We present a novel approach for measuring the differential static scalar polarizability of a target ion utilizing a “polarizability scale” scheme with a reference ion co-trapped in a linear Paul trap. The differential static scalar polarizability of the target ion can be precisely extracted by measuring the ratio of the ac Stark shifts induced by an add-on infrared laser shed on both ions. This method circumvents the need for the calibration of the intensity of the add-on laser, which is usually the bottleneck for measurements of the polarizability of trapped ions. As a demonstration, ${}^{27}{\mathrm{Al}}^{+}$ (the target ion) and ${}^{40}{\mathrm{Ca}}^{+}$ (the reference ion) are used in this work, with an add-on laser at 1068 nm injected into the ion trap along the trap axis. The differential static scalar polarizability of ${}^{27}{\mathrm{Al}}^{+}$ is extracted to be 0.416(14) a.u. by measuring the ratio of the ac Stark shifts of both ions. Compared to the most recent result [ Phys. Rev. Lett. 123, 033201 (2019)], the relative uncertainty of the differential static scalar polarizability of ${}^{27}{\mathrm{Al}}^{+}$ is reduced by approximately a factor of 4, to 3.4%. This improvement is expected to be further enhanced by using an add-on laser with a longer wavelength.

Blackbody radiation (BBR) temperature and its uncertainty mainly contribute to the BBR shift uncertainty, which is one of the challenges in most ion optical clocks. Here, an improved BBR temperature evaluation method based on the analysis of the effective solid angle of an ion trapping system using the finite element method is presented. To effectively suppress the BBR temperature uncertainty, the structure of an ion trap was optimized to reduce the effective solid angle of the insulating supports, and a BBR shield was employed to reduce the influence of the surrounding BBR in the newly developed ion trap system. Due to radiofrequency field, it is difficult to evaluate the temperature of BBR shield accurately using contact-temperature-sensors inside the vacuum chamber. We used a well shielded platinum resistance temperature sensor to measure the temperature of the shield from the outside of the vacuum chamber. Through a detailed evaluation, the BBR temperature uncertainty of this newly designed system is 0.17 K, corresponding to a BBR frequency shift uncertainty of 2 × 10⁻¹⁸ for the ⁴⁰Ca⁺ optical clock. This improvement of the BBR temperature uncertainty using the active adjustment of the distribution of the effective solid angle of the ion trapping system, without a complicated cryogenic trap, is very suitable for transportable optical clocks operating at room temperature (∼295 K).

The dynamic polarizabilities of 3 s 2 1 S 0 and 3 s 3 p 3 P 0 o states of Al⁺ are calculated using the hybrid configuration interaction and many-body perturbation theory method, and multiconfiguration Dirac–Hartree–Fock method in this work. Five ultraviolet magic wavelengths for the Al⁺ clock transition 3 s 2 1 S 0 – 3 s 3 p 3 P 0 o are predicted. Although the suitable lasers are not available presently, the potential precision measurement on these magic wavelengths for the Al⁺ clock transition would be used to extract the ratios of several certain transition matrix elements with high accuracy, and then help to improve the precision and reliability of the estimate of the BBR shift of the Al⁺ clock transition. The differential dynamic polarizabilities at certain wavelengths are evaluated, which are useful to assess the ac Stark shift of the Al⁺ clock transition frequency and helpful in the clock experiments to suppress the ac Stark shift of the clock transition as possible as it can.