Search for Variations of Fundamental Constants using Atomic Fountain Clocks

Abstract

Over five years, we have compared the hyperfine frequencies of $^{133}\mathrm{C}\mathrm{s}$ and $^{87}\mathrm{R}\mathrm{b}$ atoms in their electronic ground state using several laser-cooled $^{133}\mathrm{C}\mathrm{s}$ and $^{87}\mathrm{R}\mathrm{b}$ atomic fountains with an accuracy of $\ensuremath{\sim}{10}^{\ensuremath{-}15}$. These measurements set a stringent upper bound to a possible fractional time variation of the ratio between the two frequencies: $\frac{d}{dt}\mathrm{ln}[({\ensuremath{\nu}}_{\mathrm{R}\mathrm{b}})/({\ensuremath{\nu}}_{\mathrm{C}\mathrm{s}})]=(0.2\ifmmode\pm\else\textpm\fi{}7.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}16}\text{ }{\mathrm{y}\mathrm{r}}^{\ensuremath{-}1}$ ($1\ensuremath{\sigma}$ uncertainty). The same limit applies to a possible variation of the quantity $({\ensuremath{\mu}}_{\mathrm{R}\mathrm{b}}/{\ensuremath{\mu}}_{\mathrm{C}\mathrm{s}}){\ensuremath{\alpha}}^{\ensuremath{-}0.44}$, which involves the ratio of nuclear magnetic moments and the fine structure constant.