  We investigate the effect of nuclear spins on the phase shift and
polarisation rotation of photons scattered off a quantum dot-cavity system. We
show that as the phase shift depends strongly on the resonance energy of an
electronic transition in the quantum dot, it can provide a sensitive probe of
the quantum state of nuclear spins that broaden this transition energy. By
including the electron-nuclear spin coupling at a Hamiltonian level within an
extended input-output formalism, we show how a photon scattering event acts as
a nuclear spin measurement, which when rapidly applied leads to an inhibition
of the nuclear spin dynamics via the quantum Zeno effect, and a corresponding
stabilisation of the optical resonance. We show how such an effect manifests in
the intensity autocorrelation $g^{(2)}(\tau)$ of scattered photons, whose
long-time bunching behaviour changes from quadratic decay for low photon
scattering rates (weak laser intensities), to ever slower exponential decay for
increasing laser intensities as optical measurements impede the nuclear spin
evolution.
