This paper explores the novel concept of programmable spatiotemporal entanglement, realized through engineered disordered photonic crystals (DPhCs). We propose a theoretical framework that leverages the unique light-matter interaction within these disordered photonic structures. This interaction is characterized by phenomena such as Anderson localization and can be effectively described using random matrix theory. Our goal is to generate and control highly complex entangled states, addressing limitations of traditional methods. Conventional approaches for entanglement generation often struggle with scalability, robust control, and high-dimensional encoding across both spatial and temporal degrees of freedom simultaneously. By introducing controlled disorder into photonic crystal designs, we aim to harness the rich scattering phenomena to tailor the correlations between entangled photons across their spatiotemporal wavefronts. The proposed methodology involves embedding nonlinear optical elements within these disordered structures to facilitate spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing (SFWM). In such environments, the localized modes and the modified density of states profoundly influence the properties of the emitted photon pairs. Programmability is envisioned through external control mechanisms, such as adaptive wavefront shaping of the pump light or tunable disorder elements. These mechanisms would allow for dynamic manipulation of entanglement properties like dimensionality, purity, and Schmidt mode distributions. We discuss the potential for robust, high-dimensional quantum states and their implications for advanced quantum communication, quantum imaging, and novel quantum computing architectures. This work lays the groundwork for a new paradigm in quantum state engineering, exploiting complexity to achieve unprecedented control over multiphoton entanglement.
This paper explores the novel concept of programmable spatiotemporal entanglement, realized through engineered disordered photonic crystals (DPhCs). We propose a theoretical framework that leverages the unique light-matter interaction within these disordered photonic structures. This interaction is characterized by phenomena such as Anderson localization and can be effectively described using random matrix theory. Our goal is to generate and control highly complex entangled states, addressing limitations of traditional methods. Conventional approaches for entanglement generation often struggle with scalability, robust control, and high-dimensional encoding across both spatial and temporal degrees of freedom simultaneously. By introducing controlled disorder into photonic crystal designs, we aim to harness the rich scattering phenomena to tailor the correlations between entangled photons across their spatiotemporal wavefronts. The proposed methodology involves embedding nonlinear optical elements within these disordered structures to facilitate spontaneous parametric down-conversion (SPDC) or spontaneous four-wave mixing (SFWM). In such environments, the localized modes and the modified density of states profoundly influence the properties of the emitted photon pairs. Programmability is envisioned through external control mechanisms, such as adaptive wavefront shaping of the pump light or tunable disorder elements. These mechanisms would allow for dynamic manipulation of entanglement properties like dimensionality, purity, and Schmidt mode distributions. We discuss the potential for robust, high-dimensional quantum states and their implications for advanced quantum communication, quantum imaging, and novel quantum computing architectures. This work lays the groundwork for a new paradigm in quantum state engineering, exploiting complexity to achieve unprecedented control over multiphoton entanglement.
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.
We propose a novel, physically-constrained and differentiable approach for the generation of D-dimensional qudit states via spontaneous parametric down-conversion (SPDC) in quantum optics. We circumvent any limitations imposed by the inherently stochastic nature of the physical process and incorporate a set of stochastic dynamical equations governing its evolution under the SPDC Hamiltonian. We demonstrate the effectiveness of our model through the design of structured nonlinear photonic crystals (NLPCs) and shaped pump beams; and show, theoretically and experimentally, how to generate maximally entangled states in the spatial degree of freedom. The learning of NLPC structures offers a promising new avenue for shaping and controlling arbitrary quantum states and enables all-optical coherent control of the generated states. We believe that this approach can readily be extended from bulky crystals to thin Metasurfaces and potentially applied to other quantum systems sharing a similar Hamiltonian structures, such as superfluids and superconductors.
Programmable preparation of entangled quantum states is a central requirement for scalable quantum information processing, quantum networking and photonic quantum computing. Topological photonic platforms offer an attractive route towards robust quantum-state generation by encoding information in symmetry- protected optical modes, yet the generated entangled states are typically dictated by the lattice geometry and therefore lack programmability. Here we demonstrate programmable preparation of topological entangled states by inverse engineering the nonlinear optical pump profile of an integrated photonic lattice. Our approach enables deterministic control over both the dimensionality and modal structure of the generated entangled state while preserving its topological character. We experimentally realize silicon photonic topological superlattices in which the nonlinear generation pathway itself becomes programmable via tailored excitations. The superlattices host a multiband manifold of co localized topological interface modes, while coherently controlled inputs synthesize pump superpositions within this protected basis. We showcase this principle by selectively addressing topological biphoton eigenstates, steering correlations to produce a desired target state in a high-dimensional Hilbert space, and inverse-designing pump states that generate targeted Schmidt dimensionalities. Site-resolved two-photon correlation measurements remain reproducible across nominally identical fabricated devices, demonstrating robustness to realistic nanofabrication-induced disorder. Programmable preparation of topological entangled states establishes a pathway towards exploiting topological photonic modes as application-specific quantum resources, enabling tailored input states for high-dimensional quantum communication, quantum networking and photonic quantum computing.
Non-Hermitian quantum mechanics has emerged as a powerful framework for describing open quantum systems, particularly in optical platforms where engineered gain and loss can lead to exotic phenomena. This paper theoretically investigates the synthesis of non-Hermitian quantum light within driven photonic crystals. We propose a methodology that leverages the unique dispersion engineering capabilities of photonic crystals, coupled with controlled introduction of gain and loss elements and strong classical driving fields. Our approach aims to generate novel quantum light states characterized by non-Hermitian properties, such as modified photon statistics, entanglement, and the manifestation of exceptional points in quantum correlations. The paper outlines the theoretical foundations, reviews relevant prior work in non-Hermitian optics and quantum light generation in photonic structures, and details a specific methodology involving coupled resonator systems and nonlinear optical processes. We predict that such driven non-Hermitian photonic crystals can offer unprecedented control over quantum light properties, enabling the generation of squeezed states with enhanced sensitivity, robust entangled photon pairs, and potentially new regimes for quantum metrology and information processing. The discussion addresses the implications of these findings for fundamental quantum optics and their potential experimental realizations, highlighting the challenges and promising avenues for future research.
Here we investigate the all-optical control of spectral correlations in spontaneous parametric down-conversion. We show that when photon pairs are projected onto high-order spatial modes, the spatial structure of the pump field defines the phase-matching function of the nonlinear interaction. Thus, by structuring the pump field in both space and spectrum, the biphoton spectral correlations are fully controlled. Considering a standard periodically-poled crystal as the nonlinear medium, we show that the Gouy phase matching method proposed here can generate both spectrally uncorrelated and high-dimensional spectrally entangled photon pairs, similarly to what is achieved with aperiodically-poled crystals. Furthermore, we show that our method can generate a wider class of quantum states if the pump field is a spatiotemporal wavepacket, that is, if its spatial and spectral structures are correlated.