to a 6.2 GHz microwave drive for a range of powers ${\ensuremath{P_S}}$ at the microwave generator. As expected, the oscillation frequency increases with power and decoherence causes the amplitude of the oscillations to decay with time.

However, there are two unexpected features in the data. First, the escape rate [$\Gamma_{\infty}$]{} at long time (once the oscillations have decayed away) increases with [$P_S$]{}, whereas for an ideal two-level system, the excited state population saturates at high power. Furthermore, the highest measured escape rates far exceed the value of $2.2 \times 10^6\ {\ensuremath{{\ensuremath{\mathrm{1/s}}}}}$ predicted for [$\Gamma_{1}$]{} at this bias current, strongly suggesting that the states [$\left| 2 \right>$]{} and higher are becoming occupied. As the escape rates from these levels are very large, only a small population would be required to account for the observed $\Gamma$. Second, at high power, the oscillation maxima increase over the first few cycles \[see Fig. \[F031806DGtot\](a)\]; this is due to the rise time of the microwave current amplitude, which will be discussed in Sec. \[SDecoherence\].

In Sec. \[SStrong\], we will show how more complete measurements reveal that the higher excited states impact the Rabi oscillation frequencies in ways that are in quantitative agreement with predictions from 