A cavity-QED simulator of dynamical phases of a BCS superconductor*

In this work we describe a way to simulate dynamical phases of a BCS superconductor using an ensemble of cold atoms confined in an optical cavity. The absence or presence of Cooper pairs is encoded using the internal electronic states of the atoms, while cavity mediated atom-atom interactions provide the analogue of the electron-electron attraction. By carefully controlling the relative strength of the interactions with respect to the tunable dispersion relation of the effective Cooper pairs, this cavity-QED simulator provides a realistic way to probe, in real time and without the need of ultrafast probes, the dynamical phase diagram of the BCS model as a function of the system parameters and/or the initial non-equilibrium state. Given the level of control attained in state-of-the-art cavities, our work paves the way for the study of non-equilibrium features of quantum magnetism and superconductivity by harnessing atom-light interactions in cold atomic gases.