In the process of Spontaneous Parametric Down Conversion (SPDC), a pump photon spontaneously splits inside a quadratic nonlinear crystal to signal and idler photons. By spatially modulating the nonlinear coefficient, we form a bulk nonlinear metamaterial that can shape the first and second order correlations of the down-converted signal and idler photons in either the spatial domain or the spectral domains. These degrees of freedom span a multi-dimensional Hilbert space, which is beneficial for quantum information applications. Recently, we have designed and fabricated, using electric field poling, bulk nonlinear metamaterials in KTiOPO4, for generating spatially entangled signal-idler pairs. This includes a bi-photon Bell state in the Hermite-Gauss basis, or a state with 3 dominant pairs of coincidences, approximating a bi-photon qutrit. As for the spectral domain, we generated a variety of quantum states: high purity frequency uncorrelated states, frequency-bin Bell states and frequency entangled bi-photon qudit states. By increasing the pump power, we reach the regime of bright squeezed vacuum sources, enabling the generation of a square cluster state in the frequency domain.
In the process of Spontaneous Parametric Down Conversion (SPDC), a pump photon spontaneously splits inside a quadratic nonlinear crystal to signal and idler photons. By spatially modulating the nonlinear coefficient, we form a bulk nonlinear metamaterial that can shape the first and second order correlations of the down-converted signal and idler photons in either the spatial domain or the spectral domains. These degrees of freedom span a multi-dimensional Hilbert space, which is beneficial for quantum information applications. Recently, we have designed and fabricated, using electric field poling, bulk nonlinear metamaterials in KTiOPO4, for generating spatially entangled signal-idler pairs. This includes a bi-photon Bell state in the Hermite-Gauss basis, or a state with 3 dominant pairs of coincidences, approximating a bi-photon qutrit. As for the spectral domain, we generated a variety of quantum states: high purity frequency uncorrelated states, frequency-bin Bell states and frequency entangled bi-photon qudit states. By increasing the pump power, we reach the regime of bright squeezed vacuum sources, enabling the generation of a square cluster state in the frequency domain.
Quantum states of light, such as fixed photon number (Fock) states, entangled states, and squeezed states, offer important advantages with respect to classical states of light, such as coherent states and thermal states, in different areas: they enable secure communication and distribution of encryption keys, enable realization of sensors with higher sensitivity and resolution, and are considered candidates for quantum computing and simulation applications. To accommodate these applications, suitable methods for generating the quantum states are needed. Today, the quantum states are often produced by a spontaneous nonlinear process in a standard nonlinear material, followed by a series of optical elements necessary for encoding the desired state on the generated photons. In this review, we consider an alternative approach of structuring the nonlinearity of the crystal so that the desired quantum state will be generated directly at the crystal, without the need for additional elements. Our main focus here is on bulk crystals having structured second-order nonlinearity. The rising interest in these nonlinear metamaterials is fueled by advancements in the ability to efficiently simulate and design spontaneous parametric downconversion (SPDC) processes, as well as by new capabilities of structuring the nonlinearity of ferroelectric crystals, either by electric field poling or by laser-induced writing. As a result, nonlinear metamaterials were recently used to directly shape the spatial and spectral correlations of quantum light that is generated in SPDC. The paper covers the theoretical background and the design and fabrication methods of bulk nonlinear metamaterials for generating quantum light, as well as a series of demonstrations of the use of metamaterials in quantum optical 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.
Nonlinear holography shapes the amplitude and phase of generated new harmonics using nonlinear processes. Classical nonlinear holography influenced many fields in optics, from information storage, demultiplexing of spatial information, and all-optical control of accelerating beams. Here, we extend the concept of nonlinear holography to the quantum regime. We directly shape the spatial quantum correlations of entangled photon pairs in two-dimensional patterned nonlinear photonic crystals using spontaneous parametric down conversion, without any pump shaping. The generated signal-idler pair obeys a parity conservation law that is governed by the nonlinear crystal. Furthermore, the quantum states exhibit quantum correlations and violate the Clauser-Horne-Shimony-Holt inequality, thus enabling entanglement-based quantum key distribution. Our demonstration paves the way for controllable on-chip quantum optics schemes using the high-dimensional spatial degree of freedom.
The efficient and controllable generation of entangled photon pairs is a cornerstone for advancing quantum technologies, including quantum computing, communication, and sensing. Traditional methods, primarily relying on spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing (SFWM) in bulk nonlinear crystals or waveguides, often suffer from low efficiency, bulky form factors, and limited control over the spectral and spatial properties of the generated photons. This paper explores a transformative approach leveraging resonant Bound States in the Continuum (BICs) within nanophotonic structures to overcome these limitations. BICs are extraordinary optical resonances characterized by theoretically infinite quality (Q) factors, enabling extreme light localization and immense field enhancement within subwavelength volumes. By integrating nonlinear optical materials into BIC-supporting structures, such as photonic crystal slabs or metasurfaces, the local electric field strength experienced by the nonlinear medium can be dramatically increased, boosting the efficiency of entangled photon generation. Furthermore, the sharp, tailor-able spectral response of BICs offers unprecedented control over the joint spectral amplitude of the photon pairs, promising high degrees of spectral purity and entanglement fidelity. This work outlines the theoretical underpinnings, potential device architectures, and anticipated advantages of BIC-enhanced entangled photon sources, paving the way for compact, high-brightness, and spectrally engineered quantum light sources critical for next-generation quantum technologies.
Spontaneous parametric downconversion (SPDC) in quantum optics is an invaluable resource for the realization of high-dimensional qudits with spatial modes of light. One of the main open challenges is how to directly generate a desirable qudit state in the SPDC process. This problem can be addressed through advanced computational learning methods; however, due to difficulties in modeling the SPDC process by a fully differentiable algorithm, progress has been limited. Here, we overcome these limitations and introduce a physically constrained and differentiable model, validated against experimental results for shaped pump beams and structured crystals, capable of learning the relevant interaction parameters in the process. We avoid any restrictions induced by the stochastic nature of our physical model and integrate the dynamic equations governing the evolution under the SPDC Hamiltonian. We solve the inverse problem of designing a nonlinear quantum optical system that achieves the desired quantum state of downconverted photon pairs. The desired states are defined using either the second-order correlations between different spatial modes or by specifying the required density matrix. By learning nonlinear photonic crystal structures as well as different pump shapes, we successfully show how to generate maximally entangled states. Furthermore, we simulate all-optical coherent control over the generated quantum state by actively changing the profile of the pump beam. Our work can be useful for applications such as novel designs of high-dimensional quantum key distribution and quantum information processing protocols. In addition, our method can be readily applied for controlling other degrees of freedom of light in the SPDC process, such as spectral and temporal properties, and may even be used in condensed-matter systems having a similar interaction Hamiltonian.