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arXiv:2601.21250

3D imaging of the biphoton spatiotemporal wave packet

Yang Xue, Ze-Shan He, Hao-Shu Tian, Qin-Qin Wang, Bin-Tong Yin, Jun Zhong, Xiao-Ye Xu, Chuan-Feng Li, Guang-Can Guo

quant-phphysics.opticsSubmitted Jan 29, 2026• Announced Jan 30, 2026• 0 citations
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Abstract

Photons are among the most important carriers of quantum information owing to their rich degrees of freedom (DoFs), including various spatiotemporal structures. The ability to characterize these DoFs, as well as the hidden correlations among them, directly determines whether they can be exploited for quantum tasks. While various methods have been developed for measuring the spatiotemporal structure of classical light fields, owing to the technical challenges posed by weak photon flux, there have so far been no reports of observing such structures in their quantum counterparts, except for a few studies limited to correlations within individual DoFs. Here, we propose and experimentally demonstrate a self-referenced, high-efficiency, and all-optical method, termed 3D imaging of photonic wave packets, for comprehensive characterization of the spatiotemporal structure of a quantum light field, i.e., the biphoton spatiotemporal wave packet. Benefiting from this developed method, we successfully observe the spatial-spatial, spectral-spectral, and spatiotemporal correlations of biphotons generated via spontaneous parametric down-conversion, revealing rich local and nonlocal spatiotemporal structure in quantum light fields. This method will further advance the understanding of the dynamics in nonlinear quantum optics and expand the potential of photons for applications in quantum communication and quantum computing.

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Photons are among the most important carriers of quantum information owing to their rich degrees of freedom (DoFs), including various spatiotemporal structures. The ability to characterize these DoFs, as well as the hidden correlations among them, directly determines whether they can be exploited for quantum tasks. While various methods have been developed for measuring the spatiotemporal structure of classical light fields, owing to the technical challenges posed by weak photon flux, there have so far been no reports of observing such structures in their quantum counterparts, except for a few studies limited to correlations within individual DoFs. Here, we propose and experimentally demonstrate a self-referenced, high-efficiency, and all-optical method, termed 3D imaging of photonic wave packets, for comprehensive characterization of the spatiotemporal structure of a quantum light field, i.e., the biphoton spatiotemporal wave packet. Benefiting from this developed method, we successfully observe the spatial-spatial, spectral-spectral, and spatiotemporal correlations of biphotons generated via spontaneous parametric down-conversion, revealing rich local and nonlocal spatiotemporal structure in quantum light fields. This method will further advance the understanding of the dynamics in nonlinear quantum optics and expand the potential of photons for applications in quantum communication and quantum computing.
With an extremely high dimensionality, the spatial degree of freedom of entangled photons is a key tool for quantum foundation and applied quantum techniques. To fully utilize the feature, the essential task is to experimentally characterize the multiphoton spatial wave function including the entangled amplitude and phase information at different evolutionary stages. However, there is no effective method to measure it. Quantum state tomography is costly, and quantum holography requires additional references. Here, we introduce quantum Shack-Hartmann wavefront sensing to perform efficient and reference-free measurement of the biphoton spatial wave function. The joint probability distribution of photon pairs at the back focal plane of a microlens array is measured and used for amplitude extraction and phase reconstruction. In the experiment, we observe that the biphoton amplitude correlation becomes weak while phase correlation shows up during free-space propagation. Our work is a crucial step in quantum physical and adaptive optics and paves the way for characterizing quantum optical fields with high-order correlations or topological patterns.
The spectral distribution of photon pairs produced by spontaneous parametric downconversion (SPDC) is one of the most exploited degrees of freedom in multiphoton experiments. Consequently, the characterization of such correlations is, without a doubt, a task of utmost importance. Common methods for measuring the joint spectral intensity (JSI) of correlated photon pairs often exhibit several drawbacks, such as the requirement for a bright source to offset high losses or the need for two-dimensional measurements, which can lead to prolonged acquisition times. In this work, we experimentally demonstrate a technique that allows for the reconstruction of the JSI from a single interferometric measurement, thus reducing the dimensionality of the problem. The reconstructed JSIs show good agreement with those obtained directly through a fiber spectrometer, confirming the effectiveness of our approach. This technique significantly enhances the efficiency of JSI characterization, offering a resource-efficient method for quantum state characterization in SPDC-based experiments.
The field of high-dimensional quantum photonics involves the use of multimode photonic degrees-of-freedom such as the spatial, temporal, or spectral structure of light to encode multi-level quantum states. Recent years have seen rapid progress in the development of methods to generate, manipulate, and distribute such quantum states of light and their use in a range of quantum technology applications that offer practical advantages over conventional qubit-based approaches. High-dimensional quantum states of light encoded in photonic time-bins, frequency-bins, transverse-spatial modes, waveguide paths, and temporal modes have enabled noise-robust fundamental tests of quantum mechanics, error-resilient and high-capacity quantum communication protocols, andas well as efficient approaches for quantum information processing, to name just a few examples. However, research in this field has progressed fairly independently, with little exchange across different photonic degrees-of-freedom or between experiment and theory and no comprehensive comparison between degrees-of-freedom. This roadmap aims to bridge this gap by surveying progress in each area and identifying shared challenges and opportunities that cut across two or more photonic degrees-of-freedoms. We review early work and state-of-the-art experimental techniques under development for high-dimensional quantum states encoded in single and entangled photons, as well as theoretical tools for their measurement and certification. We outline the main outstanding challenges for theory and each experimental degree-of-freedom, identifying promising future directions of research that may enable these to be overcome. We end by discussing interconnections and shared challenges centered around their distribution, measurement, and manipulation, with a view towards their integration into next-generation quantum technology platforms and applications.
Abstract High-dimensional biphoton states are promising resources for quantum applications, ranging from high-dimensional quantum communications to quantum imaging. A pivotal task is fully characterizing these states, which is generally time-consuming and not scalable when projective measurement approaches are adopted; however, new advances in coincidence imaging technologies allow for overcoming these limitations by parallelizing multiple measurements. Here we introduce biphoton digital holography, in analogy to off-axis digital holography, where coincidence imaging of the superposition of an unknown state with a reference state is used to perform quantum state tomography. We apply this approach to single photons emitted by spontaneous parametric down-conversion in a nonlinear crystal when the pump photons possess various quantum states. The proposed reconstruction technique allows for a more efficient (three orders of magnitude faster) and reliable (an average fidelity of 87%) characterization of states in arbitrary spatial modes bases, compared with previously performed experiments. Multiphoton digital holography may pave the route toward efficient and accurate computational ghost imaging and high-dimensional quantum information processing.
Light is fully described by its three degrees of freedom (DoFs), wavelength/time, space/momentum, and polarization. A deep understanding of the DoFs is central in both classical and quantum optical research. By exploring the unique possibilities that correlations of different DoFs or the correlation of one DoF with other systems offer, new technological opportunities arise. This thesis offers new experimental and theoretical perspectives on optical correlations of laser pulses and photon pairs generated in spontaneous parametric down-conversion (SPDC). This thesis introduces spectral vector beams - light pulses in which wavelength and polarization are correlated. These beams can be used for high-speed spectro-scopic measurements, where the lights spectrum can be obtained from polarization measurements alone. I extend this concept by the third DoF, correlating wavelength, space, and polarization within a single light pulse. I investigate the similarity of the loss of their degree of polarization in imprecise measurements to the loss of coherence of nonseparable quantum systems. Additionally, the thesis explores the conservation of orbital angular momentum (OAM) in photon pairs produced with SPDC. I show, that the OAM of a pump light field is transferred to the photon pair in agreement with the conservation of OAM. For the first time, I demonstrate that this conservation law is also valid for a single-photon pump. This work not only explores fundamental descriptions but also provides the ex- perimental framework to generate light fields with complex hybrid correlations. The research demonstrates the potential for a deeper understanding of light’s versatile DoFs.
High-dimensional biphoton states are promising resources for quantum applications, ranging from high-dimensional quantum communications to quantum imaging. A pivotal task is fully characterising these states, which is generally time-consuming and not scalable when projective measurement approaches are adopted. However, new advances in coincidence imaging technologies allow for overcoming these limitations by parallelising multiple measurements. Here, we introduce biphoton digital holography, in analogy to off-axis digital holography, where coincidence imaging of the superposition of an unknown state with a reference one is used to perform quantum state tomography. We apply this approach to single photons emitted by spontaneous parametric down-conversion in a nonlinear crystal when the pump photons possess various quantum states. The proposed reconstruction technique allows for a more efficient (3 order-of-magnitude faster) and reliable (an average fidelity of 87%) characterisation of states in arbitrary spatial modes bases, compared with previously performed experiments. Multi-photon digital holography may pave the route toward efficient and accurate computational ghost imaging and high-dimensional quantum information processing.