optical pumping rate into ground-level dark states (Sec. \[sec:g-states\]) by roughly a factor of $A_m/A_g$ as one would expect. The actual dark states depend on the repumper polarization. For $\pi$ polarization, $|3\rangle$ and $|6\rangle$ are dark states, for $\sigma^+$, $|5\rangle$ and $|6\rangle$ are dark, and for $\sigma$ polarization, the dark states are superpositions of $|3\rangle$ and $|5\rangle$ and of $|4\rangle$ and $|6\rangle$.

![\[fig:m-states\](Color online) For $B=0$, the scattering rate is independent of the repumper polarization \[$\pi$, $\sigma$, or $\sigma^+$; solid (black) curve\]. For a $\sigma$ polarized repumper, a field of 100$\mu$T ($2 g_m \mu_\mathrm{B} B/\hbar \approx 0.09 \Gamma$) destabilizes the dark states completely \[dashed (red) curve\]. $\Omega_\mathrm{c} = \Omega_\mathrm{r} = \Gamma$, $\delta_\mathrm{c} = -\Gamma/2$, $\delta_\mathrm{r} = \Gamma/2$, $\gamma_{g,m}=\Gamma/10$, and cooling laser $\sigma$ polarized.](Fig06-m-states){width=".85\columnwidth"}

When the repumper is $\sigma$ polarized, the dark states can again be destabilized using a magnetic field. The relation between the optical pumping rate and the required field is not as simple as in Sec. \[sec:g-states\] because the decay probability $A_m$ is low. However, a field of 100$\mu$T (dark state evolution rate $2 g_m \mu_\mathrm{B} B/\hbar \approx 0.09 \Gamma$) is enough to fully destabilize the dark states for the parameters in Fig. \[fig:m-states\] \[dashed (red) curve\].

Polarization 