Hyperfine-induced electric dipole contributions to the electric octupole and magnetic quadrupole atomic clock transitions

Abstract

Hyperfine-induced electric dipole contributions may significantly increase probabilities of otherwise very weak electric octupole and magnetic quadrupole atomic clock transitions (e.g. transitions between s and f electron orbitals). These transitions can be used for exceptionally accurate atomic clocks, quantum information processing and search for dark matter. They are very sensitive to new physics beyond the Standard Model, such as temporal variation of the fine structure constant, the Lorentz invariance and Einstein equivalence principle violation. We formulate conditions under which the hyperfine-induced electric dipole contribution dominates. Due to the hyperfine quenching the electric octupole clock transition in 173 Yb + is two orders of magnitude stronger than that in currently used 171 Electric octupole (E3) and magnetic quadrupole (M2) atomic optical transitions, which correspond to transitions between s and f electron orbitals, can be used as optical clocks of exceptionally high accuracy [1][2][3][4][5]. They also present unique opportunities for fundamental research by being sensitive to new physics beyond the Standard Model. The transitions are very sensitive to the temporal variation of the fine structure constant α (α = e 2 /hc) [2][3][4][5][6][7][8][9][10], to the local Lorentz invariance (LLI) violation [11], the effect of dark matter [12][13][14][15][16][17][18], etc. For example, the 4f 14 6s 2 S 1/2 − 4f 13 6s 2 2 F o 7/2 transition in Yb + offers opportunities for frequency measurements with fractional accuracy ∼ 10 −18 [1]. The work is in progress in many laboratories [19][20][21]. Measuring the ratio of frequency of this transition to the frequency of the 4f 14 6s 2 S 1/2 − 4f 14 5d 2 D 3/2 transition in the same ion put the strongest limit on the temporal variation of the fine structure constant and (by including the Cs hyperfine transition) on the proton-to-electron mass ratio [8,9,[22][23][24]. The use of the electric octupole transition in Yb + for the search of LLI violation may lead to five orders of magnitude improvement over current best bounds on the LLI violation in the electron-photon sector [11].Many similar opportunities come with the use of optical transitions in highly-charged ions (HCI) [2][3][4][5]10]. For example, the spectrum of the Ir 17+ ion has been recently measured [25] with the prospect of using the 4f 13 5s 3 F o 4 − 4f 12 5s 2 3 H 6 transition for the time keeping and fundamental research.Electrical octupole and magnetic quadrupole transitions are very weak, typical linewidth can be as small as few nHz. This may lead to certain difficulties in the measurements. In this paper we demonstrate that the electric dipole transition (E1) induced by hyperfine interaction can be significantly larger than the electric octupole or magnetic quadrupole transitions. Therefore, choosing right isotope might be important for the measurements.At least one or more of the following conditions is needed for the domination of the hyperfine-induced E1 transitions.• The hyperfine mixin...

Hyperfine structure of $^{173}\mathrm{Yb}^+$: toward resolving the $^{173}\mathrm{Yb}$ nuclear octupole moment puzzle

“…This estimate is also consistent with that of Ref. [26], where they claimed a similar 10% theoretical uncertainty for these two constants using a different computational method. We assign a 10% theoretical uncertainty to the D constant due to its stable convergence trend with the increasing size of the virtual orbital set.…”

“…Comparing our computed values (see Table II) with theoretical values by Dzuba and Flambaum [26], we observe that our A values match, while there is a roughly 10% discrepancy in values of B. Itano (cited in Ref. [30]) has previously computed the A and B constants for the 4f 13 6s 2 (J = 7/2) state in 171 Yb + and 173 Yb + .…”

“…Since the lifetimes of the states in 173 Yb + ( 2 F o 7/2 ) are all expected to on the order of 1 day or longer [26], the achievable precision of these measurements is likely to be limited by practical considerations (as opposed to T 1 ). In particular, since a small magnetic field will be used to isolate the M F = 0 ↔ 0 transitions, second-order Zeeman shifts of the clock states can lead to decoherence.…”

“…The values of hyperfine constants A and B for 171 Yb + and 173 Yb + in the 2 F o 7/2 state are also given in Ref. [26], and are used as a comparison to our values.…”

Excitation of E1-forbidden atomic transitions with electric, magnetic, or mixed multipolarity in light fields carrying orbital and spin angular momentum [Invited]

“…C. The coupling scheme to use for 171 Yb + is the one with the coefficients (4) with the proper quantum number for angular momentum is F F F = J J J + I I I, not accounting for electric hyperfine interaction, e.g. [59].…”