Precise determination of micromotion for trapped-ion optical clocks

摘要: As relative systematic frequency uncertainties in trapped-ion spectroscopy are approaching the low $10^{-18}$ range, motional shifts account for a considerable fraction of uncertainty budget. Micromotion, driven motion fundamentally connected to principle Paul trap, is particular concern these systems. In this article, we experimentally investigate at level three common methods minimizing and determining micromotion amplitude. We develop generalized model quantitative application photon-correlation technique, which applicable commonly encountered regime where transition linewidth comparable rf drive frequency. show that fractional due 2nd-order Doppler shift below $1\times 10^{-20}$ can be achieved. The evaluation verified an interleaved measurement with conceptually simpler resolved sideband method. If not performed deep within Lamb-Dicke regime, temperature-dependent offset $10^{-19}$ observed measurements sampling intrinsic micromotion. By direct comparison measurements, simple implement parametric heating method sensitive as well.