Probing light-induced changes in cavity-embedded materials via quantum photon coincidence spectroscopy

The regime of strong light-matter coupling in microcavities presents a promising avenue for controlling the electronic phases of materials. However, monitoring the resulting changes and attributing them to cavity photons remains challenging. In this talk, we show that weak driving of a cavity with an embedded Mott insulator can be used for both control and observation. As cavity photons become entangled with material excitations, they can induce changes to the state of matter while simultaneously acting as a witness to the process, which we predict is observable via the antibunching or bunching of emitted photons, detectable via second-order photon coherence measurements. To demonstrate this, we develop an input-output formalism that relates the statistics of transmitted photons to non-perturbative, light-induced changes in the material. For Ising ferromagnets in optical cavities, we find that light can push the material across its quantum critical point, which is reflected in strong antibunching of photons transmitted through the cavity.