Search for Variations of Fundamental Constants using Atomic Fountain Clocks

Over five years, we have compared the hyperfine frequencies of ¹³³Cs and ⁸⁷Rb atoms in their electronic ground state using several laser-cooled ¹³³Cs and ⁸⁷Rb atomic fountains with an accuracy of ~10^-15. These measurements set a stringent upper bound to a possible fractional time variation of the ratio between the two frequencies: $d/dtln[({{ν}}Rb)/({{ν}}Cs)]=(0.2±{}7.0)×{}{10}^{{-}16} {yr}^{{-}1}$ ($1{σ}$ uncertainty). The same limit applies to a possible variation of the quantity $({{μ}}Rb/{{μ}}Cs){{α}}^{{-}0.44}$, which involves the ratio of nuclear magnetic moments and the fine structure constant.