[Paper Review] Nonlinear generation of quantum-entangled photons from high-Q states in dielectric nanoparticles

Alexander N. Poddubny, Daria A. Smirnova|arXiv (Cornell University)|Aug 14, 2018

Plasmonic and Surface Plasmon Research19 references17 citations

TL;DR

This paper proposes resonant enhancement of quantum-entangled photon pair generation in AlGaAs nanodisks via spontaneous parametric downconversion (SPDC) by exciting high-quality (high-Q) quasi-bound states in continuum (BICs). The mechanism relies on multipolar hybridization between magnetic dipole and magnetic octupole modes, which creates a high-Q state at resonance with the pump frequency, leading to a sharp increase in entangled photon emission when signal and idler frequencies sum to the high-Q mode frequency. The enhancement is confirmed by full-wave simulations and a 3-level analytical model.

ABSTRACT

We develop multipolar theory of nonlinear generation of entangled photons from subwavelength dielectric particles due to the spontaneous parametric downconversion. We demonstrate that optical excitation in resonance with the high-quality supercavity mode of the aluminum gallium arsenide (AlGaAs) nanodisk leads to a strong enhancement of generation of entangled photon pairs associated with electric and magnetic dipole modes. Our rigorous numerical results are corroborated by an analytical model, universally describing formation of high-$Q$ resonant states and dark states due to the interference and interplay of the parent multipoles, namely, magnetic dipoles and magnetic octupole. Our findings and description can be instructive for quantum and nonlinear nanophotonics applications.

Motivation & Objective

• To develop a multipolar theory for nonlinear generation of entangled photons in dielectric nanoparticles.
• To demonstrate resonant enhancement of SPDC via high-Q states in AlGaAs nanodisks.
• To explain the multipolar origin of high-Q and dark states through interference of electric and magnetic multipoles.
• To provide a universal analytical model for high-Q and dark states in dielectric nanoparticles.
• To enable efficient, compact, and integrable quantum light sources at the nanoscale.

Proposed method

• Utilizes a rigorous Green-function-based quantum-optical theory for two-photon generation in arbitrary nonlinear nanostructures.
• Employs the t-matrix or extended boundary condition method to model scattering and field distributions in dielectric nanodisks.
• Applies a 3-level analytical model to describe hybridization between magnetic dipole and magnetic octupole modes.
• Uses vector spherical harmonics expansions to decompose electromagnetic fields into multipolar components (J and H functions).
• Calculates nonlinear coupling matrix elements via integrals over the χ(2) susceptibility in the nanodisk volume.
• Performs full-wave numerical simulations for AlGaAs nanodisks with varying aspect ratios (r/h), focusing on M=0 and M=1 modes.

Experimental results

Research questions

• RQ1 How do high-Q resonant states in dielectric nanoparticles enhance entangled photon generation via SPDC?
• RQ2 What is the multipolar origin of high-Q and dark states in subwavelength dielectric nanodisks?
• RQ3 How does hybridization between magnetic dipole and magnetic octupole modes lead to enhanced SPDC efficiency?
• RQ4 Can a universal analytical model describe both high-Q and dark states in dielectric nanoparticles?
• RQ5 What role does angular momentum projection (M) play in the selection rules for entangled photon emission?

Key findings

• A sharp enhancement in entangled photon pair generation is observed when the sum of signal and idler photon frequencies matches the high-Q mode frequency, with a maximum at r/λi + r/λs = 0.2875.
• The SPDC spectrum exhibits a prominent peak at an aspect ratio r/h = 0.71, coinciding with the formation of a high-Q state in the linear scattering spectrum.
• The spectrally integrated degenerate SPDC efficiency increases significantly near r/h = 0.71, as shown in the inset of Figure 6.
• The high-Q state arises from destructive interference between radiation channels due to hybridization of magnetic dipole and magnetic octupole modes.
• The analytical 3-level model successfully describes both high-Q and dark states, generalizing previous 2-state models.
• The two-photon wavefunction shows a sharp maximum when the pump excites the high-Q mode, confirming resonant enhancement of entangled photon emission.