While the measurements were performed at 110 mK, this is not expected to have a significant impact on the Rabi oscillations, as the temperature was well below $\hbar {\ensuremath{\omega_{0 1}}} / k_B \approx 325\ {\ensuremath{{\ensuremath{\mathrm{mK}}}}}$.[@Lisenfeld07a]

![\[F010206H1\] (Color online) Multiphoton, multilevel Rabi oscillations plotted in the time and frequency domains. (a) The escape rate $\Gamma$ (measured at 110 mK) is plotted as a function of the time after which a 6.5 GHz, $-11$ dBm microwave drive was turned on and the current bias $I_b$ of the qubit; $\Gamma$ ranges from 0 (white) to $3 \times 10^8\ {\ensuremath{{\ensuremath{\mathrm{1/s}}}}}$ (black). (b) The normalized power spectral density of the time-domain data from $t = 1$ to 45 ns is shown with a grayscale plot. The dashed line segments indicate the Rabi frequencies obtained from the rotating wave model for transitions involving (from top to bottom) 1, 2, 3, and 4 photons, evaluated with junction parameters $I_{01} = 17.828\ {\ensuremath{\mu {\ensuremath{\mathrm{A}}}}}$ and $C_1 = 4.52\ {\ensuremath{{\ensuremath{\mathrm{pF}}}}}$, and microwave current ${\ensuremath{I_{r\!f}}}= 24.4\ {\ensuremath{{\ensuremath{\mathrm{nA}}}}}$. Corresponding grayscale plots calculated with a seven-level density-matrix simulation are shown in (c) and (d).](010206H1v3.eps){width="3.0in"}

From Fig. \[F010206H1\](a), we see that the oscillation frequency depends on the current bias. This variation can be 