  We present an analytic solution describing the quantum state of a single
photon after interacting with a moving mirror in a cavity. This includes
situations when the photon is initially stored in a cavity mode as well as when
the photon is injected into the cavity. In addition, we obtain the spectrum of
the output photon in the resolved-sideband limit, which reveals spectral
features of the single-photon strong-coupling regime in this system. We also
clarify the conditions under which the phonon sidebands are visible and the
photon-state frequency shift can be resolved.
