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 quadrature and correlation functions of photons scattered off it. We construct a mapping from the correlation functions of the scattered photons to those of a correlated insulator, particularly for Mott insulators described by a single-band Hubbard model at half-filling. We show how frequency filtering before photodetection plays a crucial role in determining this mapping. If the ground state of the insulator is a gapped spin liquid, we show that a $G^{(2)}$ (two-photon coherence) measurement can detect the presence of anyonic excitations with fractional mutual statistics. We also show that homodyne measurements 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. Moreover, a slew 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.