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arXiv:1208.0552 · Physical Review A

Determination of the 5d6s 3D1 state lifetime and blackbody-radiation clock shift in Yb

K. Beloy, Jeff A. Sherman, N. Lemke, N. Hinkley, Chris W. Oates, Andrew D. Ludlow

Published Nov 29, 2012• 68 citations
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Abstract

The Stark shift of the ytterbium (Yb) optical clock transition due to room-temperature blackbody radiation is dominated by a static Stark effect, which was recently measured to high accuracy [J. A. Sherman et al., Phys. Rev. Lett. 108, 153002 (2012)]. However, room-temperature realization of the clock at ${10}^{\ensuremath{-}18}$ uncertainty requires a dynamic contribution to this static approximation. This dynamic term largely depends on a single electric dipole matrix element for which theoretically and experimentally derived values disagree significantly. We determine this important matrix element by two independent methods, which yield consistent values. Along with precise radiative lifetimes of $6s6p\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{}$ and $5d6s\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}^{}$, we report the clock shift due to an ideal 300 K blackbody environment to 0.05$%$ precision.

DOI
10.1103/physreva.86.051404

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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)

•Dec 16, 2025•0 citations
The Stark shift of the ytterbium (Yb) optical clock transition due to room-temperature blackbody radiation is dominated by a static Stark effect, which was recently measured to high accuracy [J. A. Sherman et al., Phys. Rev. Lett. 108, 153002 (2012)]. However, room-temperature realization of the clock at 10\ensuremath−18{10}^{\ensuremath{-}18}10\ensuremath−18 uncertainty requires a dynamic contribution to this static approximation. This dynamic term largely depends on a single electric dipole matrix element for which theoretically and experimentally derived values disagree significantly. We determine this important matrix element by two independent methods, which yield consistent values. Along with precise radiative lifetimes of 6s6p3P16s6p\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{P}_{1}^{}6s6p3P1​ and 5d6s3D15d6s\phantom{\rule{0.16em}{0ex}}{}^{3}\phantom{\rule{-0.16em}{0ex}}{D}_{1}^{}5d6s3D1​, we report the clock shift due to an ideal 300 K blackbody environment to 0.05% precision.
We evaluated the static and dynamic polarizabilities of the 5s21S05{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}5s21S0​ and 5s5p3P0o5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}5s5p3P0o​ states of Sr using the high-precision relativistic configuration interaction combined with the all-order method. Our calculation explains the discrepancy between the recent experimental $5{s}^{2}\phantom{\rule{0.16em}{0ex}}{}^{1}{S}_{0}\ensuremath{-}5s5p\phantom{\rule{0.16em}{0ex}}{}^{3}{P}_{0}^{o}$ dc Stark shift measurement $\ensuremath{\Delta}\ensuremath{\alpha}=247.379(7)$ [Middelmann et al., Phys. Rev. Lett. 109, 263004 (2012)] and the earlier theoretical result of 261(4) a.u. [Porsev and Derevianko, Phys. Rev. A 74, 020502(R) (2006)]. Our present value of 247.5 a.u. is in excellent agreement with the experimental result. We also evaluated the dynamic correction to the BBR shift with 1% uncertainty; $\ensuremath{-}0.1492(16)Hz.ThedynamiccorrectiontotheBBRshiftisunusuallylargeinthecaseofSr(70.1492(16) Hz. The dynamic correction to the BBR shift is unusually large in the case of Sr (70.1492(16)Hz.ThedynamiccorrectiontotheBBRshiftisunusuallylargeinthecaseofSr(7%$) and it enters significantly into the uncertainty budget of the Sr optical lattice clock. We suggest future experiments that could further reduce the present uncertainties.
Measurement of the reduced dipole matrix element in Ba+^++
We present a high-precision measurement of the reduced electric-dipole matrix element ⟨P1/2∥r∥S1/2⟩\langle P_{1/2}\|r\|S_{1/2}\rangle⟨P1/2​∥r∥S1/2​⟩ in 138Ba+^{138}\mathrm{Ba}^+138Ba+. By comparing off-resonant scattering rates with dispersive Stark-shift measurements, we determine the matrix element to be 3.322 7(12)3.322\,7(12)3.3227(12), corresponding to a P1/2P_{1/2}P1/2​ excited-state radiative lifetime of 7.866 3(56)7.866\,3(56)7.8663(56)~ns. Combining our experimental results with a prior model for the differential scalar polarizability Δα0(ω)Δα_0(ω)Δα0​(ω), we extract the static value Δα0(0)=−73.09(12)Δα_0(0) = -73.09(12)Δα0​(0)=−73.09(12)a.u. This determination directly improves the evaluation of the blackbody radiation (BBR) shift, minimizing a prominent systematic limitation in room-temperature Ba+\mathrm{Ba}^+Ba+ optical clock error budgets. These results provide a stringent benchmark for atomic-structure calculations and advance high-precision applications in quantum metrology and tests of fundamental physics.
Presently, the Stark effect contributes the largest source of uncertainty in a ytterbium optical atomic clock through blackbody radiation. By employing an ultracold, trapped atomic ensemble and high stability optical clock, we characterize the quadratic Stark effect with unprecedented precision. We report the ytterbium optical clock's sensitivity to electric fields (such as blackbody radiation) as the differential static polarizability of the ground and excited clock levels ${\ensuremath{\alpha}}_{\mathrm{clock}}=36.2612(7)\text{ }\text{ }\mathrm{kHz}\text{ }(\mathrm{kV}/\mathrm{cm}{)}^{\ensuremath{-}2}$. The clock's uncertainty due to room temperature blackbody radiation is reduced by an order of magnitude to $3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}17}$.
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.
We evaluated the C(6) coefficients of Yb-Yb, Yb-alkali, and Yb-group II van der Waals interactions with 2% uncertainty. The only existing experimental result for such quantities is for the Yb-Yb dimer. Our value, C(6)=1929(39) a.u., is in excellent agreement with the recent experimental determination of 1932(35) a.u. We have also developed a new approach for the calculation of the dynamic correction to the blackbody radiation shift. We have calculated this quantity for the Yb 6s(2) (1)S(0)-6s6p (3)P(0)(o) clock transition with 3.5% uncertainty. This reduces the fractional uncertainty due to the blackbody radiation shift in the Yb optical clock at 300 K to the 10(-18) level.
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)