In a recent paper [Gorshkov et al., Phys. Rev. Lett. 98, 123601 (2007)] and
in the two preceding papers [Gorshkov et al., Phys. Rev. A 76, 033804 (2007);
76, 033805 (2007)], we used a universal physical picture to optimize and
demonstrate equivalence between a wide range of techniques for storage and
retrieval of photon wave packets in homogeneously broadened Lambda-type atomic
media, including the adiabatic reduction of the photon group velocity,
pulse-propagation control via off-resonant Raman techniques, and
photon-echo-based techniques. In the present paper, we generalize this
treatment to include inhomogeneous broadening. In particular, we consider the
case of Doppler-broadened atoms and assume that there is a negligible
difference between the Doppler shifts of the two optical transitions. In this
situation, we show that, at high enough optical depth, all atoms contribute
coherently to the storage process as if the medium were homogeneously
broadened. We also discuss the effects of inhomogeneous broadening in solid
state samples. In this context, we discuss the advantages and limitations of
reversing the inhomogeneous broadening during the storage time, as well as
suggest a way for achieving high efficiencies with a nonreversible
inhomogeneous profile.
