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

TL;DR

This paper investigates specific metastable states in Hf and W ions as highly sensitive atomic clocks for detecting variations in the fine structure constant, with potential applications in dark matter and new physics searches.

Contribution

It identifies suitable metastable states in Hf and W ions as highly sensitive atomic clocks and calculates their properties using advanced relativistic many-body methods.

Findings

BBR shifts range between 10^{-16} and 10^{-18}

Enhancement coefficient for α variation reaches 8.3

Multiple isotopes enable new physics searches

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, Land\'{e} $g$-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.