Photon storage in Lambda-type optically dense atomic media. III. Effects of inhomogeneous broadening

In a recent paper [A.V. Gorshkov et al., e-print quant-ph/0604037 (2006)] and in the two preceding papers [A.V. Gorshkov et al., e-print quant-ph/0612082 (2006); e-print quant-ph/0612083 (2006)], 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 both in atomic vapors and in solid state systems. In particular, we show that for the case of Doppler-broadened atoms, at high enough optical depth, all atoms contribute coherently to the storage process as if the medium were homogeneously broadened. Furthermore, 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