  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.

Atomic Physics;Quantum Physics