Polarizability assessments of ion-based optical clocks

Abstract

It is shown that the dynamic differential scalar polarisability of the S 1/2 −D 5/2 transition in 138 Ba + can be determined to an inaccuracy below 0.5% across a wide wavelength range (λ > 700 nm). This can be achieved using measurements for which accurate determination of laser intensity is not required, and most of the required measurements are already in the literature. Measurement of a laser-induced ac-stark shift of the clock transition would then provide an in situ measurement of the laser's intensity to the same 0.5% level of inaccuracy, which is not easily achieved by other means. This would allow accurate polarisability measurements for clock transitions in other ions, through comparison with 138 Ba + . The approach would be equally applicable to Sr + and Ca + , with the latter being immediately applicable to Al + /Ca + quantum logic clocks.

Tune-out and magic wavelengths, and electric quadrupole transition properties of the singly charged alkaline-earth metal ions

“…Also, our ground state polarizability value for ground state is in very good agreement with the value reported by Safronova et al [26]. Along with this, our values for the 6S 1/2 , 5D 3/2 and 5D 5/2 states are also compared with the RCC calculations by Sahoo et al [19] and Barrett et al [25]. For ground state, the agreement is reasonable between our and their reported values.…”

“…For ground state, the agreement is reasonable between our and their reported values. Similarly, for the 5D 5/2 state, our values match well with Sahoo et al and Barrett et al [19,25] within uncertainty limits. However, our polarizability value for the 5D 3/2 state lies just outside the uncertainty limits of the value by Sahoo et al [19].…”

Measurements of the branching ratios for 6P1/2 decays in Ba+138

“…and 6P 3/2 r 5D 5/2 = 4.091(3) a.u. The latter matrix element is a prominent contributor to ∆α 0 (ω) of the S 1/2 -to-D 5/2 clock transition and will allow a precise model of ∆α 0 (ω) to be constructed as discussed in [16]. The matrix elements also provide a new estimate of 6.271(8) ns for the P 3/2 lifetime.…”

“…Our own interest in the branching ratio is of relevance to polarisability assessments in optical atomic clocks. Measured atomic properties of 138 Ba + can be combined to provide an accurate model of the dynamic differential scalar polarisability ∆α 0 (ω) for the S 1/2 − D 5/2 clock transition [16]. With such a model, ac-Stark shifts of the clock transition could provide an in situ calibration of laser intensities.…”

Spectroscopy of Trapped ¹³⁸Ba⁺ Ions for Atomic Parity Violation and Optical Clocks

“…Currently, there is experimental data available only on the polarizability of the Ba + ground state [98,99], with some unresolved inconsistencies between different measurements and calculations [98][99][100], and an older measurement of the differential polarizability of the Ba + 2 S 1/2 -2 D 5/2 transition [80], but also see the recent Ref. 101 on assessing the differential polarizability. A first precision measurement of a Ba + clock transition has very recently appeared on arXiv [102].…”