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We consider a model of a light-matter system, in which a system of fermions(or bosons) is coupled to a photonic mode that drives a phase transitions inthe matter degrees of freedom. Starting from a simplified analytical model, weshow that the entanglement between light and matter vanishes at small and largecoupling strength, and shows a peak in the proximity of the transition. Weperform numerical simulations for a specific model (relevant to both solidstate and cold atom platforms), and show that the entanglement displayscritical behavior at the transition, and features maximum susceptibility, asdemonstrated by a maximal entanglement capacity. Remarkably, light-matterentanglement provides direct access to critical exponents, suggesting a novelapproach to measure universal properties without direct matter probes.

Critical light-matter entanglement at cavity mediated phase transition