  We investigate in detail the optimal conditions for a high fidelity transfer
from a single-polariton state to a single-photon state and subsequent homodyne
detection of the single photon. We assume that, using various possible
techniques, the single polariton has initially been stored as a spin-wave
grating in a cloud of cold atoms inside a low-finesse cavity. This state is
then transferred to a single-photon optical pulse using an auxiliary beam. We
optimize the retrieval efficiency and determine the mode of the local
oscillator that maximizes the homodyne efficiency of such a photon. We find
that both efficiencies can have values close to one in a large region of
experimental parameters.
