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 approximately 10(-15). These measurements set a stringent upper bound to a possible fractional time variation of the ratio between the two frequencies: d/dt ln([(nu(Rb))/(nu(Cs))]=(0.2+/-7.0)x 10(-16) yr(-1) (1sigma uncertainty). The same limit applies to a possible variation of the quantity (mu(Rb)/mu(Cs))alpha(-0.44), which involves the ratio of nuclear magnetic moments and the fine structure constant.
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