individual resonances are no longer discernible, but as in Fig. \[fig:3\]C, the modulation envelope persists [@Berns06a]. At the lowest frequencies ($\nu < 10\,{\rm MHz}$), state $|1R\rangle$ is reached via adiabatic passage through the $\Delta_{01}$ crossing (Fig. \[fig:4\]C), and the population transfer and cooling become conveniently independent of detuning (see $\nu=5 ~ {\rm MHz}$ in Fig. \[fig:4\]E). As shown in Fig. \[fig:4\]E, we achieve an effective qubit temperature $T_{\rm eff}$ = 3 mK, even for $T_{\rm bath}$ = 300 mK. In our qubit, our determination of $T_{\rm eff}$ was limited primarily by decoherence (linewidth), which limited the resolution with which we could distinguish the states $|0R\rangle$ and $|0L\rangle$ near degeneracy. Nonetheless, we can estimate the ideally resolvable cooling factor $\alpha_{\rm c}$ for this type of cooling process using Eq. \[Boltzmann\], $$\alpha_{\rm c} \equiv \frac{T_{\rm bath}}{T_{\rm eff}} =
 \frac{\varepsilon_{1R \to 0R}}{\Delta},$$ where $\varepsilon_{1R \to 0R} \approx h \times 25$ GHz is the energy separation where the relaxation $|1R\rangle \to |0R\rangle$ occurs and $\Delta \approx h \times 0.01$ GHz for our qubit, yielding a cooling factor $\alpha_{\rm c} \sim 2500$. For a bath temperature $T_{\rm bath} = 50$ mK, this would correspond to an effective temperature $T_{\rm eff} = 20$ $\mu$K in our 