the top axes indicate the normalized barrier height $N_s$, calculated using the extracted junction parameters.](EnergyGammav3.eps){width="3.0in"}

Figure \[FEnergyGamma\](a) shows a spectrum of transitions for the qubit junction. With a microwave drive of fixed frequency applied to the device, the total escape rate was measured while ramping the biases. The open circles indicate the values of $I_b$ where the microwave drive caused the largest enhancement in the escape rate (over its background value in the absence of microwaves).

As shown by the solid line, we fit these points to the theoretical values of [$\omega_{0 1}$]{}, yielding $I_{01} = 17.930\ {\ensuremath{\mu {\ensuremath{\mathrm{A}}}}}$ and $C_1 = 4.50\ {\ensuremath{{\ensuremath{\mathrm{pF}}}}}$. These values are likely to differ from the actual critical current and capacitance of the qubit junction, both in principle, due to the simplifications in the Hamiltonian mentioned above, and in practice, as this fitting procedure is sensitive to inaccuracies in the simultaneous ramping of $I_b$ and $I_f$, constant offset flux that biases the SQUID (from, for example, trapped flux near the device), and drifts in the detection electronics. Nonetheless, when we repeated the measurement at elevated temperature, the location of the transitions between higher levels agreed to within 0.2% of predictions for [$\omega_{1 2}$]{} (dashed) 