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.

Figure 1

(a) Simplified level scheme of the ${}^{171}\mathrm{Y}\mathrm{b}^{+}$ ion. A modulation sideband of the cooling laser is used to repump the ion from the $F=0$ ground state. (b) Excitation spectrum of the ${}^{2}S_{1/2}(F=0,m_F=0)\to {}^{2}D_{3/2}(F=2,m_F=0)$ transition, obtained with probe pulses of 90 ms duration and 20 probe cycles for each value of the detuning.

Figure 2

Results of absolute frequency measurements of the ${}^{171}\mathrm{Y}\mathrm{b}^{+}$ standard versus the date of the measurement (MJD: Modified Julian Date).

Figure 3

(a) Relative frequency drift rate versus sensitivity factor $A$ for the $S\to D$ reference transitions in the ${\mathrm{H}\mathrm{g}}^{+}$ and ${\mathrm{Y}\mathrm{b}}^{+}$ ions and for the $1S\to 2S$ transition in atomic hydrogen. The solid line is the result of a weighted linear regression. A significant deviation of the slope from zero would indicate a nonzero time derivative of the fine structure constant $\alpha$. (b) Constraints on the variability of $\alpha$ and $\mathrm{R}\mathrm{y}$ as obtained from the experimental points in (a). Stripes mark the $1\sigma$ uncertainty of the individual measurements and the central hatched area is bounded by the standard uncertainty ellipse resulting from the combination of all three experiments.