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 changed2-8. 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 cavity9,10. 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 factor11,12, and for increasing the coherence time for quantum sensing.

Momentum-exchange interactions in a Bragg atom interferometer suppress Doppler dephasing.

Large ensembles of laser-cooled atoms interacting through infinite-range photon-mediated interactions are powerful platforms for quantum simulation and sensing. Here we realize momentum-exchange interactions in which pairs of atoms exchange their momentum states by collective emission and absorption of photons from a common cavity mode, a process equivalent to a spin-exchange or XX collective Heisenberg interaction. The momentum-exchange interaction leads to an observed all-to-all Ising-like interaction in a matter-wave interferometer. A many-body energy gap also emerges, effectively binding interferometer matter-wave packets together to suppress Doppler dephasing in analogy to Mössbauer spectroscopy. The tunable momentum-exchange interaction expands the capabilities of quantum interaction-enhanced matter-wave interferometry and may enable the realization of exotic behaviors, including simulations of superconductors and dynamical gauge fields.