density matrix. Specifically, we examine situations where both reservoirs are initially in thermal quantum states but have different temperatures. Understanding how these reservoirs shape the dynamics of the emitters is crucial for understanding light-matter interactions in complex electromagnetic environments and for improving intrinsic emitter properties within structured environments.
We present results on the controlled dynamics of an externally driven four-level quantum emitter coupled to a plasmonic metamaterial, specifically a periodic two-dimensional array of metal-coated dielectric nanospheres. For the study of the system's dynamics, we combine the density matrix approach for the quantum emitter with ab initio electromagnetic calculations for the plasmonic nanostructure. We then present results for the time evolution of the populations of the different levels of the quantum emitter in both the presence and the absence of the plasmonic nanostructure. The dependence of the population dynamics to different distances of the quantum emitter from the plasmonic nanostructure is also studied.
We provide a theoretical study for the dynamical behavior of two-photon Rabi oscillations in two coupled quantum dots. Each dot is a three-level quantum system (ground, one-exciton, and biexciton states). We describe the optical dynamics within the density matrix formalism framework. The two-photon Rabi oscillations are found to be significantly affected by the strength of the interdot dipolar interaction. Using a detuned laser pulse with an exciton state of the driven quantum dot in our numerical simulations, a direct coherent excitation between the biexciton states can be established, but whether Rabi oscillations can be observed depend mainly on the strength of the dipolar interaction and bandwidth of the excitation laser. When the strength of the dipolar coupling is less than the excitation laser bandwidth, the time-dependent populations of the various two biexciton states of the system exhibit coherent oscillations with several frequencies. However, as we increase the dipolar coupling strength, the population transfer between the quantum dots levels amazingly becomes forbidden, and the excitation gets trapped at the initial state. The reduction of the influence of the dipolar interaction leads to a manipulation of two-photon Rabi oscillation in an ultrashort timescale (∼ps), opening possibilities to achieve ultrafast quantum state control and quantum logic gate generation.