We experimentally investigate an optical frequency standard based on the (2)S1/2(F=0)→(2)F7/2(F=3) electric octupole (E3) transition of a single trapped (171)Yb+ ion. For the spectroscopy of this strongly forbidden transition, we utilize a Ramsey-type excitation scheme that provides immunity to probe-induced frequency shifts. The cancellation of these shifts is controlled by interleaved single-pulse Rabi spectroscopy, which reduces the related relative frequency uncertainty to 1.1×10(-18). To determine the frequency shift due to thermal radiation emitted by the ion's environment, we measure the static scalar differential polarizability of the E3 transition as 0.888(16)×10(-40) J m(2)/V(2) and a dynamic correction η(300 K)=-0.0015(7). This reduces the uncertainty due to thermal radiation to 1.8×10(-18). The residual motion of the ion yields the largest contribution (2.1×10(-18)) to the total systematic relative uncertainty of the clock of 3.2×10(-18).
We experimentally investigate an optical frequency standard based on the (2)S1/2(F=0)→(2)F7/2(F=3) electric octupole (E3) transition of a single trapped (171)Yb+ ion. For the spectroscopy of this strongly forbidden transition, we utilize a Ramsey-type excitation scheme that provides immunity to probe-induced frequency shifts. The cancellation of these shifts is controlled by interleaved single-pulse Rabi spectroscopy, which reduces the related relative frequency uncertainty to 1.1×10(-18). To determine the frequency shift due to thermal radiation emitted by the ion's environment, we measure the static scalar differential polarizability of the E3 transition as 0.888(16)×10(-40) J m(2)/V(2) and a dynamic correction η(300 K)=-0.0015(7). This reduces the uncertainty due to thermal radiation to 1.8×10(-18). The residual motion of the ion yields the largest contribution (2.1×10(-18)) to the total systematic relative uncertainty of the clock of 3.2×10(-18).
We experimentally investigate an optical frequency standard based on the 467 nm (642 THz) electric-octupole reference transition (2)S(1/2)(F=0)→(2)F(7/2)(F=3) in a single trapped (171)Yb(+) ion. The extraordinary features of this transition result from the long natural lifetime and from the 4f(13)6s(2) configuration of the upper state. The electric-quadrupole moment of the (2)F(7/2) state is measured as -0.041(5)ea(0)(2), where e is the elementary charge and a(0) the Bohr radius. We also obtain information on the differential scalar and tensorial components of the static polarizability and of the probe-light-induced ac Stark shift of the octupole transition. With a real-time extrapolation scheme that eliminates this shift, the unperturbed transition frequency is realized with a fractional uncertainty of 7.1×10(-17). The frequency is measured as 642 121 496 772 645.15(52) Hz.
We report on an evaluation of an optical clock that uses the ^{2}S_{1/2}→^{2}D_{5/2} transition of a single ^{88}Sr^{+} ion as the reference. In contrast to previous work, we estimate the effective temperature of the blackbody radiation that shifts the reference transition directly during operation from the corresponding frequency shift and the well-characterized sensitivity to thermal radiation. We measure the clock output frequency against an independent ^{171}Yb^{+} ion clock, based on the ^{2}S_{1/2}(F=0)→^{2}F_{7/2}(F=3) electric octupole (E3) transition, and determine the frequency ratio with a total fractional uncertainty of 2.3×10^{-17}. Relying on a previous measurement of the ^{171}Yb^{+} (E3) clock frequency, we find the absolute frequency of the ^{88}Sr^{+} clock transition to be 444 779 044 095 485.277(59) Hz. Our result reduces the uncertainty by a factor of 3 compared with the previously most accurate measurement and may help to resolve so far inconsistent determinations of this value. We also show that for three simultaneously interrogated ^{88}Sr^{+} ions, the increased number causes the expected improvement of the short-term frequency instability of the optical clock without degrading its systematic uncertainty.
Spectroscopic frequency shifts due to residual motion of the probed atoms significantly contribute to the uncertainty budgets of state-of-the-art optical ion clocks. For clock transitions with second-order Doppler and quadratic Stark shifts of opposite signs, it is possible to configure electrodynamic ion confinement such that these two shift effects become anticorrelated causing zero net shift. Here, we introduce a spectroscopic interrogation protocol which leads, for systems with unknown and varying motional energy gain rates, to first-order auto-suppression of corresponding frequency shifts without requiring the opposite-sign configuration. We experimentally demonstrate the proposed method on a new ytterbium ion optical clock probing the 467 nm electric octupole (E3) transition, where the combined fractional uncertainty contribution from motion-induced frequency shifts is reduced from 1.3×10−18 to 0.3×10−18. An interleaved optical frequency ratio measurement against ytterbium's electric quadrupole transition (E2) at 435 nm delivers an E3/E2 frequency ratio of 0.932829404530965340(39). Combined with previously published ratio data this leads to a limit for a potential fractional temporal variation of the fine-structure constant of 2.4(2.7)×10−19/yr, in agreement with existing bounds.
We report on precision laser spectroscopy of the ${^{2}S}_{1/2}(F=0)\text{\ensuremath{-}}{^{2}F}_{7/2}(F=3,{m}_{F}=0)$ clock transition in a single ion of 171Yb+. A linewidth of <40Hz is observed and frequency instability due to fluctuation of the ac Stark shift is reduced through improved stability of the beam alignment. The absolute value of the transition frequency, determined using an optical frequency comb, is $642\text{ }121\text{ }496\text{ }772\text{ }657\ifmmode\pm\else\textpm\fi{}12\text{ }\text{Hz}$ with a fractional uncertainty of $2\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$. This is a factor of 50 better than the previously published value [Hosaka et al., IEEE Trans. Instrum. Meas. 54, 759 (2005)].
Frequency standards based on optical transitions between electronic states of trapped ions have reached uncertainties below 10−18 [1]. The Stark shift caused by room-temperature blackbody radiation (BBR) causes the largest correction for most high-performance optical clock. The systematic uncertainty of 171Yb+ clocks based on the 2S1/2 (F = 0) → 2D3/2 (F = 2) electric quadrupole (E2) and 2S1/2 (F = 0) → 2F7/2 (F = 3) electric octupole (E3) transitions is currently limited to 28×10−18 and 1.5×10−18, respectively, by the fractional accuracy of the differential polarizability Δαdc of approximately 2% [2]. In the scope of this thesis, a dual species clock based on 171Yb+ and 88Sr+ ions was set up, operated and evaluated, to overcome this barrier. Since Δαdc is known with a smaller fractional uncertainty of 0.04% for the 2S1/2 → 2D5/2 E2 transition of 88Sr+ [3], this allows for a transfer of Δαdc from 88Sr+ to 171Yb+ following a method proposed in [4]. The optical intensity of a laser is calibrated with the Stark shift it causes on the 88Sr+ clock transition, allowing for the determination of Δαdc of the 171Yb+ clock transitions. This allows for a reduction of the fractional uncertainty of Δαdc for both 171Yb+ clock transitions below 0.4% and clock operation on the E2 and E3 transition with a fractional BBR shift uncertainty of 0.84×10−18 and 0.24×10−18 is enabled, respectively. However the value of Δαdc determined in this thesis does not agree with [2], a fractional offset of approximately 14% is observed. To investigate this discrepancy further, Δαdc is measured in the same manner as in [2] for the 88Sr+ clock transition. The same offset of approximately 14% is found, calling the accuracy of at least one of these methods into question. Finally, the first optical frequency ratio ℛ between the 88Sr+ clock transition and the 171Yb+ E3 transition is measured. The fractional uncertainty of ℛ is 23×10−18. ℛ in combination with the absolute frequency of the E3 transition allows for the determination of the 88Sr+ absolute frequency νSr+ with an uncertainty limited by the caesium references. The value of νSr+ falls outside of the recommended range, but is corroborated by measurements of the same quantity by other institutes [5, 6]. [1] M. Marshall et al., Phys. Rev. Lett. 135, 033201 (2025) [2] N. Huntemann et al., Phys. Rev. Lett. 116, 063001 (2016) [3] T. Lindvall et al., Phys. Rev. Lett. 135, 043402 (2025) [4] M. D. Barrett et al., Phys. Rev. A 100, 043418 (2019) [5] C. Marceau et al., Metrologia 62.4, 045001 (2025) [6] T. Lindvall et al., Phys. Rev. Appl. 24, 044082 (2025)
International atomic clock comparison achieving 5×10−18 uncertainty
Two single-ion optical clocks, located in the United Kingdom and in Germany, are compared remotely via a 2220\,km long optical fiber link. Both clocks are based on the 2S1/2(F=0)↔2F7/2(F=3) electric octupole (E3) transition in 171Yb+. Using more than 106 seconds of measurement data, we determine a fractional frequency difference of 1.0(4.8)×10−18, demonstrating agreement of the independently developed systems. To our knowledge, this constitutes the first international clock comparison reaching a fractional uncertainty below 5×10−18, an important milestone towards an anticipated optical redefinition of the SI second. The measurement uncertainty is dominated by that of the relativistic redshift correction between the two sites, which includes time-varying gravity potential differences. We exploit the large baseline between the two clocks to search for violations of Lorentz invariance. In the absence of statistically significant modulations, we improve constraints on the Robertson-Mansouri-Sexl parameter α by approximately a factor of five in the uncertainty, and provide limits on corresponding parameters within the Standard-Model Extension framework.