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Entropy

Interaction and Entanglement of a Pair of Quantum Emitters near a Nanoparticle: Analysis beyond Electric-Dipole Approximation

Miriam Kosik, Karolina Słowik

Published Jan 23, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.3390/e22020135

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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.
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.
Summary form only given. In the pioneering work of Purcell, the possibility to control spontaneous emission lifetimes of quantum emitters by tailoring their electromagnetic surroundings was widely investigated and verified in various types of cavities or band-gap environments. This includes semiconductor microstructures, photonic crystals, and plasmonic nanoparticles. Due to the extraordinary ability of plasmonic nanostructures to confine light into subwavelength spatial domains, steps beyond the paradigmatic electric dipole approximation in the theoretical description of this process may be necessary. In this contribution, we focus on the case of multiple in general nonidentical two-level emitters, sharing the same electromagnetic surroundings, whose local density of states could be tailored by a neighbouring nanostructure. In this case, the surroundings may serve as a long-distance emitter-emitter interaction carrier, or it may trigger collective emission processes, in analogy to Dicke superradiance. We describe these phenomena taking into account the electric dipole, magnetic dipole and electric quadrupole components of light-matter interaction Hamiltonian.
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.
The generation of quantum entanglement is important for a wide range of quantum technology protocols. In nanophotonics, a promising platform for quantum technologies, entanglement generation via plasmon-mediated coupling in quantum dot qubits is often modeled within the dipole limit, where only dipolar plasmons of the mediating nanoparticle are considered, and the local response approximation, where nonlocal corrections are ignored. However, multipolar effects manifest strongly at coupling distances less than the nanoparticle size, while nonlocal optical effects stem from a size-induced dielectric response. We investigated these two important effects in the generation of two-qubit entanglement mediated by plasmonic coupling. A cavity quantum electrodynamic approach is employed, where the induced plasmonic effects lead to modified transition rates in the dynamics of the coupled quantum dot qubits. We find that multipolar modes and size-dependent damping lead to entanglement decay at small coupling distances and limit mediated entanglement with certain particle sizes. We discuss potential implications of multipolar modes in entanglement-based quantum sensing.
Placing quantum emitters close to a metallic nanowire, an effective interaction can be achieved over distances large compared to the resonance wavelength due to the strong coupling between emitters and the surface plasmon modes of the wire. This leads to modified collective decay rates, as well as to Lamb and dipole-dipole shifts. In this paper, we present a general method for calculating these level shifts, which we subsequently apply to the case of a pair of atoms coupled to the guided modes of a nanowire.
This review is devoted to the study of effects of quantum optics in nanostructures. The mechanisms by which the rates of radiative and nonradiative decay are modified are considered in the model of a two-level quantum emitter (QE) near a plasmonic nanoparticle (NP). The distributions of the intensity and polarization of the near field around an NP are analyzed, which substantially depend on the polarization of the external field and parameters of plasmon resonances of the NP. The effects of quantum optics in the system NP + QE plus external laser field are analyzed-modification of the resonance fluorescence spectrum of a QE in the near field, bunching/antibunching phenomena, quantum statistics of photons in the spectrum, formation of squeezed states of light, and quantum entangled states in these systems.