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arXiv:2002.05268

Generating ${\rm N00N}$-states of surface plasmon-polariton pairs with a nanoparticle

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

Published Feb 12, 2020• 0 citations
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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 $χ^{(2)}$ response. As a particular example, we study the generation of surface plasmon-polariton pairs with a ${\rm GaAs}$ nanoparticle located at the silver-air interface. We show that for certain excitation geometries, ${\rm N00N}$-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 ${\rm N00N}$-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 ${\rm N00N}$-states of surface waves using spontaneous parametric down-conversion in $χ^{(2)}$ nanoparticles.

DOI
10.48550/arxiv.2002.05268

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Generating N00N{\rm N00N}N00N-states of surface plasmon-polariton pairs with a nanoparticle
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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 ${\ensuremath{\chi}}^{(2)}$ 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.
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.
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.
Surface plasmon polaritons (SPPs) are collective excitations of free electrons propagating along a metal-dielectric interface. Although some basic quantum properties of SPPs, such as the preservation of entanglement, the wave-particle duality of a single plasmon, the quantum interference of two plasmons, and the verification of entanglement generation, have been shown, more advanced quantum information protocols have yet to be demonstrated with SPPs. Here, we experimentally realize quantum state teleportation between single photons and SPPs. To achieve this, we use polarization-entangled photon pairs, coherent photon-plasmon-photon conversion on a metallic subwavelength hole array, complete Bell-state measurements and an active feed-forward technique. The results of both quantum state and quantum process tomography confirm the quantum nature of the SPP mediated teleportation. An average state fidelity of [Formula: see text] and a process fidelity of [Formula: see text], which are well above the classical limit, are achieved. Our work shows that SPPs may be useful for realizing complex quantum protocols in a photonic-plasmonic hybrid quantum network.