effective qubit temperature is obtained by fitting an effective temperature that would have been required in equilibrium to achieve the observed qubit population $p_{0R}$, $$p_{0R} = \frac{ \varepsilon}{\sqrt{ \varepsilon^2 + \Delta^2}}
  \left[ \tanh \left( \frac{\sqrt{ \varepsilon^2 + \Delta^2}}{2 k_{\textrm{B}} T_{\textrm{eff}}} \right)
  + 1 \right].$$

Universal cooling (cooling that is independent of flux detuning) occurs near an optimal driving amplitude $A^*$ (Fig. \[fig:4\]C). This is demonstrated in Fig. \[fig:4\]D where we present the $|0R\rangle$ state population $P_{\rm sw}$ measured as a function of the microwave amplitude $A$ and flux detuning $\delta f_{\rm dc}$ for $\nu=5\,{\rm MHz}$. Cooling and the diamond feature can be understood in terms of the energy level diagram (Fig. \[fig:5\]C). As the amplitude of the microwave pulse is increased from $V=0$, population transfer first occurs when the $\Delta_{0,0}$ avoided crossing is reached, [*i.e.*]{} $A>|\delta f_{\rm {dc}}|$; this defines the front side of the observed diamond, symmetric about the qubit step (see also Fig. \[fig:3\]A). For amplitudes $A^*/2 \leq A \leq A^*$, the $\Delta_{0,1}$ ($\Delta_{1,0}$) side avoided crossing dominates the dynamics, resulting in a second pair of thresholds $A = A^*-|\delta f_{\rm {dc}}|$, which define the back side of the diamond. In the region outside of the diamond’s backside, 