Detection and Manipulation of F=9/2 nuclear spin ground states in a Strontium Cavity QED System

Cavity quantum electrodynamics (cavity QED) is a powerful platform for the quantum simulation of many-body physics. In this work, we demonstrate a single-shot readout of the populations of all ten nuclear spin ground states using a high-finesse cavity and state manipulation with RF coils. This scheme enables inducing cavity-mediated interactions close to one excited hyperfine manifold while performing readout via a separate manifold, ~GHz-detuned from the first. We show that this approach is compatible with quantum nondemolition (QND) measurements, facilitating ground-state entanglement for applications in state-of-the-art optical atomic clocks and magnetometers. Finally, we present another nondestructive technique that enables high-bandwidth readout exceeding the cavity linewidth limit.