Using photon correlations to observe quantum phase transitions in strongly interacting cavity-embedded materials

We show that photon correlation measurements can probe emergent magnetic properties of Mott insulators strongly coupled to a cavity photon mode, establishing a new quantum-optical tool for observing quantum phase transitions in strongly-correlated materials. When placed in a cavity, light-matter coupling entangles cavity photons to magnetic excitations, imprinting the photons with information about magnetic correlations. Remarkably, this same information about magnetic correlations is transmitted to the coherence properties of an easily observable output field, which we prove by generalizing quantum optical input-output relations to many body quantum systems. To illustrate this, we consider a ladder Mott insulator in a cavity and demonstrate using DMRG that spin dimer correlations reveal a gapless mode at the quantum phase transition to a dimerized state. Our work shows that this gapless mode can be observed in quantum photon correlations of the output field, providing a new experimental tool for interrogating quantum materials and their phase transitions.