Limit on the Present Temporal Variation of the Fine Structure Constant

The comparison of different atomic transition frequencies over time can be used to determine the present value of the temporal derivative of the fine structure constant $\alpha$ in a model-independent way without assumptions on constancy or variability of other parameters, allowing tests of the consequences of unification theories. We have measured an optical transition frequency at 688 THz in ${}^{171}\mathrm{Y}\mathrm{b}^{+}$ with a cesium atomic clock at 2 times separated by 2.8 yr and find a value for the fractional variation of the frequency ratio $f_{\mathrm{Y}\mathrm{b}}/f_{\mathrm{C}\mathrm{s}}$ of $(-1.2\pm 4.4)\times {10}^{-15}{\mathrm{y}\mathrm{r}}^{-1}$, consistent with zero. Combined with recently published values for the constancy of other transition frequencies this measurement sets an upper limit on the present variability of $\alpha$ at the level of $2.0\times {10}^{-15}{\mathrm{y}\mathrm{r}}^{-1}$ $(1\sigma )$, corresponding so far to the most stringent limit from laboratory experiments.