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 ²S_1/2 (F = 0) → ²D_3/2 (F = 2) electric quadrupole (E2) and ²S_1/2 (F = 0) → ²F_7/2 (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 Δα_dc 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 Δα_dc is known with a smaller fractional uncertainty of 0.04% for the ²S_1/2 → ²D_5/2 E2 transition of ⁸⁸Sr⁺ [3], this allows for a transfer of Δα_dc 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 Δα_dc of the ¹⁷¹Yb⁺ clock transitions. This allows for a reduction of the fractional uncertainty of Δα_dc 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 Δα_dc determined in this thesis does not agree with [2], a fractional offset of approximately 14% is observed. To investigate this discrepancy further, Δα_dc 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 ν_Sr⁺ with an uncertainty limited by the caesium references. The value of ν_Sr⁺ 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)