Investigation of the gravitational-potential dependence of the fine-structure constant using atomic dysprosium

Abstract

Radio-frequency $E1$ transitions between nearly degenerate, opposite-parity levels of atomic dysprosium (Dy) were monitored over an 8-month period to search for a variation in the fine-structure constant $\ensuremath{\alpha}$. During this time period, data were taken at different points in the gravitational potential of the Sun. The data are fitted to the variation in the gravitational potential yielding a value of $(\ensuremath{-}8.7\ifmmode\pm\else\textpm\fi{}6.6)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ for ${k}_{\ensuremath{\alpha}}$, the variation of $\ensuremath{\alpha}$ in a changing gravitational potential. This value gives the first laboratory limit independent of assumptions regarding other fundamental constants. In addition, our value of ${k}_{\ensuremath{\alpha}}$ combined with other experimental constraints is used to extract the first limits on ${k}_{e}$ and ${k}_{q}$. These coefficients characterize the variation of ${m}_{e}∕{m}_{p}$ and ${m}_{q}∕{m}_{p}$ in a changing gravitational potential, where ${m}_{e}$, ${m}_{p}$, and ${m}_{q}$ are electron, proton, and quark masses. The results are ${k}_{e}=(4.9\ifmmode\pm\else\textpm\fi{}3.9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$ and ${k}_{q}=(6.6\ifmmode\pm\else\textpm\fi{}5.2)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5}$. All these results indicate the absence of significant variation at the present level of sensitivity.