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arXiv:2610.14796

Inverse identification of thermal-radiative parameters for reduced effective-temperature uncertainty in an ion optical clock

Jie Zhao, Yani Zuo, Shaoyang Dai, Chaowei Wang, Ang Huang, Jian Song, Guangyao Wang, Fangfei Wu, Haotian Shi, Zhengyong Li, Fang Fang

Published Oct 10, 2026• 0 citations
arXivHTMLPDF

Abstract

The blackbody-radiation (BBR) shift remains a leading systematic uncertainty of room-temperature single-ion optical clocks. Accurate evaluation of this shift requires the effective temperature at the ion position, which is difficult because RF heating, low and spatially varying surface emissivity and inaccessible trap surfaces make this quantity difficult to measure directly. Here, we developed a hybrid inversion framework that combines radiance-domain infrared thermography, black-painted high-emissivity reference regions, a finite-element model of a 171Yb+ end-cap ion trap and a reduced-order surrogate for repeated forward calculations and parameter identification. The surrogate reproduced the FE test fields with a full-field mean absolute error (MAE) of 0.02220 mK. The calibrated model predicted the ion-position effective temperature with a combined standard uncertainty of 155.0 mK, corresponding to a temperature-related BBR frequency-shift uncertainty of 1.647 x 10^-19 for the 2S1/2-2F7/2 (467 nm) E3 transition. This method provides a reproducible route for reducing and tracing the BBR uncertainty of room-temperature trapped-ion optical clocks.

DOI
10.48550/arxiv.2610.14796

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The blackbody-radiation (BBR) shift remains a leading systematic uncertainty of room-temperature single-ion optical clocks. Accurate evaluation of this shift requires the effective temperature at the ion position, which is difficult because RF heating, low and spatially varying surface emissivity and inaccessible trap surfaces make this quantity difficult to measure directly. Here, we developed a hybrid inversion framework that combines radiance-domain infrared thermography, black-painted high-emissivity reference regions, a finite-element model of a 171Yb+ end-cap ion trap and a reduced-order surrogate for repeated forward calculations and parameter identification. The surrogate reproduced the FE test fields with a full-field mean absolute error (MAE) of 0.02220 mK. The calibrated model predicted the ion-position effective temperature with a combined standard uncertainty of 155.0 mK, corresponding to a temperature-related BBR frequency-shift uncertainty of 1.647 x 10^-19 for the 2S1/2-2F7/2 (467 nm) E3 transition. This method provides a reproducible route for reducing and tracing the BBR uncertainty of room-temperature trapped-ion optical clocks.
The uncertainty of the ac Stark shift due to thermal radiation represents a major contribution to the systematic uncertainty budget of state-of-the-art optical atomic clocks. In the case of optical clocks based on trapped ions, the thermal behavior of the rf-driven ion trap must be precisely known. This determination is even more difficult when scalable linear ion traps are used. Such traps enable a more advanced control of multiple ions and have become a platform for new applications in quantum metrology, simulation, and computation. Nevertheless, their complex structure makes it more difficult to precisely determine its temperature in operation and thus the related systematic uncertainty. We present here scalable linear ion traps for optical clocks, which exhibit very low temperature rise under operation. We use a finite-element model refined with experimental measurements to determine the thermal distribution in the ion trap and the temperature at the position of the ions. The trap temperature is investigated at different rf-drive frequencies and amplitudes with an infrared camera and integrated temperature sensors. We show that for typical trapping parameters for In+, Al+, Lu+, Ca+, Sr+, or Yb+ ions, the temperature rise at the position of the ions resulting from rf heating of the trap stays below 700 mK and can be controlled with an uncertainty on the order of a few 100 mK maximum. The corresponding uncertainty of the trap-related blackbody radiation shift is in the low 10−19 and even 10−20 regime for 171Yb+(E3) and 115In+, respectively.
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)
Abstract In many of the high-precision optical frequency standards with trapped atoms or ions that are under development to date, the ac Stark shift induced by thermal radiation leads to a major contribution to the systematic uncertainty. We present an analysis of the inhomogeneous thermal environment experienced by ions in various types of ion traps. Finite element models which allow the determination of the temperature of the trap structure and the temperature of the radiation were developed for five ion trap designs, including operational traps at PTB and NPL and further optimized designs. Models were refined based on comparison with infrared camera measurement until an agreement of better than 10% of the measured temperature rise at critical test points was reached. The effective temperature rises of the radiation seen by the ion range from 0.8 K to 2.1 K at standard working conditions. The corresponding fractional frequency shift uncertainties resulting from the uncertainty in temperature are in the 10 −18 range for optical clocks based on the Sr + and Yb + E2 transitions, and even lower for Yb + E3, In + and Al + . Issues critical for heating of the trap structure and its predictability were identified and design recommendations developed.
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.
The Stark shift due to blackbody radiation (BBR) is the key factor limiting the performance of many atomic frequency standards, with the BBR environment inside the clock apparatus being difficult to characterize at a high level of precision. Here we demonstrate an in-vacuum radiation shield that furnishes a uniform, well-characterized BBR environment for the atoms in an ytterbium optical lattice clock. Operated at room temperature, this shield enables specification of the BBR environment to a corresponding fractional clock uncertainty contribution of 5.5×10(-19). Combined with uncertainty in the atomic response, the total uncertainty of the BBR Stark shift is now 1×10(-18). Further operation of the shield at elevated temperatures enables a direct measure of the BBR shift temperature dependence and demonstrates consistency between our evaluated BBR environment and the expected atomic response.