Cavity Mediated Collective Spin Exchange Interactions in a Strontium Superradiant Laser

Laser cooled and quantum degenerate atoms are widely being pursued as quantum simulators that may explain the behavior of strongly correlated material systems, and as the basis of today's most precise sensors. A key challenge towards these goals is to understand and control coherent interactions between the atoms. Here, we observe long-range exchange interactions mediated by an optical cavity, which manifest as tunable spin-spin interactions on the pseudo spin-1/2 system composed of the millihertz linewidth clock transition in strontium. We observe the so-called one axis twisting dynamics, the emergence of a many-body energy gap, and signatures of gap protection of the optical coherence against certain sources of decoherence. These effects manifest in the output of a pulsed, superradiant laser operating on the millihertz linewidth transition. Our observations will aid in the future design of versatile quantum simulators that take advantage of the unique control and probing capabilities of cavity QED and the rich internal structure of long-lived Sr atoms. They also open a route for the next generation of atomic clocks that utilize quantum correlations for enhanced metrology.