from which it quickly relaxes to the ground state $|0R\rangle$. Efficient cooling only occurs when the driving-induced population transfer to $|0R\rangle$ is faster than the thermal repopulation of $|0L\rangle$. The hierarchy of relaxation and absorption rates required, $ \Gamma_{0R,1R}\gg \Gamma_{0L,1R},\Gamma_{0L,0R}$, is achieved in our system owing to a relatively weak tunneling between wells, which inhibits the interwell relaxation and absorption processes $|1R\rangle \to |0L\rangle$ and $|0R\rangle \to |0L\rangle$, compared with the relatively strong intrawell relaxation process $|1R\rangle \to |0R\rangle$.

Figure \[fig:4\]B shows the qubit step at $T_{\rm bath}$ = 150 mK in equilibrium with the bath (top) and after a 3-$\mu$s cooling pulse at 5 MHz (bottom). Under equilibrium conditions, the average level populations exhibit a thermally-broadened qubit step about $\delta f_{\rm {dc}} = 0$, with a width proportional to $T_{\rm bath}$. The presence of microwave excitation targeting the $|0L\rangle \to |1R\rangle$ transition, followed by relaxation, acts to increase the ground-state population and, thereby, sharpens the qubit step. Cooling can thus be quantified in terms of an effective temperature $T_{\rm eff} < T_{\rm bath}$, a signature that is evident from the narrowing of the qubit steps in Fig. \[fig:4\]B after cooling. More precisely, using the notation from Fig. \[fig:2\], the 