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arXiv:1712.02335 · Physical Review Applied

Probing Time Dilation in Coulomb Crystals in a High-Precision Ion Trap

J. Keller, D. Kalincev, T. Burgermeister, A. P. Kulosa, Alexandre Didier, T. Nordmann, J. Kiethe, T.E. Mehlstäubler

Published Jan 7, 2019• 44 citations
arXivHTMLPDF

Abstract

Optical clocks based on trapped ions can achieve systematic frequency uncertainties below 10${}^{\ensuremath{-}18}$, enabling relativistic geodesy and precise tests of fundamental physics. However, today's single-ion clocks require averaging times of over a week to resolve frequencies at this level, and no multi-ion clock has been implemented, due to difficulties in controlling ion motion. The authors present an ion-trap array that confines up to 100 clock ions with time-dilation shifts in the low-10${}^{\ensuremath{-}19}$ range, and measure the driven motion of individual ions within an ion crystal. These results point to the next generation of ion clocks, and the realization of clock schemes that have languished.

DOI
10.1103/physrevapplied.11.011002

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Optical clocks based on trapped ions can achieve systematic frequency uncertainties below 10\ensuremath−18{}^{\ensuremath{-}18}\ensuremath−18, enabling relativistic geodesy and precise tests of fundamental physics. However, today's single-ion clocks require averaging times of over a week to resolve frequencies at this level, and no multi-ion clock has been implemented, due to difficulties in controlling ion motion. The authors present an ion-trap array that confines up to 100 clock ions with time-dilation shifts in the low-10\ensuremath−19{}^{\ensuremath{-}19}\ensuremath−19 range, and measure the driven motion of individual ions within an ion crystal. These results point to the next generation of ion clocks, and the realization of clock schemes that have languished.
Trapped-ion optical clocks are capable of achieving systematic fractional frequency uncertainties of 10−1810^{-18}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, versatile platform for extending clock spectroscopy to arrays of Coulomb crystals consisting of several tens of ions, while allowing systematic shifts as low as 10−1910^{-19}10−19. The concept is applicable to all clock transitions with low differential electric quadrupole moments. We observe 3D excess micromotion amplitudes of all individual ions inside a Coulomb crystal with nm resolution and prove that the related frequency shifts can be controlled simultaneously at the 10−1910^{-19}10−19 level. Using this method, we demonstrate regions of 400400400 μ\muμm and 222 mm length in our trap array with time dilation shifts due to micromotion close to 1×10−191\times10^{-19}1×10−19 and below 10−1810^{-18}10−18, respectively. Further measurements of the trapping environment and cooling dynamics calculations for mixed In+{}^++ / Yb+{}^++ crystals show that achievable clock uncertainties due to multi-ion operation in our setup are below 1×10−191\times10^{-19}1×10−19. This work will enable clock operation with multiple ions and open up the possibility of new interrogation schemes which allow optical clock stabilities beyond classical limits.
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 an rf trap array designed for precision spectroscopy on simultaneously trapped ion ensembles. For the example of an In+{\mathrm{In}}^{+}In+ clock, sympathetically cooled with Yb+{\mathrm{Yb}}^{+}Yb+ ions, we show in our system that the expected systematic frequency uncertainties related to multi-ion operation can be below $1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}19}$. Our results pave the way to advanced spectroscopy schemes such as entangled clock spectroscopy and cascaded clock operation.
A multi-ion optical clock with 5×10−19\mathbf{5 \times 10^{-19}}5×10−19 uncertainty
Today's most accurate clocks are based on laser spectroscopy of electronic transitions in single trapped ions and feature fractional frequency uncertainties below 1×10−181\times10^{-18}1×10−18. Scaling these systems to multiple, simultaneously interrogated ions reduces measurement times, driving recent advances in multi-ion clocks. However, maintaining state-of-the-art systematic uncertainties while increasing the number of ions remains a central challenge. Here, we report on a multi-ion optical atomic clock with a fractional frequency uncertainty of 5.3×10−195.3\times10^{-19}5.3×10−19 and up to 10 \Sr ions. Ion-resolved state detection enables minimization of position-dependent shifts, with residual effects suppressed below the 10−2010^{-20}10−20-level. Clock operation with eight to ten ions reduces the measurement time by a factor of 4.8 compared to single-ion operation. A comparison with an established \Yb single-ion clock yields an unperturbed frequency ratio of 0.6926711632159660405(20)0.6926711632159660405(20)0.6926711632159660405(20), with a statistical uncertainty of 0.9×10−180.9\times10^{-18}0.9×10−18 and a combined uncertainty of 2.9×10−182.9\times 10^{-18}2.9×10−18. These results demonstrate robust multi-ion clock operation with reduced averaging time and state-of-the-art accuracy.
Single ion frequency standards have demonstrated in several experiments excellent results and are approaching fractional frequency uncertainties of 10^-18. As dominant contributions to the uncertainty are linked to the ion trap properties a further reduction would be possible by an improved ion trap. Due to the interrogation of a single ion these frequency standards are currently limited by the intrinsically low signal-to-noise ratio and require long averaging times on the order of several days. This limitation is critical for various applications that require a high frequency resolution on short timescales. One possibility to improve the clock stability is to increase the number of clock ions. However, this approach further increases the requirements for the ion trap. Therefore, for the realization of a multi-ion clock that aims at simultaneously reducing the frequency stability and uncertainty the control over the characteristics of the ion trap is crucial. This thesis continues previous work towards the realization of a multi-ion optical clock based on ion Coulomb crystals of 115In+ ions which are sympathetically cooled by 172Yb+ ions. The existing design for a segmented linear ion trap has been refined and a reliable trap manufacturing process for a trap based on gold coated aluminium nitride wafers has been developed. Manufacturing tolerances below 10 μm allowed to reduce the axial micromotion amplitudes substantially. For a region of more than 300 μm the uncertainty contribution of the three-dimensional micromotion amplitude is shown to be below 10^-19. Additionally the radial ion heating rate of the trap has been measured to be 1.1 phonons/s for a trap frequency of 490 kHz. The time dilation shift due to the heating rate on the radial trap axis is found to be (2.1 ± 0.3) x 10^-20 1/s. The trap design has also been optimized for a low trap temperature rise due to the applied rf voltage. Trap temperature measurements with Pt100 sensors installed on the trap showed a maximum temperature increase of 1.21 K at an rf voltage amplitude of 1 kV. By comparing the measurement results to FEM simulations the uncertainty contribution of the trap temperature to the black-body radiation shift has been deduced to be 2.4 x 10^-20. As the ion trap provides a high level of control on Coulomb crystals it also provides an ideal test bed for studying atomic many-body systems. This work presents results of the investigations on topological defects in two-dimensional Coulomb crystals. The emphasis was placed on the effects of mass defects and external electric fields on the stability of the topological defects. It is shown that these effects can be used to manipulate and create topological defects deterministically.
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 .