J. Keller

We present a scalable mixed-species Coulomb crystal clock based on the $^1S_0$ $\leftrightarrow$ $^3P_0$ transition in $^{115}$In$^+$. $^{172}$Yb$^+$ ions are co-trapped and used for sympathetic cooling. Reproducible interrogation conditions for mixed-species Coulomb crystals are ensured by a conditional preparation sequence with permutation control. We demonstrate clock operation with a 1In$^+$-3Yb$^+$ crystal, achieving a relative systematic uncertainty of $2.5\times10^{-18}$ and a relative frequency instability of $1.6\times10^{-15}/\sqrt{τ/1\;\mathrm{s}}$. We report on absolute frequency measurements with an uncertainty of $1.3\times10^{-16}$ and optical frequency comparisons with clocks based on $^{171}$Yb$^+$ (E3) and $^{87}$Sr. With a fractional uncertainty of $4.4\times10^{-18}$, the former is - to our knowledge - the most accurate frequency ratio value reported to date. For the $^{115}$In$^+$/$^{87}$Sr ratio, we improve upon the best previous measurement by more than an order of magnitude. We also demonstrate operation with four $^{115}$In$^+$ clock ions, which reduces the instability to $9.2\times10^{-16}/\sqrt{τ/1\;\mathrm{s}}$.

Trapped ions are ideally suited for precision spectroscopy, as is evident from the remarkably low systematic uncertainties of single-ion clocks. The major weakness of these clocks is the long averaging time, necessitated by the low signal of a single atom. An increased number of ions can overcome this limitation and allow for the implementation of novel clock schemes. However, this presents the challenge to maintain the excellent control over systematic shifts of a single particle in spatially extended and strongly coupled many-body systems. We measure and deduce systematic frequency uncertainties related to spectroscopy with ion chains in a newly developed rf trap array designed for precision spectroscopy on simultaneously trapped ion ensembles. For the example of an In${}^+$ clock, sympathetically cooled with Yb${}^+$ ions, we show in our system that the expected systematic frequency uncertainties related to multi-ion operation can be below $1\times10^{-19}$. Our results pave the way to advanced spectroscopy schemes such as entangled clock spectroscopy and cascaded clock operation.

Trapped-ion optical clocks are capable of achieving systematic fractional frequency uncertainties of $10^{-18}$ and possibly below. However, the stability of current ion clocks is fundamentally limited by the weak signal of single-ion interrogation. We present an operational, scalable platform for extending clock spectroscopy to arrays of Coulomb crystals consisting of several tens of ions, while allowing systematic shifts as low as $10^{-19}$. Using a newly developed technique, we observe 3D excess micromotion amplitudes inside a Coulomb crystal with atomic spatial resolution and sub-nanometer amplitude uncertainties. We show that in ion Coulomb crystals of 400$μ$m and 2mm length, time dilation shifts of In${}^+$ ions due to micromotion can be close to $1\times10^{-19}$ and below $10^{-18}$, respectively. In previous ion traps, excess micromotion would have dominated the uncertainty budget for spectroscopy of even a few ions. By minimizing its contribution and providing a means to quantify it, this work opens up the path to precision spectroscopy in many-body ion systems, enabling entanglement-enhanced ion clocks and providing a well-controlled, strongly coupled quantum system.

In order to improve the short-term stability of trapped-ion optical clocks, we are developing a frequency standard based on ${}^{115}$In${}^+$ / ${}^{172}$Yb${}^+$ Coulomb crystals. For this purpose, we have developed scalable segmented Paul traps which allow a high level of control for multiple ion ensembles. In this article, we detail on our recent results regarding the reduction of the leading sources of frequency uncertainty introduced by the ion trap: 2nd-order Doppler shifts due to micromotion and the heating of secular motion, as well as the black-body radiation shift due to warming of the trap. We show that the fractional frequency uncertainty due to each of these effects can be reduced to well below $10^{-19}$.

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.