Witnessing spin entanglement in a one-dimensional Hubbard chain with resonant inelastic x-ray scattering

Entanglement is a key property of quantum materials and crucial resource for quantum information science, yet few experimental methods exist to probe it in macroscopic solids. One promising approach to detect entanglement is via the Quantum Fisher Information (QFI) calculated from material response functions, such as the dynamical spin structure factor ¹, as was recently demonstrated in inelastic neutron scattering experiments^2,3. Here, we extend this approach to resonant inelastic x-ray scattering (RIXS), determining the dynamical spin structure factor in absolute units from RIXS measurements of the magnetic excitation spectrum, in combination with calculations and comparison to theory. In Sr₂CuO₃, a prototypical cuprate system, we witness at least 6-partite spin entanglement. This entanglement is robust, with 4-partite entanglement persisting up to 220 K.

Witnessing entanglement with RIXS opens possibilities to study entanglement in new contexts, including in thin films or light-induced phases. Furthermore, RIXS is sensitive to a broad range of spin, charge, and orbital excitations, which are also expected to be entangled. Hence RIXS may provide a route to discover more general entangled states in quantum materials. Our work provides a new framework for understanding collective properties and phases of quantum materials through understanding the structure of entanglement.

1. Hauke, P., et al. Nat Phys 12, 778–782 (2016). DOI: 10.1038/NPHYS3700

2. Scheie, A., et al. PRB 103, 224434 (2021). DOI: 10.1103/PhysRevB.103.224434

3. Laurell, P., et al. PRL 127, 037201 (2021). DOI: 10.1103/PhysRevLett.127.037201

4. TenHuisen, S. F. R., et al. forthcoming