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arXiv:2306.00781 · Physical Review Research

Nonperturbative theory of spontaneous parametric down-conversion in open and dispersive optical systems

Aleksa Krstić, Frank Setzpfandt, Sina Saravi

Published Dec 11, 2023• 8 citations
arXivHTMLPDF

Abstract

We develop a nonperturbative formulation based on the Green's function quantization method that can describe spontaneous parametric down-conversion in the high-gain regime in nonlinear optical structures with arbitrary amount of loss and dispersion. This formalism opens the way for description and design of arbitrary complex and/or open nanostructured nonlinear optical systems in quantum technology applications, such as squeezed-light generation, nonlinearity-based quantum sensing, and hybrid quantum systems mediated by nonlinear interactions. As an example case, we numerically investigate the scenario of integrated quantum spectroscopy with undetected photons, in the high-gain regime, and uncover novel gain-dependent effects in the performance of the system.

DOI
10.1103/physrevresearch.5.043228

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We develop a nonperturbative formulation based on the Green's function quantization method that can describe spontaneous parametric down-conversion in the high-gain regime in nonlinear optical structures with arbitrary amount of loss and dispersion. This formalism opens the way for description and design of arbitrary complex and/or open nanostructured nonlinear optical systems in quantum technology applications, such as squeezed-light generation, nonlinearity-based quantum sensing, and hybrid quantum systems mediated by nonlinear interactions. As an example case, we numerically investigate the scenario of integrated quantum spectroscopy with undetected photons, in the high-gain regime, and uncover novel gain-dependent effects in the performance of the system.
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Single-photon and correlated two-photon sources are important elements for optical information systems. Nonlinear downconversion light sources are robust and stable emitters of single photons and entangled photon pairs. However, the rate of downconverted light emission, dictated by the properties of low-symmetry nonlinear crystals, is typically very small, leading to significant constraints in device design and integration. In this Letter, we study principles of spontaneous emission control (i.e., the Purcell effect) generalized to describe the enhancement of nonlinear generation of quantum light through spontaneous parametric downconversion. We develop a theoretical framework based on eigenmode analysis to study quantum nonlinear emission in a general anisotropic, dispersive, and lossy media. Our theory provides an unprecedented insight into the emission process. We find that spontaneous parametric downconversion in a media with hyperbolic dispersion is broadband and phase-mismatch-free. We further predict a significant enhancement of the downconverted emission rate in experimentally realistic nanostructures. Our theoretical formalism and approach to Purcell enhancement of nonlinear optical processes provides a framework for description of quantum nonlinear optical phenomena in complex nanophotonic structures.
Single-photon and correlated two-photon sources are important elements for optical information systems. Nonlinear downconversion light sources are robust and stable emitters of single photons and entangled photon pairs. However, the rate of downconverted light emission, dictated by the properties of low-symmetry nonlinear crystals, is typically very small, leading to significant constrains in device design and integration. In this paper, we show that the principles for spontaneous emission control (i.e. Purcell effect) of isolated emitters in nanoscale structures, such as metamaterials, can be generalized to describe the enhancement of nonlinear light generation processes such as parametric down conversion. We develop a novel theoretical framework for quantum nonlinear emission in a general anisotropic, dispersive and lossy media. We further find that spontaneous parametric downconversion in media with hyperbolic dispersion is broadband and phase-mismatch-free. We predict a 1000-fold enhancement of the downconverted emission rate with up to 105 photon pairs per second in experimentally realistic nanostructures. Our theoretical formalism and approach to Purcell enhancement of nonlinear optical processes, provides a framework for description of quantum nonlinear optical phenomena in complex nanophotonic structures.
Strongly driven nonlinear optical processes such as spontaneous parametric down-conversion and spontaneous four-wave mixing can produce multiphoton nonclassical beams of light which have applications in quantum information processing and sensing. In contrast to the low-gain regime, new physical effects arise in a high-gain regime due to the interactions between the nonclassical light and the strong pump driving the nonlinear process. Here, we describe and experimentally observe a gain-induced group delay between the multiphoton pulses generated in a high-gain type-II spontaneous parametric down-conversion source. Since the group delay introduces distinguishability between the generated photons, it will be important to compensate for it when designing quantum interference devices in which strong optical nonlinearities are required.