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Hf$^{12+}$ ion: Highly Charged Ion for Next-Generation Atomic Clocks and Tests of Fundamental Physics

Saleh O. Allehabi, V. A. Dzuba, V. V. Flambaum

TL;DR

This paper evaluates Hf$^{12+}$ as a candidate for next-generation optical clocks and sensitive tests of fundamental physics. Using the CIPT method to handle its open $4f$ shell, the authors compute energies, lifetimes, and transition properties for two clock transitions: a strongly $p$–$f$-type transition with high $\alpha$-sensitivity and an anchor E2 transition within the ground-state configuration. They demonstrate exceptionally small polarizabilities and Blackbody Radiation shifts, along with reduced quadrupole shifts, and propose sympathetic cooling with Be$^+$ to enable practical implementation. The study shows that Hf$^{12+}$ combines high precision timekeeping with powerful sensitivity to potential variations in the fine-structure constant, offering a viable route for precision metrology and tests of new physics.

Abstract

We use advanced computational techniques to study the electronic structure of the Hf$^{12+}$ ion, with the goal of assessing its potential for use in highly accurate atomic optical clocks and search for new physics. Such clocks should combine low sensitivity to external perturbations with high sensitivity to a possible time variation of the fine-structure constant $α$. The system features two clock transitions. One is an $f-p$ transition in terms of single-electron states, which exhibits strong sensitivity to variations in $α$. The other is an electric-quadrupole (E2) transition between states of the ground-state configuration, which can serve as an anchor transition for measuring one frequency against the other. All three relevant states possess very small and nearly equal static dipole polarizabilities, resulting in an extremely small blackbody-radiation shift. The quadrupole shift is also small and can be further suppressed. Altogether, Hf$^{12+}$ appears to be a highly promising candidate for both precision timekeeping and searches for new physics.

Hf$^{12+}$ ion: Highly Charged Ion for Next-Generation Atomic Clocks and Tests of Fundamental Physics

TL;DR

This paper evaluates Hf as a candidate for next-generation optical clocks and sensitive tests of fundamental physics. Using the CIPT method to handle its open shell, the authors compute energies, lifetimes, and transition properties for two clock transitions: a strongly –-type transition with high -sensitivity and an anchor E2 transition within the ground-state configuration. They demonstrate exceptionally small polarizabilities and Blackbody Radiation shifts, along with reduced quadrupole shifts, and propose sympathetic cooling with Be to enable practical implementation. The study shows that Hf combines high precision timekeeping with powerful sensitivity to potential variations in the fine-structure constant, offering a viable route for precision metrology and tests of new physics.

Abstract

We use advanced computational techniques to study the electronic structure of the Hf ion, with the goal of assessing its potential for use in highly accurate atomic optical clocks and search for new physics. Such clocks should combine low sensitivity to external perturbations with high sensitivity to a possible time variation of the fine-structure constant . The system features two clock transitions. One is an transition in terms of single-electron states, which exhibits strong sensitivity to variations in . The other is an electric-quadrupole (E2) transition between states of the ground-state configuration, which can serve as an anchor transition for measuring one frequency against the other. All three relevant states possess very small and nearly equal static dipole polarizabilities, resulting in an extremely small blackbody-radiation shift. The quadrupole shift is also small and can be further suppressed. Altogether, Hf appears to be a highly promising candidate for both precision timekeeping and searches for new physics.

Paper Structure

This paper contains 10 sections, 18 equations, 1 figure, 5 tables.

Table of Contents

  1. Introduction
  2. Method of Calculation: CIPT Approach
  3. Calculation of transition probabilities and lifetimes
  4. Results and discussion
  5. Energy levels, g-factors, transition amplitudes, and lifetimes
  6. Cooling of the Hf$^{12+}$ ions
  7. Polarizabilities and blackbody radiation shifts
  8. Quadrupole shift
  9. Sensitivity of clock transitions to the variation of the fine structure constant.
  10. Conclusion

Figures (1)

  • Figure 1: First seven energy levels of the Hf$^{12+}$ ion. The diagram is based on the data presented in Table \ref{['t:Energy']}. Possible clock transitions are shown in red as the E2 and M1+E2 transitions. Letter F marks states of the $4f^{12}$ configuration; letter P marks states of the $4f^{11}5p$ configuration. Corresponding values of the total angular momentum $J$ are shown on the top.