Extended Data Fig. 2: Micromotion analysis with resolved sideband spectroscopy.

In part a and b Rabi oscillations on the carrier and the micromotion sideband for optimal compensation settings are plotted. From a comparison of the Rabi frequencies \({\varOmega }_{{\rm{car}}}=2\pi \times 32.0(0.8)\)kHz and \({\varOmega }_{{\rm{MM}}}=2\pi \times 7.0(0.5)\)kHz in combination with the applied laser powers of \({P}_{411}=32\)μW and \({P}_{411}=840\)μK, respectively we obtain a residual micromotion energy of \({\overline{E}}_{{\rm{eMM}}}/{k}_{{\rm{B}}}=21.5(1.5)\)μK. Part c shows a frequency scan over the carrier transition, carried out with a laser power of \({P}_{411}=61\)μW. A clear peak is visible. For the data plotted in part d the frequency of the laser is shifted by \(-{\varOmega }_{{\rm{rf}}}=-1.85\)MHz compared to c and the power is increased to \({P}_{411}=21.7\)mW. At the expected resonance frequency for the micromotion sideband we do not see a clear peak, only the background is higher compared to c due to off-resonant carrier excitation at these high laser powers. If we shift the ion out of the optimal position for minimal micromotion we observe a clear resonance again as plotted in e. We conclude that the Rabi frequency \({\varOmega }_{{\rm{MM}}}\) on the micromotion sideband presented in e is not larger than the Rabi frequency on the carrier \({\varOmega }_{{\rm{car}}}\) presented in c. From this we obtain an upper limit of the axial micromotion at the optimal position of \({\overline{E}}_{{\rm{eMM}}}/{k}_{{\rm{B}}}=33\)μK. Error bars correspond to quantum projection noise.