Rabi frequency $\Omega_m$ increases with $d$. For these parameters, we find that $\Omega_m \propto d^{0.67}$. Furthermore, $\Omega(\tau)$ starts to become much more heavily weighted at the start of the pulse. Both of these observations can be understood as the optimal storage scheme slowly changes from a photon echo type storage towards an EIT-based storage as the adiabatic limit is approached. Lastly, the widths of these control pulses are not ultrafast, i.e. they do not require a mode-locked laser but rather are achievable with more flexible techniques such as direct intensity modulation. The combination of relatively high total efficiencies and realistic control pulses make it seem that storage of a quantum dot photon in an atomic gas like Rb is certainly feasible with current technology.

Importantly, the peak Rabi frequency $\Omega_m$ of the control pulse surpasses 50$\gamma$ even for relatively low $d$. For such large values of $\Omega_m$, the more complicated level structure of the storage medium will begin to play a significant role in the dynamics. For instance, the excited-state splittings of the commonly-used $D_2$ transitions of $^{87}$Rb are around 100 MHz ($\approx 30\gamma$). As a result, the three-level $\Lambda$ treatment is insufficient to describe broadband, on-resonance storage and more 