adiabatic limit, $Td\gamma \gg 1$, an analytic solution for $\Omega(\tau)$ could be found and that the efficiency scaled as $\eta_s \propto d/(1+d)$. For broadband photon storage, the adiabatic limit is not necessarily met and the optimal $\Omega(\tau)$ must be found numerically. Gorshkov *et al.* used a gradient ascent algorithm in Ref. [@ref:Gorshkov_PRA4] to numerically optimize $\eta_s$ and found that the results matched the analytical solution in the adiabatic limit. In addition, it was shown that photons beyond the adiabatic regime ($1/T \approx d \gamma$) could also be stored efficiently by using this optimization technique. This is the approach we will use in the following analysis and now briefly review. Because we take a numerical approach, we now restrict the discussion to near-resonant storage schemes and exclude off-resonant Raman based storage which would require a much larger computational domain so as to capture the rapidly varying detuning ($\delta_g,\delta_s \gg \sqrt{d \gamma/T_1}$). Gorshkov *et al* mentioned in Ref. [@ref:Gorshkov_PRA4] how one can obtain the optimal control pulse for Raman-based storage from the optimal control pulse found for resonant storage, but we do not pursue this here. We do, however, note that the control pulse required for Raman storage can be several orders 