Witnessing Quantum Entanglement Using Resonant Inelastic X-ray Scattering

We devise a method to use resonant inelastic x-ray scattering (RIXS) to detect entanglement in a quantum material.  We show how the non-Hermitian, non-local RIXS operator can be related to an instance of the quantum Fisher information (QFI) and then to a bound on the multipartite entanglement.   We apply our approach to the model iridate dimer systems Ba₃CeIr₂O₉ and Ba₃TaIr₂O₉ to test directly for entanglement of the electronic orbitals between neighboring Ir sites.  By taking into account the symmetries of the system, we are able to show that RIXS measurements can certify the presence of entanglement between dimer sites.  We consider the role of both polarization and incident energy of the incident photon on the ability to use RIXS as a means to detect multipartite entanglement.