Stabilization of an optical transition energy via nuclear Zeno dynamics in quantum-dot-cavity systems

We investigate the effect of nuclear spins on the phase shift and polarization 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 dynamics via the quantum Zeno effect, and a corresponding stabilization of the optical resonance. We show how such an effect manifests in the intensity autocorrelation g(2)(τ) of scattered photons, whose long-time bunching behavior 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.