Witnessing Entanglement in a 1D Hubbard Chain via RIXS

Entanglement is an essential property of quantum materials and a crucial resource for quantum information science, yet few experimental methods exist to measure it in macroscopic solids. Here we demonstrate that resonant inelastic x-ray scattering (RIXS) measurements on Sr₂CuO₃, a prototypical cuprate spin system, witness at least 6-partite entanglement. This entanglement is robust, with 4-partite entanglement persisting up to 220 K.<br/><br/>To witness multipartite entanglement, we make use of the Quantum Fisher Information (QFI), which can be directly related to the dynamical spin structure factor¹, an approach which has recently been demonstrated in inelastic neutron scattering experiments^2,3. We extend this formalism to RIXS, determining the dynamical spin structure factor of Sr₂CuO₃ in absolute units from RIXS measurements of the 2-spinon continuum in combination with calculations and comparison to theory.<br/><br/>Witnessing entanglement with RIXS opens possibilities to study entanglement in a broad variety of contexts, including in thin films or in light-induced phases in- and out-of-equilibrium. Furthermore, moving beyond spin entanglement, RIXS is sensitive to a broad range of spin, charge, and orbital excitations. These degrees of freedom are also expected to be entangled, hence RIXS may provide a route to discover more general entangled states in real materials. This will provide a new framework for understanding collective properties and phases of quantum materials through understanding the structure of entanglement.<br/><br/>1. Hauke, P., Heyl, M., Tagliacozzo, L. & Zoller, P. Measuring multipartite entanglement through dynamic susceptibilities. <i>Nat Phys</i> <b>12</b>, 778–782 (2016). DOI: 10.1038/NPHYS3700<br/>2. Scheie, A., Laurell, P., Samarakoon, A. M., Lake, B., Nagler, S.E., Granroth, G. E., Okamoto, S., Alvarez, G., & Tennant, D. A<i>.</i> Witnessing entanglement in quantum magnets using neutron scattering. <i>Physical Review B</i> <b>103</b>, 224434 (2021). DOI: 10.1103/PhysRevB.103.224434<br/>3. Laurell, P., Scheie, A., Mukherjee, C. J., Koza, M. M., Enderle, M., Tylczynski, Z., Okamoto, S., Coldea, R., & Tennant, D.A<i>.</i> Quantifying and Controlling Entanglement in the Quantum Magnet Cs₂CoCl₄. <i>Physical Review Letters</i> <b>127</b>, 037201 (2021). DOI: 10.1103/PhysRevLett.127.037201