  A major challenge in generating single photons with a single emitter is to
excite the emitter while avoiding laser leakage into the collection path.
Ideally, any scheme to suppress this leakage should not result in a loss in
efficiency of the single-photon source. Here, we investigate a scheme in which
a single emitter, a semiconductor quantum dot, is embedded in a microcavity.
The scheme exploits the splitting of the cavity mode into two
orthogonally-polarised modes: one mode is used for excitation, the other for
collection. By linking experiment to theory, we show that the best population
inversion is achieved with a laser pulse detuned from the quantum emitter. The
Rabi oscillations have an unusual dependence on pulse power. Our theory
describes them quantitatively allowing us to determine the absolute photon
creation probability. For the optimal laser detuning, the population innversion
is 98\%. The Rabi oscillations depend on the sign of the laser-pulse detuning.
We show that this arises from the non-trivial effect of phonons on the exciton
dynamics. The exciton-phonon interaction is included in the theory and gives
excellent agreement with all the experimental results.
