Review of Photon Storage in a $\Lambda$-system {#sec:3L}
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Photon storage in a three level, $\Lambda$-type system has been the subject of many articles and reviews [@ref:Sangouard_RMP_2011]. Here, we briefly touch on the main points and restrict the discussion to those schemes described by the theory of Gorshkov *et al*, namely those based on Electromagnetically Induced Transparency (EIT), off-resonant Raman, or photon echo interactions [@ref:Gorshkov_PRL07; @ref:Gorshkov_PRA2]. In that work, these three schemes were shown to yield similar storage efficiencies for the same optical depth of the $\Lambda$ medium and are in this sense equivalent. However, there are tradeoffs in the actual physical implementation for these schemes which will be discussed later.

The basic picture of photon storage in such a system is shown in Fig. \[fig:fig1\]. Each atom in the ensemble is composed of two ground states ${\ensuremath{|g\rangle}}$ and ${\ensuremath{|s\rangle}}$ that can be optically coupled to the excited state ${\ensuremath{|1\rangle}}$. These two transitions can be individually addressed using a sufficient ground state splitting or by selection rules so as to avoid cross-coupling. The storage procedure starts with all of the atoms initialized into ${\ensuremath{|g\rangle}}$. Then a quantum field $\mathcal{E}(\tau)$ which is to be stored, addresses the ${\ensuremath{|g\rangle}}-{\ensuremath{|1\rangle}}$ transition while a 