Measurements ofAl+27andMg+25magnetic constants for improved ion-clock accuracy

Abstract

We have measured the quadratic Zeeman coefficient for the 1 S0 ↔ 3 P0 optical clock transition in 27 Al + , C2 = −71.944(24) MHz/T 2 , and the unperturbed hyperfine splitting of the 25 Mg + 2 S 1/2 ground electronic state, ∆W/h = 1 788 762 752.85(13) Hz, with improved uncertainties. Both constants are relevant to the evaluation of the 27 Al + quantum-logic clock systematic uncertainty. The measurement of C2 is in agreement with a previous measurement and a new calculation at the 1 σ level. The measurement of ∆W is in good agreement with a recent measurement and differs from a previously published result by approximately 2σ. With the improved value for ∆W , we deduce an improved value for the nuclear-to-electronic g-factor ratio gI /gJ = 9.299 308 313(60) × 10 −5 and the nuclear g-factor for the 25 Mg nucleus gI = 1.861 957 82(28) × 10 −4 . Using the values of C2 and ∆W presented here, we derive a quadratic Zeeman shift of the 27 Al + quantum-logic clock of ∆ν/ν = −(9241.8 ± 3.7) × 10 −19 , for a bias magnetic field of B ≈ 0.12 mT.

From megahertz to terahertz qubits encoded in molecular ions: theoretical analysis of dipole-forbidden spectroscopic transitions in N2+

“…By averaging two stretched Zeeman transitions, the first-order shift is canceled, and the clock only depends on second-order Zeeman shifts. 73 This averaging technique is not an option for qubit applications. The second-order sensitivity of Al + , B7.2 Â 10 À4 mHz mG À2 , is five orders of magnitude smaller than the sensitivity of N 2 + ''magic'' transitions analysed here.…”

Evaluation of the systematic shifts of a ${}^{40}\textrm{Ca}^+-{}^{27}\textrm{Al}^+$ optical clock

“…External magnetic influence is the dominant effect that causes a frequency shift of the clock transition in our 27 Al + clock. Considering the first-order and second-order terms in the magnetic field, the two atomic resonance frequencies will be shifted [21]:…”

Ion Clock Busts into New Precision Regime

“…Here B DC is the static magnetic field measured in real time and B AC is constrained based on microwave frequency measurements made on the 25 Mg þ ion as well as the uncertainty in the hyperfine constant A hfs [30]. We have recently made improved measurements of both C 2 and A hfs that are presented elsewhere [31]. The mean quadratic Zeeman shift for a day of operation is Δν=ν ¼ −ð9241.8 AE 3.7Þ × 10 −19 , where the exact value of the shift depends on the measured with the measurements generated by a Monte Carlo analysis accounting for the nonorthogonality of the probe directions and assuming the worst-case scenario of either 0 or π phase between ion motion along these directions.…”