  We introduce a simple model for electromagnetically induced transparency in
which all fields are treated quantum mechanically. We study a system of three
separated atoms at fixed positions in a one-dimensional multimode optical
cavity. The first atom serves as the source for a single spontaneously emitted
photon; the photon scatters from a three-level Lambda-configuration atom which
interacts with a single-mode field coupling two of the atomic levels; the third
atom serves as a detector of the total transmitted field. We find an analytical
solution for the quantum dynamics. From the quantum amplitude describing the
excitation of the detector atom we extract information that provides exact
single-photon analogs to wave delays predicted by semi-classical theories. We
also find complementary information in the expectation value of the electric
field intensity operator.
