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Optics Express

Entanglement of quantum emitters interacting through an ultra-thin noble metal nanodisk

Vasilios D. Karanikolas

Published Jul 12, 2020• 8 citations
Publisher

Abstract

Ultra-thin metallic nanodisks, supporting localized plasmon (LP) modes, are used as a platform to facilitate high entanglement between distant quantum emitters (QEs). High Purcell factors, with values above 103, are probed for a QE placed near to an ultra-thin metallic nanodisk, composed of the noble metals Au, Ag, Al, and Cu. The disk supports two sets of localized plasmon modes, which can be excited by QEs with different transition dipole moment orientations. The two QEs are placed on opposite sides of the nanodisk, and their concurrence is used as a measure of the entanglement. We observe that the pair of QEs remains entangled for a duration that surpasses the relaxation time of the individual QE interacting with the metallic disk. Simultaneously, the QEs reach the entangled steady state faster than in the case where the QEs are in free space. Our results reveal a high concurrence value for a QES separation distance of 60 nm, and a transition energy of 0.8 eV (λ = 1550 nm). The robustness exhibited by this system under study paves the way for future quantum applications.

DOI
10.1364/oe.396268

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•Apr 2, 2015•0 citations
Ultra-thin metallic nanodisks, supporting localized plasmon (LP) modes, are used as a platform to facilitate high entanglement between distant quantum emitters (QEs). High Purcell factors, with values above 103, are probed for a QE placed near to an ultra-thin metallic nanodisk, composed of the noble metals Au, Ag, Al, and Cu. The disk supports two sets of localized plasmon modes, which can be excited by QEs with different transition dipole moment orientations. The two QEs are placed on opposite sides of the nanodisk, and their concurrence is used as a measure of the entanglement. We observe that the pair of QEs remains entangled for a duration that surpasses the relaxation time of the individual QE interacting with the metallic disk. Simultaneously, the QEs reach the entangled steady state faster than in the case where the QEs are in free space. Our results reveal a high concurrence value for a QES separation distance of 60 nm, and a transition energy of 0.8 eV (λ = 1550 nm). The robustness exhibited by this system under study paves the way for future quantum applications.
Ultra-thin noble metal nanodisks facilitate high entanglement between distant quantum emitters (QEs). The ultra-thin noble metal nanodisk supports localized plasmon resonances; when these modes are excited high Purcell factors, of a single QE, and high coupling values, between a pair of QEs, are observed. We present that the entanglement time of the QEs surpasses the relaxation time of the individual QEs interacting with the metallic disk and reach the steady state faster than the case the QE are placed in free-space.
We investigate relaxation dynamics in the system of two identical quantum dipole emitters (QDEs) located near a metal nanoparticle (MNP) exhibiting a dipolar localized surface plasmon (LSP) resonance at the frequency of the QDE radiative transition. Considering one QDE to be brought into an optically active excited state and weakly coupled to the resonant LSP, we show that a stable superposition state of two QDEs is formed during the transition time, which is much shorter than the QDE spontaneous decay time and determined by the efficiency of resonant interaction between the QDEs and induced LSP. It is elucidated that the superposition state is established as a result of redistribution of the energy of the initially excited QDE so that the corresponding steady-state QDE fields induced at the MNP site cancel each other. The degree of steady-state entanglement characterized by the concurrence is found dependent only on the ratio of distances between the QDEs and the MNP, reaching its maximum value of $\ensuremath{\sim}0.65$, when the separation between the MNP and the initially excited QDE is larger by $\ensuremath{\sim}20%$ than the distance from the other QDE to the MNP.
We theoretically investigate the entanglement between two well-separated quantum emitters (QEs) mediated by dark-gap-plasmon waveguides. Both the plasmon-QE coupling strength and the energy transfer efficiency between QEs are crucial for entanglement based on analytical results. To overcome the low energy transfer efficiency brought by common plasmonic waveguides, we construct a simple dark-gap-plasmon waveguide. Such a structure consists of two parallel silver nanowires, where dark plasmon modes are formed in the gap between the two nanowires. The leaky (or radiative) feature of propagating plasmons is highly suppressed, which results in the quality factors of the dark plasmon modes reaching the material limit. Thus, the energy transfer efficiency can reach more than 94% with a distance even over ten working wavelengths ($>10\phantom{\rule{4pt}{0ex}}\textmu{}\mathrm{m}$). Meanwhile, by introducing a tip dimer structure in the nanowire gap, the plasmon-QE coupling can reach a strong coupling regime with realistic parameters. The influences from the geometric parameters of the system are also considered. The energy transfer efficiency is robust to the geometric variations due to the dark feature of the plasmon responses.
We present a novel photonic model that enables an efficient computation of the two-photon Purcell effect of a quantum emitter in the vicinity of an arbitrary photonic structure. Our framework is relevant for the plasmonic nanocavities used to enhance higher-order light-matter interactions, as it goes beyond the dipolar approximation. The computation of Purcell factors through classical electromagnetic simulations determines the influence of the environment without tedious analytic calculations. We demonstrate that placing a hydrogen-like emitter close to a silver nanodisk enhances the transition rate by 5 and 11 orders of magnitude via electric dipole and quadrupole two-photon transitions, respectively. This process has exciting implications for future research, including the potential for efficient entangled two-photon sources.
The theoretical method to study strong coupling between an ensemble of quantum emitters (QEs) and surface plasmons excited by the nanoparticle cluster has been presented by using a rigorous first-principles electromagnetic Green's tensor technique. We have demonstrated that multi-qubit entanglements for two-level QEs can be produced at different coupling resonance frequencies, when they locate in the hot spots of the metallic nanoparticle cluster. The duration of quantum beats for such an entanglement can reach two orders longer than that for the entanglement in a photonic cavity. The phenomenon originates from collective coupling resonance excitation of the cluster. At the frequency of single scattering resonance, the entanglement cannot be produced although the single QE spontaneous decay rate is very big.
We investigate relaxation dynamics of a quantum dipole emitter (QDE), e.g., a molecule or quantum dot, located near a metal nanoparticle (MNP) exhibiting a dipolar localized surface plasmon (LSP) resonance at the frequency of the QDE radiative transition. It is shown that under the condition of the QDE-MNP characteristic relaxation time being much shorter than that of the QDE in free-space but much longer than the LSP lifetime. It is also shown that energy dissipation in the QDE-MNP system is relatively weak with the probability of the photon emission being about 0.75, a number which, rather surprisingly, does not explicitly depend on the metal absorption characteristics. The degree of entanglement measured by the concurrency takes the maximum value, while the distances between the QDEs and metal ball approximately are equal.