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arXiv:1712.09571 · Scientific Reports

Multifrequency multi-qubit entanglement based on plasmonic hot spots

Junfeng Ren, Tong Wu, Xiangdong Zhang

Published Sep 9, 2015• 20 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/srep13941

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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 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.
The Dicke subradiance and superradiance resulting from the interaction between surface plasmons of nanospheres and an ensemble of quantum emitters have been investigated by using a Green's function approach. Based on such an investigation, we propose a scheme for a deterministic multi-qubit quantum phase gate. The case of single sphere has been compared with nanosphere cluster which possesses hot spots. The potential application of present phenomena to the quantum-information processing is anticipated.
Spontaneous emission from ensembles of quantum emitters (QEs) such as atoms, molecules or semiconductor quantum dots can be greatly enhanced by cooperative effects arising from electromagnetic correlations. We describe a cooperative mechanism for emission of light by an ensemble of QEs based upon cooperative energy transfer from QEs to localized surface plasmons in metal-dielectric structures followed by plasmon radiation at a rate that scales with the ensemble size. For large QE ensembles saturating the plasmon mode volume, we derive universal, i.e. independent of local field distribution, expression for cooperative Purcell factor that can by far exceed the field enhancement limits for individual QE in a hot spot. We also derive radiated power spectrum that retains the plasmon resonance lineshape and, in contrast to common cooperative mechanisms, is insensitive to natural variations of QEs' emission frequencies.
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.
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.
In this paper, we study the collective effects which appear as a pair of quantum emitters is positioned in close vicinity to a plasmonic nanoparticle. These effects include multipole-multipole interaction and collective decay, the strengths and rates of which are modified by the presence of the nanoparticle. As a result, entanglement is generated between the quantum emitters, which survives in the stationary state. To evaluate these effects, we exploit the Green's tensor-based quantization scheme in the Markovian limit, taking into account the corrections from light-matter coupling channels higher than the electric dipole. We find these higher-order channels to significantly influence the collective rates and degree of entanglement, and in particular, to qualitatively influence their spatial profiles. Our findings indicate that, apart from quantitatively modifying the results, the higher-order interaction channels may introduce asymmetry into the spatial distribution of the collective response.