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arXiv:2404.05850

Witnessing Quantum Entanglement Using Resonant Inelastic X-ray Scattering

Tianhao Ren, Yao Shen, Lajer, Marton, Sophia F. R. TenHuisen, Jennifer Sears, Wei He, Mary H. Upton, D. Casa, P. Becker, Matteo Mitrano, M. P. M. Dean, Robert Konik

Published Apr 8, 2024• 2 citations
arXivHTMLPDF

Abstract

Although entanglement is both a central ingredient in our understanding of quantum many-body systems and an essential resource for quantum technologies, we only have a limited ability to quantify entanglement in real quantum materials. Thus far, entanglement metrology in quantum materials has been limited to measurements involving Hermitian operators, such as the detection of spin entanglement using inelastic neutron scattering. Here, we devise a method to extract the quantum Fisher information (QFI) from non-Hermitian operators and formulate an entanglement witness for resonant inelastic x-ray scattering (RIXS). Our approach is then applied to the model iridate dimer system Ba$_3$CeIr$_2$O$_9$ and used to directly test for entanglement of the electronic orbitals between neighboring Ir sites. We find the entanglement can be detected if we account for the expected symmetries, parity, and electron number conservation, of the dimer system. We also consider the roles that the incident and outgoing x-ray polarizations and the incident photon energy play in entanglement detection. Our protocol provides a new handle for entanglement detection in quantum materials.

DOI
10.48550/arxiv.2404.05850

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Resonant inelastic X-ray scattering (RIXS) is conventionally used to probe elementary excitations and correlations in quantum materials. Here, we propose an interferometric RIXS protocol that instead creates entanglement between spatially separated regions of a solid-state material. An incident X-ray photon is coherently split by a beam splitter into two arms illuminating opposite ends of a sample. Recombining the scattered photons at a second beam splitter and detecting an energy-selected photon then projects the material into a coherent superposition of excitations at the two ends. This protocol is the X-ray, solid-state analogue of the Duan-Lukin-Cirac-Zoller (DLCZ) heralding scheme. Using a Kramers-Heisenberg formalism with quantized photon modes, we show that orthogonal and degenerate end excitations yield maximally entangled states. We illustrate this mechanism in three models: (1) two decoupled sites yield a heralded Bell state. (2) An open tight-binding chain exhibits reflection-parity-dependent interference, providing a benchmark for the interferometer's coherence. (3) A spin-1 Haldane (AKLT) chain yields an entangled pair of fractionalized edge spins. We also discuss practical considerations and challenges for realizing the protocol in X-ray experiments.
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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