Abstract Among the most prominent effects resulting from nonlinear light–matter interaction is the generation of correlated and entangled photons through various processes, notably via spontaneous parametric down‐conversion or spontaneous four‐wave mixing. Such nonlinear optical processes benefit from the concentration of electromagnetic fields in small volumes. Dielectric nanoresonators and their 2D layouts—metasurfaces—provide efficient ways to control light in subwavelength volumes enabling the enhancement of nonlinear light–matter interaction and the generation of entangled photons. Nanoresonators and metasurfaces offer a radical miniaturization of quantum light sources allowing better scalability, which opens a pathway toward arrangements of photon sources in complex subwavelength configurations for advanced photon state control. In this work, the recent progress in this emergent area of research is reviewed.
Abstract Among the most prominent effects resulting from nonlinear light–matter interaction is the generation of correlated and entangled photons through various processes, notably via spontaneous parametric down‐conversion or spontaneous four‐wave mixing. Such nonlinear optical processes benefit from the concentration of electromagnetic fields in small volumes. Dielectric nanoresonators and their 2D layouts—metasurfaces—provide efficient ways to control light in subwavelength volumes enabling the enhancement of nonlinear light–matter interaction and the generation of entangled photons. Nanoresonators and metasurfaces offer a radical miniaturization of quantum light sources allowing better scalability, which opens a pathway toward arrangements of photon sources in complex subwavelength configurations for advanced photon state control. In this work, the recent progress in this emergent area of research is reviewed.
The recent advent of optical metasurfaces, ultra-thin structures composed of nanoresonators facilitating strong light concentration [1–3], opens the path towards efficient \nfrequency conversion [4–7] in a material thousand times thinner than a human hair [8]. \nThere is a remarkable capacity to individually shape each nanoresonator of the metasurface to spatially and spectrally control the conversion process with unprecedented \nnanoscale resolution, facilitating an ultimate flexibility to selectively convert, focus, \nand image different colours with a single metasurface. The strong enhancement of the \nnonlinear processes in dielectric nanoresonators is largely due to the absence of material \nabsorption and the excitation of Mie-type bulk resonances [2]. The highest conversion \nefficiency to date has been achieved employing III-V semiconductor nanostructures, \nsuch as AlGaAs which is a non-centrosymmetric material with high quadratic nonlinear \nsusceptibility. In particular, second-harmonic generation efficiencies up to 10−4 have \nbeen recently demonstrated [8–12], six orders of magnitude higher than in plasmonics. \nSuch capabilities can make an immense fundamental and practical impact, including \nthe quantum state generation in nonlinear metasurfaces as we discuss in this chapter. \nThe quantum state of correlated photon-pairs is the essential building block for photon entanglement [13, 14], which underpins many quantum applications, including secure networks, enhanced measurement and lithography, and quantum information processing [15]. One of the most versatile techniques for the generation of correlated photons is the process of spontaneous parametric down-conversion (SPDC) [16, 17], see \nFig. 1. It allows for an arbitrary choice of energy and momentum correlations between \nthe generated photons, robust operation at room temperature, as well as for spatial and \ntemporal coherence between simultaneously pumped multiple SPDC sources. Alternative approaches based on atom-like single photon emitters, such as solid-state fluorescent atomic defects [18], quantum dots [19, 20], and 2D host materials [21, 22], have \nreached a high degree of frequency indistinguishability, purity and brightness [19, 20]. \nHowever, this comes with the expense of operation at cryogenic temperatures and lack \nof spatial coherence between multiple quantum emitters. These features might limit \npossible applications and reduce the potential for device scalability. Furthermore, the \nsmall size of the atomic sources often requires complex schemes aimed at coupling to \noptical nanoantennas and improving the photon extraction efficiency [21]. \nThe miniaturization of SPDC quantum-light sources to micro and nanoscale dimensions is a continuing quest, as it enables denser integration of functional quantum \ndevices. Traditionally, bulky cm-sized crystals were utilized for SPDC, entailing the \ndifficulty of aligning multiple optical elements after the SPDC crystal, while offering \nrelatively low photon-pair rates [17]. As a first step of miniaturization, SPDC was \nrealized in low-index-contrast waveguides, which allowed confining light down to several square micrometers transversely to the propagation direction, significantly enhancing the conversion efficiency [23]. However, this approach still requires centimetres \nof propagation length, which makes the on-chip integration with other elements challenging [24]. The introduction of high-index contrast waveguides and ring resonators \nallowed for shrinking the sizes necessary for SPDC to millimetres [25], and to tens \nof micrometers [26]. However, further miniaturisation down to the metasurfaces composed of nanoresonators requires conceptually different approaches.
We review the latest advances in the generation of quantum light with nonlinear nanoresonators in metasurfaces, which act both as sources of quantum states and nanoantennas shaping the emitted photons. We outline a general quantum theory of spontaneous photon-pair generation in arbitrary nonlinear photonic structures, including nanoresonators and metasurfaces, which provides an explicit analytical solution for the photon state expressed through the classical Green function. We formulate the correspondence between the quantum photon-pair generation and classical sum-frequency process in nonlinear media, and discuss its application in various contexts, including waveguide circuits and nanostructures. We also discuss the first experimental results demonstrating photon-pair generation in a single nonlinear nanoantenna.
Photon-based polarization entanglement in the form of Bell states and qutrits is an essential tool for understanding complex quantum phenomena and implementing various quantum technologies such as free-space quantum communication and quantum imaging. Polarization-entangled photons are conventionally generated in bulky nonlinear crystals through spontaneous parametric down-conversion (SPDC). In this approach, the photon polarization is intrinsically defined by the nonlinear tensor of the material, restricting the versatility of the generated quantum states. The recent developments of dielectric nanostructures with sub-wavelength thickness called metasurfaces [1] enable miniaturization of quantum light sources, while dramatically enhancing the photon-pair generation and allowing the preparation of complex quantum states with spectral [2] and spatial [3] entanglement. However, optically reconfigurable generation of biphoton polarization states with metasurfaces remained unexplored.
Entangled photons have acted as a workhorse in many quantum technologies, including cryptography, imaging, sensing, and computation. With the growing demands of quantum technology, the entangled photon pair sources are required to be compact and integrable. For the last few years, the field of quantum optics in the nanoscale has demonstrated photon pair generation in ’flat’ optics such as thin layers, Van der Waals crystals, micro-, nano-antennas, and metasurfaces. The word ’flat’ is used because such optical platforms have sub-wavelength thicknesses. Due to the short travel length inside the sources, they can possess multiple functions that their bulky counterparts cannot have. This doctoral thesis addresses photon pair generation in ’flat’ optics via second- and third-order nonlinear processes, which are spontaneous parametric down-conversion (SPDC) and spontaneous four-wave mixing (SFWM). The main aims of the thesis are to understand how the photon pair generation is realized via SPDC and SFWM on subwavelength-scale platforms, and to make a bridge between photon pair generation via two nonlinear processes under the presence of optical resonances. The thesis covers two experimental parts related to SPDC and SFWM, and one future expectation of the SFWM in metamaterials. The first part of the thesis addresses one of the multi-functionalities that has recently been reported: the emission direction control of the photon pairs. A 150 nm-thick gallium phosphide (GaP) metasurface is used as a source. The metasurface supports a quasi-bound state in the continuum (quasi-BIC) resonance, enhancing the electric field inside the material. I generate the entangled photons through the SPDC process. The generated photons are in two different wavelengths under the given pump wavelength: signal photon at the resonance, and idler photon out of the resonance. The photon pair generation rate is enhanced by 66 times compared to the unpatterned GaP slab since the vacuum field in the signal mode is enhanced by the resonance. The generated photons obey the transmission spectrum of the metasurface. As a result, the signal photons at resonance are mostly reflected, and the idler photons are transmitted after generation. This result is the first work of photon demultiplexing by a metasurface. The second part of the thesis covers the photon pair generation through SFWM in thin nonlinear films. Silicon-rich silicon nitride (SiN) layers are selected as the sources. The layers have an intriguing characteristic that the third-order nonlinear susceptibility (chi-3) differs with the nitrogen doping rate. I generate the photon pairs through chi-3 variant SiN layers. The thicknesses of the samples are all sub-wavelength level, having a few hundred nanometers. Time-energy correlation measurements are conducted for all samples, and the second-order correlation functions (g(2)(0)) are calculated. The maximum g(2)(0) of the samples exceeds 2. Interestingly, I observed two-photon interference effects between photon pairs generated in the layers and the fused-silica substrate, which allows me to estimate the chi-3 values of the samples by knowing the reference: chi-3 value of the substrate. The last part of the thesis introduces designs of metasurfaces and possible experimental schemes for photon pair generation through SFWM. Yet, due to its weak light-matter interaction in third-order nonlinear processes, the photon pair generation through SFWM has not been observed in metasurfaces. However, it is fairly possible to enhance the vacuum fields at the output photon modes and generate photon pairs because preliminary work in unpatterned slabs has already been observed in this thesis. Finally, I introduce a fabricated metasurface. It needs improvements, but it is quite promising for the ongoing project.
Quantum state engineering, the cornerstone of quantum photonic technologies, mainly relies on spontaneous parametric downconversion and four-wave mixing, where one or two pump photons spontaneously decay into a photon pair. Both of these nonlinear effects require momentum conservation for the participating photons, which strongly limits the versatility of the resulting quantum states. Nonlinear metasurfaces have subwavelength thickness and allow the relaxation of this constraint; when combined with resonances, they greatly expand the possibilities of quantum state engineering. Here, we generated entangled photons via spontaneous parametric downconversion in semiconductor metasurfaces with high-quality factor, quasi-bound state in the continuum resonances. By enhancing the quantum vacuum field, our metasurfaces boost the emission of nondegenerate entangled photons within multiple narrow resonance bands and over a wide spectral range. A single resonance or several resonances in the same sample, pumped at multiple wavelengths, can generate multifrequency quantum states, including cluster states. These features reveal metasurfaces as versatile sources of complex states for quantum information.