  The mechanism of extraction of information stored in a quantum memory is
studied here in detail. We consider memories containing a single excitation of
a collective atomic state, which is mapped into a single photon during the
reading process. A theory is developed for the wavepacket of the extracted
photon, leading to a simple analytical expression depending on the key
parameters of the problem, like detuning and intensity of the read field and
the number of atoms in the atomic ensemble. This theory is then compared to a
large set of experimental situations and a satisfactory quantitative agreement
is obtained. In this way, we are able to systematically study the saturation
and spectrum of the reading process, as well as clarify the role of
superradiance in the system.
