Atomic clocks highly sensitive to the variation of the fine structure constant based on Hf II, Hf IV, and W VI ions

Abstract

We demonstrate that several metastable excited states in Hf II, Hf IV and W VI ions may be good clock states since they are sufficiently long-living and are not sensitive to the perturbations. Cooling E1 transitions are available. Energy levels, Landé $g$-factors, transition amplitudes for electric dipole (E1), electric quadrupole (E2), and magnetic dipole (M1) transitions, lifetimes, and electric quadrupole moments for Hf II, Hf IV, and W VI ions are investigated using a combination of several methods of relativistic many-body calculations including the configuration interaction (CI), linearized coupled-cluster single-doubles (SD) and many-body perturbation theory (CI+SD), and also the configuration interaction with perturbation theory (CIPT). Scalar polarizabilities of the ground states and the clock states have been calculated to determine the black body radiation (BBR) shifts. We have found that the relative BBR shifts for these transitions range between 10${}^{-16}$ $-$ 10${}^{-18}$. A linear combination of two clock transition frequencies allows one to further suppress BBR. Several $5d$ - $6s$ single-electron clock transitions ensure high sensitivity of the transition frequencies to the variation of the fine structure constant $\alpha$ and may be used to search for dark matter producing this variation of $\alpha$. The enhancement coefficient for $\alpha$ variation reaches $K=8.3$. Six stable isotopes of Hf and 5 stable isotopes in W allow one to make King plots and search for new interactions mediated by scalar particles or other mechanisms.

9 pages

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Cited by in corpus (3)

• A New Clock Transition with the Highest Sensitivity to $\alpha$ Variation and Simultaneous Magic Trapping Conditions with Other Clock Transitions in Yb
• Sensing atomic superfluid rotation beyond the standard quantum limit
• Prospects for optical clocks combining high sensitivity to new physics with insensitivity to perturbations; the case of Sb${}^{+}$, Au${}^{+}$, and Hg${}^{2+}$