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Physical review. B./Physical review. B

Generating N00N states of surface plasmon polaritons with N = 2 by a single nanoparticle

Nikita A. Olekhno, Mihail I. Petrov, Ivan V. Iorsh, Andrey A. Sukhorukov, Alexander S. Solntsev

Published Jun 12, 2024• 2 citations
Publisher

Abstract

We consider a generation of two-particle quantum states in the process of spontaneous parametric down-conversion of light by a dielectric nanoparticle with a bulk ${\ensuremath{\chi}}^{(2)}$ response. As a particular example, we study the generation of surface plasmon polariton pairs with a $\mathrm{GaAs}$ nanoparticle located at the silver-air interface. We demonstrate theoretically that $\mathrm{N}00\mathrm{N}$ states of surface plasmon polariton pairs with $N=2$ can be obtained for certain excitation geometries. The effect can be physically interpreted as the result of a quantum interference between the pairs of induced sources, each emitting either signal or idler plasmons. We then relate the resulting $\mathrm{N}00\mathrm{N}$ pattern to the general symmetry properties of a dyadic Green's function of a dipole emitter exciting surface waves. It renders the considered effect as a general way towards the robust generation of $\mathrm{N}00\mathrm{N}$ states of surface waves using spontaneous parametric down-conversion in ${\ensuremath{\chi}}^{(2)}$ nanoparticles.

DOI
10.1103/physrevb.109.245416

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We consider a generation of two-particle quantum states in the process of spontaneous parametric down-conversion of light by a dielectric nanoparticle with a bulk \ensuremathχ(2){\ensuremath{\chi}}^{(2)}\ensuremathχ(2) response. As a particular example, we study the generation of surface plasmon polariton pairs with a GaAs\mathrm{GaAs}GaAs nanoparticle located at the silver-air interface. We demonstrate theoretically that N00N\mathrm{N}00\mathrm{N}N00N states of surface plasmon polariton pairs with N=2N=2N=2 can be obtained for certain excitation geometries. The effect can be physically interpreted as the result of a quantum interference between the pairs of induced sources, each emitting either signal or idler plasmons. We then relate the resulting N00N\mathrm{N}00\mathrm{N}N00N pattern to the general symmetry properties of a dyadic Green's function of a dipole emitter exciting surface waves. It renders the considered effect as a general way towards the robust generation of N00N\mathrm{N}00\mathrm{N}N00N states of surface waves using spontaneous parametric down-conversion in \ensuremathχ(2){\ensuremath{\chi}}^{(2)}\ensuremathχ(2) nanoparticles.
Generating N00N{\rm N00N}N00N-states of surface plasmon-polariton pairs with a nanoparticle
We consider a generation of two-particle quantum states in the process of spontaneous parametric down-conversion of light by a dielectric nanoparticle with χ(2)χ^{(2)}χ(2) response. As a particular example, we study the generation of surface plasmon-polariton pairs with a GaAs{\rm GaAs}GaAs nanoparticle located at the silver-air interface. We show that for certain excitation geometries, N00N{\rm N00N}N00N-states of surface plasmon-polariton pairs could be obtained. The effect can be physically interpreted as a result of quantum interference between pairs of induced sources, each emitting either signal or idler plasmon. We then relate the resulting N00N{\rm N00N}N00N-pattern to the general symmetry properties of dyadic Green's function of a dipole emitter exciting surface waves. It renders the considered effect as a general way towards a robust generation of N00N{\rm N00N}N00N-states of surface waves using spontaneous parametric down-conversion in χ(2)χ^{(2)}χ(2) nanoparticles.
In the present paper, we theoretically consider the generation of entangled photon pairs in the process of spontaneous parametric downconversion of light by a nonlinear dielectric nanoparticle. This nanoparticle is the only source of nonlinearity in the considered model. We assume that the particle is small compared to the wavelength of light so that the process is non-resonant. An intuitive theoretical description is developed for the case when the nonlinear susceptibility tensor of the material of a nanoparticle has a form of the Levi-Civita symbol. In this case, a two-photon amplitude which characterizes a spatial distribution of entangled photon pairs can be interpreted as a result of interference between two induced dipoles, both being orthogonal to the direction of polarization of the pump photon. A generation of entangled surface plasmon-polaritons by a dielectric nanoparticle located near the metal-dielectric interface is also considered.
We develop a microscopic quantum theory of surface plasmon polaritons valid for arbitrary metal-dielectric geometries. Our framework is based on the Power-Zienau-Woolley representation of quantum electrodynamics, which provides an optimal separation between electronic and photonic degrees of freedom and is therefore particularly well suited for constructing quantum descriptions of polaritonic excitations in strongly dispersive media. Within this formulation, the fundamental electronic oscillator is identified as the bulk plasmon mode, which is nonperturbatively coupled to the radiative continuum of free photon modes. This coupling induces a geometry-dependent renormalization of the bulk plasma frequency, giving rise to confined plasmonic resonances. As specific applications, we recover the localized surface plasmon modes of metallic nanoparticles, including radiative frequency shifts and decay, as well as the exact dispersion relation of propagating surface plasmon polaritons at planar interfaces. Our quantum treatment further reveals that light-matter interactions at metal-dielectric interfaces are inherently in the ultrastrong coupling regime. As a result, in the quasistatic limit, the system exhibits unconventional ground-state quantum fluctuations that can be controlled through the refractive index. These results open new intriguing perspectives in the field of quantum plasmonics.
Energy-time entangled photon pairs (EPPs), which are at the heart of numerous quantum light applications, are commonly generated in nonlinear crystals. Some highly sensitive quantum applications require the use of ultra-broadband entangled photons that cannot be generated in nonlinear crystals due to phase-matching requirements. Here, we investigate the possibility of using metallic nanoparticles (MNPs) as a means for generating entangled photons through spontaneous parametric down-conversion (SPDC). MNPs are known for their strong light-matter coupling at their localized surface plasmon resonance, and since the propagation length through them is negligible relative to optical wavelengths, we consider them as excellent candidates to serve as non-phase matched sources of ultra-broadband entangled photons. To that end, we report experimental results of classical-light second-harmonic generation in silver nanotriangles and nanocubes embedded in polyvinyl alcohol. Based on the results of our experiments, performed using the reference-free hyper-Rayleigh scattering method [A. Ashkenazy et al., J. Phys. B 145401, 2019], we present an estimation of the characteristics of SPDC in MNPs. We show that, despite of the metals' centrosymmetric structure, MNPs exhibit second order nonlinearity that is mainly of an electric dipole nature, and so they are suitable for SPDC. Moreover, we show that localized surface-plasmon resonance can play a significant role in enhancing the generated EPPs flux. Finally, we compare the SPDC capabilities of MNPs to that of commonly used nonlinear crystals and show that the expected EPPs flux from MNPs is weaker but the EPPs have very large bandwidth, which could be helpful for advanced quantum sensing, spectroscopy and communication applications.