We introduce a new class of self-configuring photonic architectures called variational optical processors (VOPs). These devices tackle the problem of decomposing and measuring multimode light fields, both partially coherent and quantum, without requiring prior knowledge of the modes involved. Classical strategies for modal decomposition—such as Karhunen-Loève expansions [1] for partially coherent beams or Schmidt decompositions [2] for bipartite quantum states—often rely on comprehensive tomography and complex data processing. By contrast, VOPs discover the relevant modes in situ through a simple optimization of detection signals at their outputs (e.g., measured optical power or coincidence counts), eliminating the overhead usually associated with scanning and reconstruction. Prior demonstrations of self-configuring photonic networks have proven the feasibility of such approaches for analyzing and generating multimode coherent optical fields [3].
We introduce a new class of self-configuring photonic architectures called variational optical processors (VOPs). These devices tackle the problem of decomposing and measuring multimode light fields, both partially coherent and quantum, without requiring prior knowledge of the modes involved. Classical strategies for modal decomposition—such as Karhunen-Loève expansions [1] for partially coherent beams or Schmidt decompositions [2] for bipartite quantum states—often rely on comprehensive tomography and complex data processing. By contrast, VOPs discover the relevant modes in situ through a simple optimization of detection signals at their outputs (e.g., measured optical power or coincidence counts), eliminating the overhead usually associated with scanning and reconstruction. Prior demonstrations of self-configuring photonic networks have proven the feasibility of such approaches for analyzing and generating multimode coherent optical fields [3].
Working with finite numbers of modes to describe, generate, and detect optical fields can be both mathematically economical and physically useful. Such a modal basis can map directly to various applications in communications, sensing, and processing. But, we need a way to generate and analyze such fields, including measurement and control of both the relative amplitudes and phases of the modal components. Ideally such an analysis scheme would operate directly on the field, without needing a separate, mutually coherent reference beam. Here, we show first how to measure all those relative amplitudes and phases automatically and simultaneously. The method repurposes a self-configuring network of 2 × 2 blocks, such as integrated Mach–Zehnder interferometers, that can automatically align itself to the optical field by a sequence of simple one-parameter power minimizations when network elements, such as phase shifters, are adjusted. The optical field is then directly deduced from the resulting settings of those elements. We show how the entire network can be calibrated for such measurements, automatically and with just two light beams. Then, using the same calibration and running the mesh backwards, we can also controllably generate an arbitrary multimode field. Explicit algorithms and formulas are given for operating this system.
Recent advances in optical imaging and communication increasingly involve high-dimensional, partially coherent light, creating a growing need for scalable tools to measure and manipulate coherence. Here, we demonstrate the automatic separation of spatially partially coherent light into "coherence modes" -- its orthogonal and mutually incoherent components. To make this separation possible, we exploit variational processing in layered self-configuring interferometer architectures in a silicon photonic circuit. This process formally finds and measures the eigenvectors and eigenvalues of the coherency matrix, hence measuring the partially coherent state, while leaving it intact and separated after optimization. Furthermore, we show that mutually incoherent beams, if spatially orthogonal, can be automatically separated even if they are completely overlapped, hence separating unknown laser beams based only on their mutual incoherence. Our experiment finds and separates the two strongest coherence modes starting from a nine-mode sampling of the partially or fully overlapping fields from two independent lasers. The method requires a number of physical components that scales linearly with the rank r of the coherency matrix and operates through a sequence of r in situ gradient-based optimizations enabled by electronic drive frequency multiplexing of interferometer phase shifters. We benchmark its performance against a mixture-based tomographic method, also implemented on chip. These results establish a scalable framework for programmable coherence analysis and control in imaging, communication, and photonic information processing.
Integrated multimode quantum optics is a promising platform for scalable continuous-variable quantum technologies leveraging multimode squeezing in both the spatial and spectral domains. However, on-chip measurement, routing and processing the relevant “supermodes” over which the squeezing resource is distributed still scales quadratically with the number of modes N , causing a rapid increase in photonic circuit size and number of required measurements. Here, we introduce a variational scheme, relying on self-configuring photonic networks (SCNs) that learn and extract the most-squeezed supermodes sequentially, reducing both the circuit size and the experimental overhead. Using homodyne measurement as a cost function, a sparse SCN discovers the l ≪ N most significant supermodes using O ( l N ) physical elements and optimization steps. We analyze and numerically simulate these architectures for both real-space and frequency-domain implementations, showing a fidelity close to unity between the learned circuit and the supermode decomposition, even in the presence of optical losses and detection noise. In the frequency domain, we show that circuit size can be further reduced by using inverse-designed surrogate networks, which emulate the layers learned thus far. Using two different frequency encoding schemes—uniformly and nonuniformly spaced frequency bins—we reduce an entire network (learning all N supermodes) to O ( N ) and even O ( 1 ) modulated cavities. Our results point toward chip-scale, resource-efficient quantum processing units and demultiplexers for continuous variable processing in multimode quantum optics, with applications ranging from quantum communication, metrology, and computation.
Entanglement is a unique feature of quantum mechanics. In coupled systems of light and matter, entanglement manifests itself in the linear superposition of multipartite quantum states (e.g., parametrized by multiple spatial, spectral, or temporal degrees of freedom of a light field). In bipartite systems, the Schmidt decomposition provides a modal decomposition of the entanglement structure over independent, separable states. Although ubiquitous as a mathematical tool to describe and measure entanglement, there exists no general efficient experimental method to decompose a bipartite quantum state onto its Schmidt modes. Here, we propose a method that relies on bipartite self-configuring optics that automatically “learns” the Schmidt decomposition of an arbitrary pure quantum state. Our method is designed for entanglement distributed over spatial or spectral degrees of freedom of a light field and can reconstruct the Schmidt modes and values by variational optimization of the network’s output powers or coincidences. We illustrate our method with numerical examples of spectral entanglement analysis for biphotons generated via spontaneous parametric down conversion and provide experimental guidelines for its realization and generalization to other degrees of freedom of light, including the influence of losses and impurities. Our method provides a versatile and scalable way of analyzing entanglement in bipartite integrated quantum photonic systems.
Multimode optical interferometers represent the most viable platforms for the successful implementation of several quantum information schemes that take advantage of optical processing. Examples range from quantum communication and sensing, to computation, including optical neural networks, optical reservoir computing, or simulation of complex physical systems. The realization of such routines requires high levels of control and tunability of the parameters that define the operations carried out by the device. This requirement becomes particularly crucial in light of recent technological improvements in integrated photonic technologies, which enable the implementation of progressively larger circuits embedding a considerable amount of tunable parameters. We formulate efficient procedures for the characterization of optical circuits in the presence of imperfections that typically occur in physical experiments, such as unbalanced losses and phase instabilities in the input and output collection stages. The algorithm aims at reconstructing the transfer matrix that represents the optical interferometer without making any strong assumptions about its internal structure and encoding. We show the viability of this approach in an experimentally relevant scenario, defined by a tunable integrated photonic circuit, and we demonstrate the effectiveness and robustness of our method. Our findings can find application in a wide range of optical setups, based on both bulk and integrated configurations.