Atomic Clocks and Variations of the Fine Structure Constant

TLDR

H‑maser, Cs, and Hg⁺ clocks depend differently on α through relativistic (Zα)² effects. The study proposes a new test for variations of α by comparing hyperfine‑transition clock rates across alkali atoms of differing Z, aiming to achieve the most sensitive laboratory limits. The method compares hyperfine‑transition clock rates in alkali atoms of varying Z, including future laser‑cooled species such as Be⁺, Rb, Cs, and Hg⁺. Recent H‑maser versus Hg⁺ clock comparisons tighten laboratory limits on α̇/α by 100‑fold to ≤3.7×10⁻¹⁴ yr⁻¹.

Abstract

We describe a new test for possible variations of the fine structure constant $\ensuremath{\alpha}$ by comparisons of rates between clocks based on hyperfine transitions in alkali atoms with different atomic number $Z$. H-maser, Cs, and Hg ${}^{+}$ clocks have a different dependence on $\ensuremath{\alpha}$ via relativistic contributions of order $(Z\ensuremath{\alpha}{)}^{2}$. Recent H-maser vs ${\mathrm{Hg}}^{+}$ clock comparison data improve laboratory limits on a time variation by 100-fold to give $\stackrel{\ifmmode \dot{}\else .\{}.fi{}}{\ensuremath{\alpha}}/\ensuremath{\alpha}\ensuremath{\le}3.7\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}14}/$yr. Future laser cooled clocks (Be ${}^{+}$, Rb, Cs, Hg ${}^{+}$, etc.), when compared, will yield the most sensitive of all tests for $\stackrel{\ifmmode \dot{}\else .\{}.fi{}}{\ensuremath{\alpha}}/\ensuremath{\alpha}$.