Precise determination of micromotion for trapped-ion optical clocks

TL;DR

This paper investigates and compares methods for precisely measuring and minimizing micromotion in trapped-ion optical clocks, achieving uncertainties below 10^-20 and improving clock accuracy.

Contribution

It develops a generalized photon-correlation model applicable to typical experimental regimes and compares it with resolved sideband and parametric heating methods.

Findings

Photon-correlation technique achieves <10^-20 fractional frequency uncertainty.

Resolved sideband method shows temperature-dependent offsets outside Lamb-Dicke regime.

Parametric heating method detects micromotion at the 10^-20 level.

Abstract

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