photon with $\mathcal{E}_{\textrm{in}}(\tau) = \Theta(\tau)\exp(-\tau/2 T_1)/\sqrt{T_1}$ using a resonant control pulse ($\delta_g=\delta_s=0$). For the parameters of the storage medium we take $\gamma = 2\pi\times3.035$ MHz, $d=75$, and $\tilde{\mu}_{1g}=\tilde{\mu}_{1s}=1$. The first four level scenario (4L+) we consider is $\Delta_e=2\pi\times100$ MHz and $\tilde{\mu}_{2g}=\tilde{\mu}_{2s}=1$ while the second scenario (4L-) has the same excited state energy splitting but $\tilde{\mu}_{2g}=-\tilde{\mu}_{2s}=1$. The optimal control pulses resulting from the gradient ascent optimization are plotted in Fig. \[fig:fig6\] for each scenario. Not only does the inclusion of a fourth level dramatically change the optimal control pulse, but the sign of the relative dipole moment also has a large effect. More importantly, the computed storage (total) efficiencies are 73.6$\%$, 77.6$\%$, and 43.5$\%$ (63.4$\%$, 65.7$\%$, and 26.3$\%$) for the 3L, 4L+, and 4L- scenarios respectively. If one naively uses the optimal control for 3L in the 4L+ case, the storage (total) efficiency is only 56.5$\%$ (48.4$\%$), while for the 4L- case 20.8$\%$ (4.8 $\%$) is obtained. From this analysis it is clear that additional excited states must be taken into account and a careful choosing of those levels is required for any implementation of broadband photon storage where the peak Rabi frequency of the control pulse is comparable to the 