  We study theoretically the spin-induced and photon-induced fluctuations of
optical signals from a singly-charged quantum dot-microcavity structure. We
identify the respective contributions of the photon-polariton interactions, in
the strong light-matter coupling regime, and of the quantum back-action induced
by photon detection on the spin system. Strong spin projection by a single
photon is shown to be achievable, allowing the initialization and measurement
of a fully-polarized Larmor precession. The spectrum of second-order
correlations is deduced, displaying information on both spin and quantum
dot-cavity dynamics. The presented theory thus bridges the gap between the
fields of spin noise spectroscopy and quantum optics.
