Hybridizing light and matter by means of cavities can be used as a tool to influence material properties.  In my talk I will discuss a model for strongly correlated fermions close to a quantum phase-transition coupled to a single mode of an optical cavity. Close to the critical point, light and matter degrees of freedom hybridize, which can be observed in an increase in their entanglement. We show that this entanglement can be related to fluctuations in the fermionic system that are in principle directly measurable through Kubo response functions.  Additionally, correlations between fermions are enhanced in finite systems as a result of the light-matter hybridization.

(Pizza and refreshments will be served after the talk.)