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arXiv:2011.07842 · Physical Review A

Directional emission of down-converted photons from a dielectric nanoresonator

Anna Nikolaeva, Kristina Frizyuk, Nikita A. Olekhno, Alexander S. Solntsev, Mihail I. Petrov

Published Apr 6, 2021• 24 citations
arXivHTMLPDF

Abstract

Creation of entangled photon pairs is one of the key topics in contemporary quantum optics. In the present article, we theoretically describe the generation of photon pairs in the process of spontaneous parametric down-conversion of light by a resonant spherical nanoparticle made of a dielectric material with bulk ${\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\chi}}}^{(2)}$ nonlinearity. We consider the nanoparticle size that satisfies the condition of excitation of resonant eigenmodes described by Mie theory. We demonstrate that a highly directional photon pair generation can be observed utilizing the nonlinear Kerker-type effect, and that this regime provides useful polarization correlations between the emitted photons.

DOI
10.1103/physreva.103.043703

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Creation of entangled photon pairs is one of the key topics in contemporary quantum optics. In the present article, we theoretically describe the generation of photon pairs in the process of spontaneous parametric down-conversion of light by a resonant spherical nanoparticle made of a dielectric material with bulk \ensuremathχ\ifmmode^\elseˆ\fi(2){\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{\ensuremath{\chi}}}^{(2)}\ensuremathχ\ifmmode^\elseˆ\fi​(2) nonlinearity. We consider the nanoparticle size that satisfies the condition of excitation of resonant eigenmodes described by Mie theory. We demonstrate that a highly directional photon pair generation can be observed utilizing the nonlinear Kerker-type effect, and that this regime provides useful polarization correlations between the emitted photons.
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.
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Photon-pair sources based on spontaneous parametric down-conversion (SPDC) are the backbone of a vast number of experimental implementations in quantum optics. Sub-wavelength-sized dielectric nanoresonators have recently emerged as a new platform for the implementation of SPDC sources [1] , that promise much potential in generating photons with engineered properties, as these nanoresonators offer a strong control over many parameters of the scattered light (directionality, polarization, …) However, the many degrees of freedom in these highly multi-modal and non-Hermitian systems makes design and formal description of pair-generation challenging.
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 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 ${\ensuremath{\chi}}^{(2)}$ nanoparticles.