  We propose to simulate dynamical phases of a BCS superconductor using an
ensemble of cold atoms trapped in an optical cavity. Effective Cooper pairs are
encoded via internal states of the atoms and attractive interactions are
realized via the exchange of virtual photons between atoms coupled to a common
cavity mode. Control of the interaction strength combined with a tunable
dispersion relation of the effective Cooper pairs allows exploration of the
full dynamical phase diagram of the BCS model, as a function of system
parameters and the prepared initial state. Our proposal paves the way for the
study of non-equilibrium features of quantum magnetism and superconductivity by
harnessing atom-light interactions in cold atomic gases.
