with the two quantum numbers $n_x$ and $n_y$. The eigenenergies of such an asymmetric harmonic confinement as a function of the magnetic field are given in Ref. .

\[tab:defs\]

  ------------------------------------------------------------------------------ ---------------------------------------------------------------------------
  label                                                                          description
  $\hbar$                                                                        reduced Planck constant
  $\mu_B$                                                                        Bohr magneton
  $\epsilon_0$, $\epsilon_r$                                                     permittivity of vacuum, relative permittivity
  $g_e$, $g_h$                                                                   electron and hole g-factor
  $E_0$                                                                          bandgap of the QD-material
  $m_e^*$, $m_h^*$                                                               electron, hole effective mass
  $\hbar\omega_c=\frac{\hbar eB}{m_e^*}$                                         electron cyclotron energy
  $\hbar\omega_x$, $\hbar\omega_y$                                               confinement energies of the asymmetric harmonic oscillator
  $\hbar\omega_0 \equiv\hbar\omega_{x}+\Delta_p\equiv\hbar\omega_{y}-\Delta_p$   confinement energy of the symmetric harmonic oscillator
  $n, L$                                                                         quantum numbers for the symmetric harmonic oscillator
  $n_x, n_y$                                                                     quantum numbers for the asymmetric harmonic oscillator
  $E_{n,L}$                                                                      eigenenergies of the symmetric harmonic oscillator
  $E_{ij}^{e}, E_{ij}^{h}$                                                       Coulomb energy between two electrons and two holes in the shells $i$, $j$
  $X_{ij}^{e}, X_{ij}^{h}$                                                       exchange Coulomb energy between an electron/hole in the shells $i$, $j$
  $\Delta_{pd}$                                                                  coupling between $p_-$- and the $d_+$-shell
  $\Omega_{\text{R}}$                                                            Rabi frequency
  $\Gamma_r=\tau_r^{-1}$                                                         radiative decay rate
  $\Gamma_A=\tau_A^{-1}$                                                         radiative Auger decay rate.
  $\Gamma_p=\tau_p^{-1}$                                                         relaxation rate from $p$- to $s$-shell
  $\Gamma_{\text{out}}=\tau_{\text{out}}^{-1}$                                   tunnel rate out of the QD after a radiative Auger decay
  $\Gamma_{\text{in}}=\tau_{\text{in}}^{-1}$                                     tunnel rate into the ionized QD
  $E_{\text{f}}^{p_{\pm}}, E_{\text{f}}^{d_{\pm}}$, and $E_{\text{f}}^{d_{0}}$   final state energies after Auger excitation into $p$- and $d$-shells
  $\Delta_{LO}, 