similar results [@Berkeland2002a].

Figure \[fig:pol-mod\] shows that the dark state destabilization due to polarization modulation is very similar to magnetic field destabilization when the dark state evolution rate is the same (cf. Fig. \[fig:m-states\]), except for some oscillations at the modulation frequency $\omega_\text{EOM}$. The two effects also sum up almost fully \[see the dotted (blue) curve in Fig. \[fig:pol-mod\]\].

![\[fig:pol-mod\](Color online) Scattering rate for stationary $\sigma$ repumper \[solid (black) curve\] and polarization modulated according to Eqs. (\[eq:EOM-pol\]) and (\[eq:EOM-ret\]) at $\omega_\text{EOM}=2\pi\times 2\;\text{MHz} \approx 0.09 \Gamma$ \[dashed (red) curve\]. Modulation at 1MHz plus a 50-$\mu$T field along $\mathbf{u}_x$ gives approximately the same result \[dotted (blue) curve\]. $\Phi_\text{EOM}=\pi$, $\Omega_\mathrm{c} = \Omega_\mathrm{r} = \Gamma$, $\delta_\mathrm{c} = -\Gamma/2$, $\delta_\mathrm{r} = \Gamma/2$, $\gamma_{g,m}=\Gamma/10$, and cooling laser $\mathbf{u}_x$ polarized.](Fig08-pol-mod2){width=".85\columnwidth"}

Figure \[fig:EOM\](a) shows the quasi-steady-state scattering rate as a function of the modulation frequency $\omega_\text{EOM}$. As shown in Fig. \[fig:pol-mod\], the dark-state destabilization is efficient already at $\omega_\text{EOM}\approx 0.1 \Gamma$ for the parameters used here. As expected, there are dips at $\Gamma$ and $\Gamma/2$, where the first- and second-order red sidebands of the repumper are at Raman resonance. Assuming we have a fixed EOM modulation frequency, this must be taken into account when choosing the repumper detuning. 