Exploring BCS-like Dynamical Phases in a Multilevel Atomic System*

Collective atom-light interactions have the potential to enable study of a large class of quantum systems both in and out of equilibrium. In previous work [1], we demonstrated an implementation of the BCS model of superconductivity using an ensemble of ~10^6 88Sr atoms coupled to a high-finesse optical cavity, including an observation of all three predicted dynamical phases for the first time [2]. We extend this exploration by considering an effective three-level system consisting of the ground state and the m = ±1 Zeeman sublevels of the ³P₁ state. By competing an applied Zeeman splitting against effective atom-atom interactions engineered in the system, we observe that we are able to control population transfer between “bright” and “dark” superpositions of the two excited states. Moreover, we demonstrate that the regimes where transfer is allowed and suppressed are separated by a dynamical phase transition and exhibit properties analogous to phases II and III of the BCS model. This physics can also be understood by considering the collective atomic dipole moment, and we show that the atom-atom interactions protect the collective dipole orientation even in the presence of an external magnetic field.

[1] D. J. Young, A. Chu et al., Nature 625, 679-684 (2024).

[2] R. J. Lewis-Swan et al., PRL 126, 173601 (2021).