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.
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.
Most modern quantum light sources are based on spontaneous parametric down-conversion (SPDC) in bulk non-linear crystals, with strict phase-matching requirements that limit their design flexibility and the range of two-photon states produced. Recent research has focused on generating quantum light via SPDC with metasurfaces [1], i.e. array of nanoresonators with sub-wavelength dimensions. At this scale, SPDC becomes independent of phase matching, allowing the use of materials with greater nonlinear susceptibility and enabling efficient photon generation with tailored properties for the angular and spectral distribution and polarization.
Entangled photon-pairs generated through spontaneous parametric down-conversion (SPDC) have evolved into an indispensable resource for various quantum communication, imaging, sensing and computing schemes. While photon-pair sources are so far mostly based on bulk-optical nonlinear components, resonant nonlinear metasurfaces with sub-wavelength thickness have recently been demonstrated as a new platform for photon-pair generation [1]–[3]. Contrary to bulk and integrated nonlinear structures where phase matching steers the pair generation efficiency in different directions and wavelengths, nanostructures can control these properties via their optical resonances. However, the tunability of spatial photon emission in multiple directions remained an open challenge.
Spontaneous parametric down-conversion (SPDC) in subwavelength nanostructures is a promising source of quantum light, owing to its multifunctionality and ability to generate complex quantum states. Nevertheless, the mechanisms governing photon-pair generation in such systems remain only partially understood. In particular, experimental investigations of key emission properties in individual resonators, such as directionality and spectral distribution, are still lacking, and predictive theoretical frameworks have not yet been experimentally validated. Here, we report the first measurement of the directional and spectral distributions of photon pairs generated via SPDC in a nanostructured resonator. Both distributions exhibit resonant behaviour, which we describe using an extended quasi-normal-mode theory. This comparison is enabled by photon-pair count rates of up to 0.45 Hz/mW -- to our knowledge, the highest reported for a nanostructured resonator. Our results provide new physical insight into nanoscale SPDC and represent an important step toward designing of efficient miniaturized quantum light sources.
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.
The aim of this thesis is to explore nonlinear nanostructures – photonic systems with one or more dimension with nanoscale feature size – as new platforms for parametric photon-pair generation. This is motivated by the need for photon-pair sources in many technological applications of quantum optics, such as quantum communication, imaging and computing. The initial hypothesis is that nonlinear nanostructures are a promising platform to complement established photon-pair source schemes based on bulk crystals or photonic integrated circuits in terms of quantum state-engineering, footprint, functional density etc. However, nonlinear pair generation, e.g. via spontaneous parametric down-conversion (SPDC), is a new subfield in nanophotonics with a very limited number of studies existing. This constitutes the knowledge-gap addressed in this thesis. Therefore, the objective is to provide first experimental demonstrations of SPDC in subwavelength-scale and nonlinear nanostructures. We investigate the ability of such systems to control the properties of two-photon quantum states such as frequency and angular spectrum or polarization entanglement. To this end we analyze nanostructures with different degrees of complexity, starting with an unstructured thin crystal with one nanoscale dimension, leading up to a 3D nano-scale resonator with subwavelength-sized features in all dimensions. Furthermore, we test different types of nonlinear materials such as lithium niobate, group III-V semiconductors and emerging, highly nonlinear materials such as molybdenum disulfide. Additionally, we also advance the theoretical understanding by developing a comprehensive model of the quantum process of nonlinear parametric pair-generation in photonic nanostructures.
Miniaturization of nonlinear optical elements is one of the major trends of modern photonics. In particular, in the ‘flatoptics’ geometry, the sample is ultrathin along the light propagation direction. For nonlinear optical effects in such samples, phase matching is satisfied automatically, which allows for the use of materials with giant nonlinear susceptibilities. The tiny thickness reduces the efficiency but it can be compensated for by using geometric and material resonances. Recently also spontaneous parametric down-conversion (SPDC), leading to the generation of entangled photons, has been implemented in ultrasmall sources: subwavelength layers, metasurfaces, even nanoantennas. The lifted constraint of phase matching gives to SPDC even more freedom than to classical frequency conversion effects. The reason is that SPDC, as a spontaneous effect, is stimulated by quantum vacuum fluctuations, which populate all modes uniformly. SPDC in ultrathin samples demonstrates very broad spectral and angular width, extremely high degrees of continuous-variable entanglement, tunable polarization entanglement, and orders of magnitude enhancement of photon pair production rate due to the geometric resonances of dielectric metasurfaces.