RJW analyzed the data. MCL developed the theory of the radiative Auger process. AJ, MCL, CS developed the theory for the time-resolved measurements. MCL, RJW, CS developed the theory for the magnetic field dispersion. MCL and RJW initiated the project and wrote the manuscript with input from all the authors.

Methods {#sec:methods}
=======

The samples are grown by molecular beam epitaxy. Sample A contains InGaAs QDs embedded in a $p$-$i$-$n$-$i$-$n$-diode structure [@Lobl2017; @Vora2015; @Javadi2017; @Grim2019]. Sample B contains GaAs QDs in AlGaAs, which are grown by GaAs-infilling of Al-droplet etched nano-holes [@Wang2007; @Huo2013]. The photon out-coupling is enhanced by a distributed Bragg mirror below the QDs. For both samples, the QDs are placed between a $p$-doped top gate and an $n$-type doped back gate. The QDs are tunnel-coupled to the back gate. This configuration stabilizes the charge environment of the QDs and enables tuning the QD charge state by applying a voltage between top and back gate [@Patel2010; @Kirsanske2017]. For the InGaAs QDs, the back gate has a distance of $40\ \text{nm}$ to the QDs, $30\ \text{nm}$ for the GaAs QDs. In a magnetic field, there is optical spin-pumping in the center of the trion charge plateau [@Kroutvar2004; @Dreiser2008]. Therefore, 