as a function of microwave current [$I_{r\!f}$]{}. Extracted values from data (including the plots in Fig. \[F031806DGtot\]) are shown as circles, while the rotating wave solution is shown for two- (dashed line) and five- (solid) level simulations, calculated using $I_{01} = 17.930\ {\ensuremath{\mu {\ensuremath{\mathrm{A}}}}}$ and $C_1 = 4.50\ {\ensuremath{{\ensuremath{\mathrm{pF}}}}}$ with ${\ensuremath{\omega_{r\!f}}}/ 2 \pi = 6.2\ {\ensuremath{{\ensuremath{\mathrm{GHz}}}}}$.](031806Dfoscv3.eps){width="3.0in"}

We fit the escape rates in Fig. \[F031806DGtot\] (and additional data for other powers not shown) to a decaying sinusoid with an offset. The extracted frequencies are shown with circles in Fig. \[F031806Dfosc\]. To compare to theory, [$\Omega_{R,0 1}$]{}, calculated using the rotating wave solution for a system with five levels, is shown with a solid line. The implied assumption that the oscillation frequencies of $\Gamma$ and $\rho_{11}$ are equal, even at high power in a multilevel system, will be addressed in Sec. \[SSummary\]. In plotting the data, we have introduced a single fitting parameter $117\ {\ensuremath{{\ensuremath{{\ensuremath{\mathrm{nA}}}}}/ \sqrt{{\ensuremath{{\ensuremath{\mathrm{mW}}}}}}}}$ that converts the power [$P_S$]{} at the microwave source to the current amplitude [$I_{r\!f}$]{} at the qubit. Good agreement is found over the full range of power.

As [$I_{r\!f}$]{} increases in Fig. \[F031806Dfosc\], the oscillation frequency is smaller than the expected linear relationship for a two-level 