can include magnetic field fluctuations or atomic motion, set the limit for the spin wave coherence time, and hence, the duration the photon can be stored. Notably, the spin wave is more robust against decoherence than many other multi-particle entangled states [@ref:Lukin_RMP_03]. The spin wave can be re-converted into a photon by using another control pulse (see Fig. \[fig:fig1\](c)-(d)). Gorshkov *et al* showed that the optimal retrieval is simply the time-reverse of storage; so-called “backwards retrieval" [@ref:Gorshkov_PRL07]. This process creates a photon propagating in the opposite direction to its initial propagation. Forwards retrieval is also possible, but will not be treated here.

For all of these storage schemes, the dynamics of the interaction between the two optical fields and the atoms is described by treating the signal field on the ${\ensuremath{|g\rangle}}-{\ensuremath{|1\rangle}}$ transition quantum mechanically while treating the ${\ensuremath{|s\rangle}}-{\ensuremath{|1\rangle}}$ control field semiclassically. The atomic level structure with relevant energy scales for photon storage in a three-level $\Lambda$ system is shown in Fig. \[fig:fig2\]. The ensemble of $\Lambda$ systems is composed of $N$ atoms distributed over a volume of length $L$ and cross-sectional area $A$ with linear density $n(z)$. In this analysis, we ignore the motion of the atoms and thereby restrict 