Strong Coupling on a Forbidden Transition in Strontium and Nondestructive Atom Counting

We observe strong collective coupling between an optical cavity and the forbidden spin singlet to triplet optical transition $^1$S$_0$ to $^3$P$_1$ in an ensemble of $^{88}$Sr. Despite the transition being 1000 times weaker than a typical dipole transition, we observe a well resolved vacuum Rabi splitting. We use the observed vacuum Rabi splitting to make non-destructive measurements of atomic population with the equivalent of projection-noise limited sensitivity and minimal heating ($<0.01$ photon recoils/atom). This technique may be used to enhance the performance of optical lattice clocks by generating entangled states and reducing dead time.