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Photonics Research

Time-varying classical local entanglement of ultrafast vector light pulses

Zhangyu Zhou, Shuoshuo Zhang, Jielei Ni, Yixuan Chen, Yuquan Zhang, Yejun He, Changjun Min, Xiaocong Yuan

Published Oct 1, 2025• 1 citation
Publisher

Abstract

As structured optical fields with spatially inhomogeneous polarization distributions, vector beams have attracted widespread attention for their great applications across multiple fields. The coupling between spatial modes and polarization states in vector beams results in nonseparability analogous to quantum entangled states, referred to as classical entanglement. This concept has garnered considerable scholarly interest, due to its capacity to facilitate quantum-inspired approaches for the characterization of vector optical fields, leading to noteworthy applications such as metrological sensing, communication encryption, and quantum computing. However, most investigations concerning classical entanglement have focused on vector optical fields within the spatial domain, while the classical entanglement characteristics of ultrafast vector beam pulses in the temporal domain remain to be revealed. Here, we investigate the classical local entanglement of ultrafast vector beam pulses in the temporal domain. Through theoretical interpretation and experimental verification, time-varying nonseparability has been demonstrated throughout the pulse duration. The dynamic evolution of spatially vectorial polarization states on femtosecond timescales was measured. The temporal evolution of the classical entanglement and the associated density matrix were analyzed using quantum state tomography. This research provides, to our knowledge, novel perspectives for investigating quantum-classical optical analogies in the temporal domain, advancing deeper fundamental understanding of entanglement.

DOI
10.1364/prj.574402

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Vector modes are fully polarized modes of light with spatially varying polarization distributions, and they have found widespread use in numerous applications such as microscopy, metrology, optical trapping, nanophotonics, and communications. The entanglement of such modes has attracted significant interest, and it has been shown to have tremendous potential in expanding existing applications and enabling new ones. However, due to the complex spatially varying polarization structure of entangled vector modes (EVMs), a complete entanglement characterization of these modes remains challenging and time consuming. Here, we have used a time-tagging event camera to demonstrate the ability to completely characterize the entanglement of EVMs. Leveraging the camera's capacity to provide independent measurements for each pixel, we simultaneously characterize the entanglement of approximately 2.6×10^{6} modes between a bipartite EVM through measuring only 16 observables in polarization. We reveal that EVMs can naturally generate various polarization-entangled Bell states. This achievement is an important milestone in high-dimensional entanglement characterization of structured light, and it could significantly impact the implementation of related quantum technologies. The potential applications of this technique are extensive, and it could pave the way for advancements in quantum communication, quantum imaging, and other areas where structured entangled photons play a crucial role.
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Quantum light is considered to be one of the key resources of the coming second quantum revolution expected to give rise to groundbreaking technologies and applications. If the spatio-temporal and polarization structure of modes is known, the properties of quantum light are well understood. This information provides the basis for contemporary quantum optics and its applications in quantum communication and metrology. However, thinking about quantum light at the most fundamental timescale, namely the oscillation cycle of a mode or the inverse frequency of an involved photon, we realize that the corresponding picture has been missing until now. For instance, how to comprehend and characterize a single photon at this timescale? To fill this gap, we demonstrate theoretically how local quantum measurements allow to reconstruct and visualize a quantum field under study at subcycle scales, even when its temporal mode structure is a priori unknown. In particular, generation and tomography of ultrabroadband squeezed states as well as photon-subtracted states derived from them are described, incorporating also single-photon states. Our results set a cornerstone in the emerging chapter of quantum physics termed time-domain quantum optics. We expect this development to elicit new spectroscopic concepts for approaching e.g. fundamental correlations and entanglement in the dynamics of quantum matter, overcoming the temporal limitation set by the oscillation cycles of both light and elementary excitations.
We present a time-domain Schmidt-mode analysis of a broadband continuous-variable entanglement of photon pairs generated via a vectorial four-wave mixing (FWM) of ultrashort laser pulses in a highly nonlinear birefringent optical fiber. We demonstrate that the time-domain eigenmodes of high-purity two-photon states generated through vectorial FWM can be steered, by varying the pump wavelength and FWM polarization geometry, from a high-purity entangled ket to a high-entropy entangled state in a space of a very high dimensionality. Moreover, this pulse-mode analysis is shown to provide a clear physical perspective on how the entanglement structure of two-photon states builds up as a result of short-pulse FWM dynamics. This insight reveals a correspondence-type relation between the quantum and classical pictures of photon-pair generation. With an eye on practical applications, a clear understanding of the temporal profile of pulse modes representing high-purity two-photon states is central to a meaningful shaping of ultrashort photon-packet waveforms for super-resolving microscopy and multiphoton spectroscopy using quantum states of light.