Quantum dot samples used in this study were synthesized using the hot injection method.\cite{Wehrenberg2002} 
Samples were kept in a glovebox after synthesis and exposure to visible and UV light was minimized.  
These conditions preserved the dots for several months.  
Two samples, Batch A and Batch B, are presented in this study, in an effort to show the robustness of the results. 
Properties of their optical characterization are shown in Table \ref{tab:QD_abs}.  
The 1S band of Batch A is broader than Batch B, an effect which is usually attributed to a wider size distribution and therefore greater inhomogeneous broadening.

\begin{table}[]
	\centering
	\caption{Batch Parameters extracted from absorption spectra.  $\langle d \rangle$: average QD diameter, as inferred by the 1S transition energy. }
	\label{tab:QD_abs}
	\begin{tabular}{l|cc}
		 													  & A    & B \\
		\hline
		$ \omega_{10} \left( \text{cm}^{-1} \right)$		  & 7570 & 6620 \\
		$ \text{FWHM} \left(\text{cm}^{-1}\right) $  		  & 780  & 540 \\
		$ \langle d \rangle  \left(\text{nm}\right)$ 		  & 4    & 4.8 \\
		$ \sigma_0 \left( \times 10^{16} \text{cm}^2 \right)$ & 1.7  & 2.9
	\end{tabular}
\end{table}

The experimental system for the TG experiment has been previously explained.\cite{Kohler2014,Czech2015} 
Briefly, two independently tunable OPAs are used to make pulses $E_1$ and $E_2$ with colors $\omega_1$ and $\omega_2$. 
The third beam, $E_{2^\prime}$, is split off from $E_2$. The TG experiment utilized here uses temporally overlapped $E_2$ and $E_{2^\prime}$. 
Previous ultrafast TG work has characterized the delay of $E_1$ as $\tau_{21}=\tau_2-\tau_1$; to connect the experimental space with the TA measurements, we will report the population delay time between the probe and the pump as $T(=-\tau_{21})$. 
Pulse timing is controlled by a motorized stage that adjusts the arrival time of $E_1$ relative to $E_2$ and $E_{2^\prime}$.

All three beams are focused onto the sample in a BOXCARS geometry and the direction $\vec{k}_1-\vec{k}_2+\vec{k}_{2^\prime}$ is isolated and sent to a monochromator to isolate the $\omega_1$ frequency with $\sim 120 \text{cm}^{-1}$ detection bandwidth. 
The signal, $N_{\text{TG}}$, was detected with an InSb photodiode. Reflective neutral density filters (Inconel) limit the pulse fluence to avoid multi-photon absorption. 
To control for frequency-dependent changes in pulse arrival time due to the OPAs and the neutral density, a calibration table was established to assign a correct zero delay for each color combination (see supporting information for more details).

The TA experiments were designed to minimally change the TG experimental conditions.  
The $E_{2^\prime}$ beam was blocked and signal in the $\vec{k}_1$ direction was measured.  
$E_2$ was chopped and the differential signal and the average signal were measured to define $T_0$ and $T$ needed to compute $\Delta A$.  
Just as in TG experiments, the excitation frequencies were scanned while the monochromator was locked at $\omega_m=\omega_1$.
% DK: perhaps leave this part out
%Finally, fluence studies resonant with the 1S band were performed to test for indications of intensity-dependent relaxation. 
%These studies showed no indication of accelerated Auger recombination rates (see supporting info).