The suppression of [$\Omega^{min}_{R,0 1}$]{} below [$\Omega_{0 1}$]{} leads to the effect seen in Fig. \[F031806Dfosc\].

Both of these effects become significant as [$\Omega_{0 1}$]{} approaches ${\ensuremath{\omega_{0 1}}} - {\ensuremath{\omega_{1 2}}}$, which is a measure of the anharmonicity of the system;[@Meier05a; @Amin06a; @Strauch06a] in the case of Fig. \[F031806Dfosc\], ${\ensuremath{\omega_{0 1}}} / 2 \pi = 6.2\ {\ensuremath{{\ensuremath{\mathrm{GHz}}}}}$ and ${\ensuremath{\omega_{1 2}}} / 2 \pi = 5.5\ {\ensuremath{{\ensuremath{\mathrm{GHz}}}}}$. Clearly, these shifts need to be considered when working at high power or at low current bias.

In order to follow experimentally the shift of the resonance condition, it was necessary to measure Rabi oscillations for different detunings of the microwave drive. We chose to do this by keeping the drive frequency [$\omega_{r\!f}$]{} fixed and changing the level spacing [$\omega_{0 1}$]{} (through $I_b$), because the power transmitted by the microwave lines had a nontrivial frequency dependence. Figure \[F010206H1\](a) shows a grayscale plot of Rabi oscillations measured from such an experiment, where black represents a high escape rate. Each horizontal line is the escape rate versus time due to a microwave current of 6.5 GHz and $-11$ dBm, which was turned on at the value of the current bias $I_b$ indicated on the vertical axis. 