  We theoretically studied the implementation of a quantum memory and an
optical transistor in a system composed by a single atom trapped inside a high
finesse cavity. In order to store and map the quantum state of an input pulse
onto internal states of the single atom (quantum memory) we employ the
electromagnetically induced transparency (EIT) phenomenon (which can work out
as an optical transistor) where the information can be transferred to the dark
state of the atom modelled by a three-level system in a {\Lambda}-type
configuration. In our model we consider a suitable temporal shape for the
control field that ensures the adiabaticity of the storage process and
retrieval of the probe pulse. The dynamic of the field inside the cavity was
obtained by master equation approach, while the outside field was calculated by
input-output formalism. We have analysed two different setups: i) two-sided and
ii) single-sided cavities. While the first setup is the most appropriate and
commonly used to observe cavity-EIT in the transmission spectrum, thus the best
configuration for the optical transistor, the maximum quantum memory efficiency
can not reach reasonable values, being limited to 50% for symmetric cavities.
On the other hand, with single-sided cavity the quantum memory efficiency
increases considerably and can reach values close to 100% in the strong
atom-field coupling regime. However this specific setup is not favourable to
observe the cavity-EIT effect in the transmission spectrum and then it is not
appropriate to control the transmission of light pulses.
