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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

Minimizing time-dilation in ion traps — Towards an optical clock with Coulomb crystals

T. E. Mehlstäubler, Karsten Pyka, Jonas Keller, Norbert Herschbach, D. M. Meier, Kristijan Kuhlmann, Maksim V. Okhapkin, S M Ignatovich

Published May 1, 2012• 0 citations
Publisher

Abstract

We present the status of our new experiment to lasercool linear chains of172Yb+and115In+ions for an optical clock based on the1S0-3P0transition in115In+. We successfully have trapped and laser-cooled Coulomb crystals of172Yb+ions in our new scalable ion trap that are used to characterize the trap and to sympathetically cool115In+ions. We could demonstrate an area of more than 65 μm, where the fractional frequency shifts due to time dilation are below 10-18for both ions.

DOI
10.1109/fcs.2012.6243653

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Physical Review A•Nov 18, 2025•4 citations
We present the status of our new experiment to lasercool linear chains of172Yb+and115In+ions for an optical clock based on the1S0-3P0transition in115In+. We successfully have trapped and laser-cooled Coulomb crystals of172Yb+ions in our new scalable ion trap that are used to characterize the trap and to sympathetically cool115In+ions. We could demonstrate an area of more than 65 μm, where the fractional frequency shifts due to time dilation are below 10-18for both ions.
We report on the design of a segmented linear Paul trap for optical clock applications using trapped ion Coulomb crystals. For an optical clock with an improved short-term stability and a fractional frequency uncertainty of 10−18, we propose 115In+ ions sympathetically cooled by 172Yb+. We discuss the systematic frequency shifts of such a frequency standard. In particular, we elaborate on high-precision calculations of the electric radiofrequency field of the ion trap using the finite element method. These calculations are used to find a scalable design with minimized excess micromotion of the ions at a level at which the corresponding second-order Doppler shift contributes less than 10−18 to the relative uncertainty of the frequency standard.
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.
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.
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.
Optical clocks have garnered widespread attention due to their unparalleled precision in the fields of time-frequency standards, geodetic measurements, and fundamental physics research. Among recent advances, highly charged ion (HCI)-based optical clocks have attracted significant scientific interest owing to their remarkable insensitivity to electromagnetic perturbations and enhanced sensitivity to potential variations of the fine-structure constant $(\ensuremath{\alpha})$. Although the recent successful demonstration of an Ar13+{\mathrm{Ar}}^{13+}Ar13+ optical clock has validated the feasibility of HCI-based systems, Ni12+{\mathrm{Ni}}^{12+}Ni12+ (featuring an ultranarrow clock transition linewidth) stands out as a superior candidate for achieving HCI optical clocks with ${10}^{\ensuremath{-}19}$ level uncertainty and stability. In this work, we report the Coulomb crystallization of highly charged nickel ions (Ni-HCIs). Through a precise deceleration and sympathetic cooling protocol in a room-temperature linear Paul trap, high-energy Ni-HCI bunches were sympathetically cooled from megakelvin energies down to the hundred-millikelvin range using laser-cooled Be+{\mathrm{Be}}^{+}Be+ ions. This work represents a pivotal step toward the realization of an optical clock based on Ni12+{\mathrm{Ni}}^{12+}Ni12+ ion.