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arXiv:2512.06718 · Physical Review Letters

Witnessing Spin-Orbital Entanglement using Resonant Inelastic X-Ray Scattering

Zecheng Shen, Shuhan Ding, Zijun Zhao, Francesco A. Evangelista, Yao Wang

quant-phcond-mat.str-elSubmitted Dec 7, 2025• Announced Dec 9, 2025• 1 citation• Revised Jun 14, 2026 (v2)
v1 · Dec 7, 2025v2 · Jun 14, 2026
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Abstract

Entanglement plays a central role in quantum technologies, yet its characterization and control in materials remain challenging. Recent developments in spectrum-based entanglement witnesses have enabled new strategies for quantifying many-body entanglement in macroscopic materials. Here, we develop a protocol for detecting spin-orbital entanglement using experiment-accessible resonant inelastic x-ray scattering (RIXS). Central to our approach is the construction of a Hermitian generator from experimentally measurable spectra, which allows us to compute the quantum Fisher information (QFI) available in spin--orbital systems. The resulting QFI provides upper bounds for $k$-producible states and thus serves as a robust witness of spin-orbital entanglement. To account for realistic experimental limitations, we further extend our framework to include relaxed QFI bounds applicable to measurements lacking full polarization resolution.

Journal reference
Phys. Rev. Lett. 136, 116504 (2026)
DOI
10.1103/nyxb-nqtq
Comments
6 pages, 3 figures

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Entanglement plays a central role in quantum technologies, yet its characterization and control in materials remain challenging. Recent developments in spectrum-based entanglement witnesses have enabled new strategies for quantifying many-body entanglement in macroscopic materials. Here, we develop a protocol for detecting spin-orbital entanglement using experiment-accessible resonant inelastic x-ray scattering (RIXS). Central to our approach is the construction of a Hermitian generator from experimentally measurable spectra, which allows us to compute the quantum Fisher information (QFI) available in spin--orbital systems. The resulting QFI provides upper bounds for kkk-producible states and thus serves as a robust witness of spin-orbital entanglement. To account for realistic experimental limitations, we further extend our framework to include relaxed QFI bounds applicable to measurements lacking full polarization resolution.
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Quantum materials are believed to host highly entangled states of matter, but probing and quantifying such entanglement has long remained experimentally elusive. Here, we use resonant inelastic X-ray scattering (RIXS) as a probe of multipartite spin entanglement. By projecting the RIXS cross section onto the appropriate spin excitation channel, we show that the Quantum Fisher Information can be extracted directly from the measured spin fluctuation spectrum. We detect at least 7-partite spin entanglement in the model one-dimensional cuprate Sr2_22​CuO3_33​, revealing one of the largest entanglement depths yet reported in a solid. The observed entanglement depth agrees with Hubbard-model expectations and persists to elevated temperatures. Our results establish RIXS as an experimental probe of many-body spin entanglement and provide a platform for extensions to charge and orbital sectors and nonequilibrium settings.
Characterizing and controlling entanglement in quantum materials is crucial for the development of next-generation quantum technologies. However, defining a quantifiable figure of merit for entanglement in macroscopic solids is theoretically and experimentally challenging. At equilibrium the presence of entanglement can be diagnosed by extracting entanglement witnesses from spectroscopic observables and a nonequilibrium extension of this method could lead to the discovery of novel dynamical phenomena. Here, we propose a systematic approach to quantify the time-dependent quantum Fisher information and entanglement depth of transient states of quantum materials with time-resolved resonant inelastic x-ray scattering. Using a quarter-filled extended Hubbard model as an example, we benchmark the efficiency of this approach and predict a light-enhanced many-body entanglement due to the proximity to a phase boundary. Our work sets the stage for experimentally witnessing and controlling entanglement in light-driven quantum materials via ultrafast spectroscopic measurements.
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