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The dynamical Casimir effect (DCE) predicts the generation of photons fromthe vacuum due to the parametric amplification of the quantum fluctuation of anelectromagnetic field\cite{casimir1,casimir2}. The verification of such effectis still elusive in optical systems due to the very demanding requirements ofits experimental implementation. This typically requires very fast changes ofthe boundary conditions of the problem, such as the high-frequency driving ofthe positions of the mirrors of a cavity accommodating the field. Here, we showthat an ensemble of two-level atoms collectively coupled to the electromagneticfield of a cavity (thus embodying the quantum Dicke model\cite{dicke}), drivenat low frequencies and close to a quantum phase transition, stimulates theproduction of photons from the vacuum. This paves the way to an effectivesimulation of the DCE through a mechanism that has recently found anoutstanding experimental demonstration\cite{esslinger}. The spectral propertiesof the emitted radiation reflect the critical nature of the system and allow usto link the detection of DCE to the Kibble-Zurek mechanism for the productionof defects when crossing a continuous phase transition\cite{KZ1,KZ2}. Weillustrate the features of our proposal by addressing a simple cavityquantum-electrodynamics (cQED) setting of immediate experimental realisation.

Photon production from the vacuum close to the super-radiant transition: When Casimir meets Kibble-Zurek