Quantum Theory of X-ray Photon Correlation Spectroscopy

Characterizing quantum materials is essential for understanding their microscopic interactions and advancing quantum technology. X-ray photon correlation spectroscopy (XPCS) with coherent X-ray sources offers access to higher-order correlations, but its theoretical basis, the Siegert relation, is derived from dynamical light scattering with independent classical scatterers, and its validity for XPCS remains unexamined. Here we present a microscopic quantum theory of XPCS derived from elecron-photon interaction Hamiltonians, introducing four configurations tied to distinct fourth-order electron-density correlation functions. We examine the validity of the Siegert relation and derive a generalized Siegert relation. Notably, the Siegert relation breaks down even in non-interacting Fermi gas due to exchange interactions. Furthermore, density matrix renormalization group calculations on 1D Kitaev chain reveal oscillatary signatures that can distinguish topologically trivial phases from topological phases with Majorana zero modes. Our work provides a robust theoretical foundation for XPCS and highlights the value of higher-order correlations in advanced X-ray and neutron sources for probing quantum materials.