Progress of the 40Ca+ ion optical clock based on the 42S1/2 – 3d 2D5/2 electric quadrupole transition is reported. By setting the drive frequency to the “magic” frequency Ω 0, the frequency uncertainty caused by the scalar Stark shift and second-order Doppler shift induced by micromotion is reduced to the 10−19 level. By precisely measuring the differential static scalar polarizability Δα 0, the uncertainty due to the blackbody radiation (BBR) shift (coefficient) is reduced to the 10−19 level. With the help of a second-order integrating servo algorithm, the uncertainty due to the servo error is reduced to the 10−18 level. The total fractional uncertainty of the 40Ca+ ion optical clock is then improved to 2.2× 10−17, whereas this value is mainly restricted by the uncertainty of the BBR shift due to temperature fluctuations. The state preparation is introduced together with improvements in the pulse sequence, and furthermore, a better signal to noise ratio (SNR) and less dead time are achieved. The clock stability of a single clock is improved to 4.8 × 10 − 15 / τ ( in seconds ) .
Progress of the 40Ca+ ion optical clock based on the 42S1/2 – 3d 2D5/2 electric quadrupole transition is reported. By setting the drive frequency to the “magic” frequency Ω 0, the frequency uncertainty caused by the scalar Stark shift and second-order Doppler shift induced by micromotion is reduced to the 10−19 level. By precisely measuring the differential static scalar polarizability Δα 0, the uncertainty due to the blackbody radiation (BBR) shift (coefficient) is reduced to the 10−19 level. With the help of a second-order integrating servo algorithm, the uncertainty due to the servo error is reduced to the 10−18 level. The total fractional uncertainty of the 40Ca+ ion optical clock is then improved to 2.2× 10−17, whereas this value is mainly restricted by the uncertainty of the BBR shift due to temperature fluctuations. The state preparation is introduced together with improvements in the pulse sequence, and furthermore, a better signal to noise ratio (SNR) and less dead time are achieved. The clock stability of a single clock is improved to 4.8 × 10 − 15 / τ ( in seconds ) .
We recently reported a 5×10-17level frequency comparison of two40Ca+optical clocks, one of which has fractional frequency uncertainty of 3.4×10-17, limited by the BBR effect. Here we present progress towards a40Ca+optical clock with uncertainty at the 10-18level. The differential static scalar polarizability Δα0 of the40Ca+ion clock transition is obtained by precisely measuring the “magic” rf drive frequency. Δα0 is measured as -7.2653(44)x10-40J m2/V2, the blackbody radiation shift is then calculated to be 0.3790(2) Hz at 300 K. The contribution of the blackbody shift coefficient to the uncertainty of the optical clock at room temperature is reduced to 5.6×10-19, the excess micromotion induced clock uncertainty is also reduced to the 10-19level by choosing the appropriate trap drive frequency. With a suppression of the BBR field temperature uncertainty to the sub-Kelvin level and improved clock stability, a robust, relatively low-cost40Ca+ion clock with uncertainty at 10-18level can be made.
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)
The strontium ion clock developed at the National Research Council of Canada has reached an uncertainty level of 5 mHz in recent years. This low level of uncertainty was achieved in great part by using methods that harness specific properties of the clock transition that allow either a very high level of cancellation or a strong suppression of frequency shifts that would otherwise dominate the uncertainty budget. The shifts controlled by these methods are the electric quadrupole shift, the tensor Stark shifts, and the micromotion shifts. With these methods in place, the main limitation to the accuracy of the clock transition frequency is the uncertainty in the evaluation of blackbody radiation (BBR) field. In this paper, we review the methods used to control the shifts to the 5 mHz level and present our plans for the evaluation of the BBR field that is expected to reduce the total uncertainty to the mHz level.
Abstract For the first time, we experimentally determine the infrared magic wavelength for the 40Ca+ 4 s 2 S 1 / 2 → 3 d 2 D 5 / 2 electric quadrupole transition by observation of the light shift canceling in 40Ca+ optical clock. A ‘magic’ magnetic field direction is chosen to make the magic wavelength insensitive to both the linear polarization purity and the polarization direction of the laser. The determined magic wavelength for this transition is 1056.37(9) nm, which is not only in good agreement with theoretical predictions (‘Dirac–Fock plus core polarization’ method) but also more precise by a factor of about 300. Using this measured magic wavelength, we also derive the differential static polarizability to be −44.32(32) a.u., which will be an important input for the evaluation of the blackbody radiation shift at room temperatures. Our work paves a way for all-optical-trapping of 40Ca+ optical clock.
With the advent of optical clocks featuring fractional frequency uncertainties on the order of 10−17 and below, new applications such as chronometric leveling with few-centimeter height resolution emerge. We are developing a transportable optical clock based on a single trapped aluminum ion, which is interrogated via quantum logic spectroscopy. We employ singly charged calcium as the logic ion for sympathetic cooling, state preparation, and readout. Here, we present a simple and compact physics and laser package for manipulation of 40Ca+. Important features are a segmented multilayer trap with separate loading and probing zones, a compact titanium vacuum chamber, a near-diffraction-limited imaging system with high numerical aperture based on a single biaspheric lens, and an all-in-fiber 40Ca+ repump laser system. We present preliminary estimates of the trap-induced frequency shifts on 27Al+, derived from measurements with a single calcium ion. The micromotion-induced second-order Doppler shift for 27Al+ has been determined to be δνEMMν=−0.4−0.3+0.4×10−18 and the black-body radiation shift is δνBBR/ν = (−4.0 ± 0.4) × 10−18. Moreover, heating rates of 30 (7) quanta per second at trap frequencies of ωrad,Ca+ ≈ 2π × 2.5 MHz (ωax,Ca+ ≈ 2π × 1.5 MHz) in radial (axial) direction have been measured, enabling interrogation times of a few hundreds of milliseconds.
We report a single-ion optical clock based on the 4S_{1/2}→3D_{5/2} transition of the ^{40}Ca^{+} ion, operated in a liquid nitrogen cryogenic environment, achieving a total systematic uncertainty of 4.4×10^{-19}. We employ a refined temperature evaluation scheme to reduce the frequency uncertainty due to blackbody radiation, and 3D sideband cooling to minimize the second-order Doppler shift. We have precisely determined the average Zeeman coefficient of the ^{40}Ca^{+} clock transition to be 14.345(15) Hz/mT^{2}, thereby significantly reducing the quadratic Zeeman shift uncertainty. Moreover, the cryogenic environment enables the lowest reported heating rate due to ambient electric field noise in trapped-ion optical clocks.