In the last few years, materials with strong second-order optical nonlinearity such as gallium arsenide, barium titanate and transition metal dichalcogenides have attracted significant attention, because they for the first time allowed efficient nonlinear optical interactions on the sub-micron scales. One of such nonlinear optical interactions - spontaneous parametric down-conversion (SPDC) - allows the generation of pairs of correlated photons and can enable photon entanglement. This is the foundation of many quantum optical applications ranging from secure communication to ultrafast quantum computing. The key challenges in this field are efficiency and the generation of on-demand quantum states.
In the last few years, materials with strong second-order optical nonlinearity such as gallium arsenide, barium titanate and transition metal dichalcogenides have attracted significant attention, because they for the first time allowed efficient nonlinear optical interactions on the sub-micron scales. One of such nonlinear optical interactions - spontaneous parametric down-conversion (SPDC) - allows the generation of pairs of correlated photons and can enable photon entanglement. This is the foundation of many quantum optical applications ranging from secure communication to ultrafast quantum computing. The key challenges in this field are efficiency and the generation of on-demand quantum states.
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.
Quantum states of light, such as single photons, pairs of entangled photons, and squeezed light are a key resource for photonic quantum technologies. All these states can be obtained via the nonlinear optical effect of spontaneous parametric down-conversion (SPDC). In SPDC, a higher-energy photon of a coherent beam (pump) splits in two lower-energy daughter photons, called signal and idler. The photons of such a pair can be entangled in polarization, time/frequency, and position/momentum. Efficient generation of photon pairs requires a high second-order susceptibilityχ(2)of the material where it occurs, and the phase matching between the pump and the down-converted photons.
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 promises of quantum computing is to enable faster and more powerful computation than would ever be possible with a classical processor based on binary logic. Quantum linear optics is one of many promising platforms to build a universal quantum computers by leveraging the interaction between indistinguishable photons. A common technique to prepare such states is photon heralding, where many identical photons can be generated and used to encode and process information. Photon pairs are typically generated from a second-order nonlinear interaction known as spontaneous parametric downconversion (SPDC). In all existing platforms, materials are used as both a source of optical nonlinearity, and a phase-matching medium, often resulting in narrow-band and non-reconfigurable operation. 2D materials promise to change this, thanks to their high nonlinearity, inherent broadband phase-matching, and highly configurable electro-optical properties. To date SPDC has only been reported in structures with many millions of atoms, stimulating experimental efforts to validate its scaling laws in structures only a few atoms thick. In this thesis we investigate SPDC in group IV transition-metal dichalcogenides (TMDCs), and describe efforts towards the experimental observation of non-resonant SPDC from a diffraction-limited area. Because of the intimate connection between the classical second-harmonic generation (SHG) and the quantum SPDC, the efficiency of one process provides insights on the other. This guides the design of single-photon coincidence measurements required to demonstrate the strong temporal correlations of these entangled states. Measurements are hindered by the presence of a broadband, temporally uncorrelated background, attributed to photoluminescence. This work improves the understanding of the nonlinear quantum optical potential of these crystals, and provides a performance benchmark for these ultra-thin materials.
) crystal to realize a new scalable, ultrathin, and efficient SPDC source. By coinciding fundamental and higher order resonances of the metasurface with the generated signal and idler frequencies, respectively, the electric field in the nonlinear media is significantly boosted. This leads to a substantial enhancement in the SPDC process which, subsequently, by using the quantum-classical correspondence principle, translates to very high photon-pair generation rates. The emitted radiation is highly directional and perpendicular to the metasurface in contrast to relevant dielectric structures. The incorporation of circular polarized excitation further increases the photon-pair generation efficiency. The presented work will lead to the design of new efficient ultrathin SPDC single-photon nanophotonic sources working at room temperature that are expected to be critical components in free-space quantum optical communications. In a more general context, our findings can have various applications in the emerging field of quantum plasmonics.