  We have developed a full quantum microscopic theory to analyze the time
evolution of transversal and longitudinal components of an exciton-single
photon system coupled to bulk acoustic phonons. These components are subjected
to two decay processes. One is radiative relaxation and the other is
pure-dephasing due to exciton-phonon interaction. The former results in a decay
with an exponent linear to time, while the latter causes a faster initial decay
than the radiative decay. We analyzed the dependence of the components on the
duration of the input one-photon pulse, temperature, and radiative relaxation
rates. Such a quantitative analysis is important for the developments of
atom-photon interfaces which enable coherent transfer of quantum information
between photons and atomic systems. We found that, for a GaAs spherical quantum
dot in which the exciton interacts with bulk phonons, the maximal probability
of the excited state can be increased up to 75 %. This probability can be
considered as the efficiency for quantum information transfer from photon to
exciton.
