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

We propose to simulate dynamical phases of a BCS superconductor using atom-light interactions in an optical cavity. The absence or presence of Cooper pairs is encoded in the internal electronic states of atoms confined within the cavity, while collective atom-atom interactions mediated by the cavity photons provide the analogue of the electron-electron attraction. Further, tunable inhomogeneous Stark and magnetic Zeeman shifts can be used to modify the dispersion relation of the effective Cooper pairs. These features allow us to controllably 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. We demonstrate the robustness of our predictions to typical experimental sources of noise, including the realization of a dynamical phase featuring persistent and robust coherent oscillations of the superconducting order parameter. Given the level of control available 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.