An optimized ion trap geometry to measure quadrupole shifts of ¹⁷¹ Yb ⁺ clocks

Abstract

We propose a new ion-trap geometry to carry out accurate measurements of the quadrupole shifts in the 171 Yb-ion. This trap will produce nearly ideal harmonic potential where the quadrupole shifts due to the anharmonic components can be reduced by four orders of magnitude. This will be useful to reduce the uncertainties in the clock frequency measurements of the 6s 2 S 1/2 → 4f 13 6s 2 2 F 7/2 and 6s 2 S 1/2 → 5d 2 D 3/2 transitions, from which we can deduce precise values of the quadrupole moments (Θs) of the 4f 13 6s 2 2 F 7/2 and 5d 2 D 3/2 states. Moreover, it may be able to affirm validity of the measured Θ value of the 4f 13 6s 2 2 F 7/2 state where three independent theoretical studies defer almost by one order in magnitude from the measurement. We also perform calculations of Θs using the relativistic coupled-cluster (RCC) method. We use these Θ values to estimate quadrupole shift that can be measured in our proposed ion trap experiment.

Accurate determination of black-body radiation shift, magic and tune-out wavelengths for the 6S1/2$ \rightarrow $ 5D3/2clock transition in Yb+

“…This is a unique feature of a truncated RCC method in contrast to other truncated many-body methods owing to the exponential form of expression in Eq. (13). In fact, it has also been employed to calculate many atomic properties of Yb + accurately in the past [6,12].…”

“…This is owing to the fact that its E1 matrix element is almost half while its transition energy is twice larger than the corresponding value of the [4f 14 5d] 2 D 3/2 → [4f 14 6p] 2 P 1/2 transition. Noticeably contributions from the [4f 13 5d6s] configurations are non-significant as seen in Table 1. Unlike for the ground state, the "Tail" contribution to α [4f 14 5d] 2 D 3/2 clock transition as -0.44(3) Hz.…”

“…Ytterbium-ion (Yb + ) is a unique system as its two quadrupole (E2) transitions, [ 13 6s 2 ] 2 F 7/2 , as shown in Fig. 1 are being undertaken for the optical frequency standards [1,2,3,4,5].…”

“…The [4f 14 6s] 2 S 1/2 → [4f 14 5d] 2 D 3/2 transition in Yb + has also been considered for probing parity nonconservation effect [6]. Since the [4f 14 6s] 2 S 1/2 → [4f 13 6s 2 ] 2 F 7/2 transition is strongly sensitive to variation of the fine structure constant (α e ) than the [4f 14 6s] 2 S 1/2 → [4f 14 5d] 2 D 3/2 transition in Yb + [7,8], combining ratio of frequencies of these clock transitions with the clock frequencies of Cs atom and combined frequencies of Hg + and Al + ions, limits on the variations of α e and proton-to-electron mass ratio are inferred [9]. In fact, all of the clock transitions in Yb + seem to be sensitive to investigating possible Lorentz symmetry violation [10].…”

“…In fact, all of the clock transitions in Yb + seem to be sensitive to investigating possible Lorentz symmetry violation [10]. Owing to long lifetime of the [4f 13 6s 2 ] 2 F 7/2 state (≥6 years), it makes the [4f 14 6s] 2 S 1/2 → [4f 13 6s 2 ] 2 F 7/2 transition highly forbidden and most suitable for the optical clock. On the other hand, lifetimes of the [4f 14 5d] 2 D 3/2 and [4f 14 5d] 2 D 5/2 states are about 55 ms and 7 ms, respectively [11,12].…”