Collective cavity quantum electrodynamics in solid-state optical clocks

Abstract: Solid-state frequency standards are generally limited by strong decoherence, rendering conventional interrogation schemes inefficient. The $<sup>{229}$Th nuclear clock provides a unique and timely platform for solid-state optical metrology and nuclear cavity quantum electrodynamics (QED), featuring a coherence time many orders of magnitude shorter than the radiative lifetime in current experiments. Here, we propose and analyze three cavity QED-enhanced clock interrogation schemes that turn this timescale mismatch into an advantage, leveraging collective coupling of thorium nuclei to nanophotonic modes to enable fast interrogation and detection despite the long population lifetime. We reveal the central role of collective cooperativity in determining the clock frequency instability, and derive the optimal conditions (power, working-point detuning, thorium density) for clock operation.