Diagnosing electronic phases of matter using photonic correlation functions

In the past couple of decades, there have been significant advances in measuring quantum properties of light, such as quadratures of squeezed light and single-photon counting. Here, we explore whether such tools can be leveraged to probe electronic correlations in the many-body quantum regime. Specifically, we show that it is possible to probe certain spin, charge, and topological orders in an electronic system by measuring the correlation functions of scattered photons. We construct a mapping from the correlators of the scattered photons to those of a correlated insulator, particularly for Mott insulators described by a single-band Fermi-Hubbard model at half-filling. We show that frequency filtering before photodetection plays a crucial role in determining this mapping.  We find that if the ground state of the insulator is a gapped spin liquid, a photon-pair correlation function, i.e.,  G⁽²⁾, can detect the presence of anyonic excitations with fractional mutual statistics. Moreover, we show that correlations between electromagnetic quadratures can be used to detect expectation values of static spin chirality operators on both the kagome and triangular lattices, thus being useful in detecting chiral spin liquids. More generally, we show that a series of hitherto unmeasured spin-spin and spin-charge correlation functions of the material can be extracted from photonic correlations. This work opens up access to probe correlated materials, beyond the linear response paradigm, by detecting quantum properties of scattered light.