Observing dynamical phases of BCS superconductors in a cavity QED simulator

In conventional Bardeen-Cooper-Schrieffer superconductors¹, electrons with opposite momenta bind into Cooper pairs due to an attractive interaction mediated by phonons in the material. Although superconductivity naturally emerges at thermal equilibrium, it can also emerge out of equilibrium when the system parameters are abruptly changed^2-8. The resulting out-of-equilibrium phases are predicted to occur in real materials and ultracold fermionic atoms, but not all have yet been directly observed. Here we realize an alternative way to generate the proposed dynamical phases using cavity quantum electrodynamics (QED). Our system encodes the presence or absence of a Cooper pair in a long-lived electronic transition in ⁸⁸Sr atoms coupled to an optical cavity and represents interactions between electrons as photon-mediated interactions through the cavity^9,10. To fully explore the phase diagram, we manipulate the ratio between the single-particle dispersion and the interactions after a quench and perform real-time tracking of the subsequent dynamics of the superconducting order parameter using nondestructive measurements. We observe regimes in which the order parameter decays to zero (phase I)^3,4, assumes a non-equilibrium steady-state value (phase II)^2,3 or exhibits persistent oscillations (phase III)^2,3. This opens up exciting prospects for quantum simulation, including the potential to engineer unconventional superconductors and to probe beyond mean-field effects like the spectral form factor^11,12, and for increasing the coherence time for quantum sensing.