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arXiv:2512.11608 · Optics Express

Tailoring quantum walks in integrated photonic lattices

A. Raymond, P. Cathala, M. Morassi, A. Lemaître, F. Raineri, S. Ducci, F. Baboux

quant-phcond-mat.mes-hallcond-mat.quant-gasphysics.opticsSubmitted Dec 12, 2025• Announced Dec 15, 2025• 1 citation
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Abstract

Unlike discrete photonic circuits, which manipulate photons step-by-step using a series of optical elements, arrays of coupled waveguides enable photons to interfere continuously across the entire structure. When composed of a nonlinear material, such arrays can also directly generate quantum states of light within the circuit. To clarify the similarities and distinctions between these two approaches of quantum walks, we conduct here a systematic comparison between linear waveguide arrays, injected with photons produced externally, and nonlinear arrays, where photon pairs are continuously generated via parametric down-conversion. We experimentally validate these predictions using III-V semiconductor nonlinear waveguide lattices with varied geometries, enabling us to tune the depth of the quantum walks over an order of magnitude and reveal the gradual emergence of non-classicality in the output state. Finally, we demonstrate an inverse-design approach to engineer \textit{aperiodic} waveguide arrays, whose optimized coupling profiles generate maximally entangled states such as the biphoton W-state. These results highlight the potential of continuously-coupled photonic systems to harness high-dimensional entanglement within compact architectures.

Journal reference
Optics Express 33, 45869 (2025)
DOI
10.1364/OE.571522
Comments
17 pages

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Harnessing high-dimensional entangled states of light presents a frontier for advancing quantum information technologies, from fundamental tests of quantum mechanics to enhanced computation and communication protocols. In this context, the spatial degree of freedom stands out as particularly suited for on-chip integration. But while traditional demonstrations produce and manipulate path-entangled states sequentially with discrete optical elements, continuously-coupled nonlinear waveguide systems offer a promising alternative where photons can be generated and interfere along the entire propagation length, unveiling novel capabilities within a reduced footprint. Here we exploit this concept to implement a compact and reconfigurable source of path-entangled photon pairs based on parametric down-conversion in semiconductor AlGaAs nonlinear waveguides arrays.
Arrays of coupled optical waveguides provide a flexible platform for manipulation of optical beams and pulses. Recently, the propagation of non-classical light in waveguide arrays has shown a surging attention. It was shown that quantum walks of correlated photon pairs realized through propagation in waveguide arrays can lead to nontrivial quantum correlations at the array output. However, all currently used schemes for quantum walks utilise correlated photon pairs generated externally to the array. Here, we propose and demonstrate numerically a novel scheme enabling simultaneous generation of correlated photon pair through spontaneous parametric downconversion (SPDC) and quantum walks inside a single photonic element an array of quadratic nonlinear waveguides. This scheme avoids entirely the need for complex interfaces between the different photonic elements and enables novel ways for control of the quantum correlations.
We demonstrate experimentally simultaneous photon-pair generation and quantum walks in a lithium niobate waveguide array, where the output photon correlations can be controlled by varying the temperature-dependent phase-matching, switching from classical to quantum statistics. Integrated optical quantum circuits are increasingly gaining attention as a solution for scalable quantum technologies with important application to quantum simulations [1]. A key mechanism for such quantum simulations can be provided by the process of quantum walks, which in quantum optics is enabled in an array of coupled optical waveguides. However, in all integrated quantum walk schemes to date, the correlated photon pairs have been generated externally to the waveguide array (WGA), making it only a passive circuit. Here we experimentally demonstrate an active quantum circuit, where the WGA is used for both photonpair generation and quantum walks of the generated photons. We show that the output photon statistics can be controlled classically by changing the phase matching conditions for photon-pair generation, which allows for controllable engineering of the spatial quantum correlations exhibited through a quantum walk [4]. Importantly, this integrated scheme also allows avoiding input losses from the state generation to the waveguides. This is crucial as input losses in devices with linear coupled waveguides currently limit feasible experimental data acquisition times and hinder possible applications. In our experiments we use an x-cut LiNbO3 WGA [see Fig. 1(a)] fabricated by titanium indiffusion [5], which consists of 40 waveguides with a spacing of 14mm. A single waveguide of the WGA is excited by a continuous wave (CW) solid state laser at a wavelength of 671nm [see Fig. 1(b)]. The WGA is kept at a temperature of ~360C (with an accuracy of 0.1C) to phase-match the Type-I (oo-e) spontaneous parametric down-conversion (SPDC) process. At the pump wavelength the mode is well confined to the central waveguide and does not show evanescent coupling to the neighboring waveguides [see Fig. 1(a)]. However, for the generated low-frequency SPDC photons the waveguide modes extend towards the neighboring waveguides and can couple through the array experiencing quantum walks. Thus the generated output photon pairs demonstrate nontrivial photon statistics. Experimentally, we measure the photon-pair correlations at a wavelength of 1342 ± 6nm (filtered by an interference filter) on two cooled InGaAs single photon detectors (IDQuantique 210) in free-running mode [see Fig. 1(b)]. The non-polarizing beamsplitter is used to separate two photons of a pair with 50% efficiency, while irises allow for individual waveguide output selection. The resulting correlation measurements are shown in Fig. 2(a), where the coincidence counts are normalized with respect to the coupling efficiency. We observe that for a sample temperature of T = 364.5C close to degenerate SPDC phase-matching, photons from down-converted pairs leave the WGA from the same waveguide {-1,-1}, {0,0} or {1,1} (here two numbers correspond to two SPDC photons), defined as bunching, or from the opposite waveguides {-1,1} or {1,-1} defined as antibunching. The highest coincidence rate is achieved in the {0,0} case, since photon pairs are generated in waveguide 0 along the whole length of the WGA. Photon pairs coming from the other waveguides, namely {-1,0}, {1,0}, {0,-1} and {0,1} lead to less coincidences. This means that probabilities of photon bunching and antibunching are simultaneously dominant, which implies a highly non-trivial Paper code: Fig. 1. (a) Schematic representation of LiNbO3 WGA with pump (blue) coupled to a central waveguide and SPDC photon pairs (red) generated in the central waveguide and propagating in the WGA in the regime of quantum walks. (b) Schematic of the experimental setup. entangled state [3]. The theoretical quantum simulations of the process based on Ref. [4] [Fig. 2(b)] are in good agreement with our experiment. To demonstrate the reconfigurability of the device we also measure the correlation of the antibunched photons in waveguide {-1,1} as the temperature is varied, shown in Fig. 2(c). The theory developed for WGAs (blue curve), taking into account structural and temperature-related inhomogeneities in the sample, fits well the experimental data (red circles with error bars). This demonstrates that changing the temperature affects the coincidence counts from various waveguides, allowing control of the output photon statistics and revealing a route to reconfigurable quantum simulations based on walks. To conclude, our work opens a path for implementing combined photon-pair generation and quantum walks for engineering of spatial quantum states in novel active quantum integrated circuits.
Quantum entanglement became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demonstrated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. Spontaneous parametric down-conversion (SPDC) in nonlinear crystals provides an efficient source for entangled photon pairs, so-called biphotons. However, SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional arrays can be simulated through classical optical beam propagation in a two-dimensional photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-like inequality.
We demonstrate a nonlinear AlGaAs photonic chip generating biphotons with high-dimensional spatial correlations. Photon pairs are generated by parametric down conversion in a waveguide array and simultaneously spread through quantum walks along the various waveguides, allowing to generate various types of high-dimensional entangled states of light. We further implement the Su-Schriefer-Heeger model and demonstrate the topological protection of the SPDC process against disorder. These results highlight nonlinear waveguide arrays as a promising platform for exploring the interplay between nonlinearity, disorder and topology in quantum photonic circuits.