New Limits on the Drift of Fundamental Constants from Laboratory Measurements

We have remeasured the absolute $1S$-$2S$ transition frequency ${\nu }_{\mathrm{H}}$ in atomic hydrogen. A comparison with the result of the previous measurement performed in 1999 sets a limit of $(-29\pm 57)\mathrm{Hz}$ for the drift of ${\nu }_{\mathrm{H}}$ with respect to the ground state hyperfine splitting ${\nu }_{\mathrm{Cs}}$ in ${}^{133}\mathrm{Cs}$. Combining this result with the recently published optical transition frequency in ${}^{199}\mathrm{Hg}^{+}$ against ${\nu }_{\mathrm{Cs}}$ and a microwave ${}^{87}\mathrm{Rb}$ and ${}^{133}\mathrm{Cs}$ clock comparison, we deduce separate limits on $\dot{\alpha }/\alpha =(-0.9\pm 2.9)\times {10}^{-15}{\mathrm{yr}}^{-1}$ and the fractional time variation of the ratio of Rb and Cs nuclear magnetic moments ${\mu }_{\mathrm{Rb}}/{\mu }_{\mathrm{Cs}}$ equal to $(-0.5\pm 1.7)\times {10}^{-15}{\mathrm{yr}}^{-1}$. The latter provides information on the temporal behavior of the constant of strong interaction.

Figure 1

Simplified experimental setup for comparison of the hydrogen $1S\mathrm{\text{−}}2S$ transition frequency with a primary frequency standard (HV, high vacuum; UHV, ultrahigh vacuum). A mode-locked femtosecond laser with repetition rate $f_{\mathrm{rep}}$ emits the frequency comb which is broadened in a photonic crystal fiber. $f_0$ is the carrier-envelope offset frequency.

Figure 2

Experimental results and averages for the 1999 and 2003 measurements of the absolute $(1S,F=1,m_F=\pm 1)\to (2S,F^{\prime }=1,m_F^{\prime }=\pm 1)$ transition frequency in atomic hydrogen. The background pressure shift of $+10\mathrm{Hz}$ as explained in 8 is added to the 1999 value.

Figure 3

Possible values for the relative drift rates $x$ and $y$ and their experimental restrictions (dashed lines) as stated by Eqs. (7). The probability density for $x$ and $y$ to be the true values is given by $P(\Delta x,\Delta y)\propto \exp [-R(\Delta x,\Delta y)/2]$ with the distances from the crossing point $\Delta x$ and $\Delta y$ and $R(\Delta x,\Delta y)=(\Delta y+6\Delta x{)}^2/{\sigma }_{\mathrm{Hg}}^2+(\Delta y+2.8\Delta x{)}^2/{\sigma }_{\mathrm{H}}^2$. The resulting elliptical uncertainty region, defined by $R(\Delta x,\Delta y)=1$, gives the standard deviation when projected on either axis by integration over the other. The uncertainties of the measured values are ${\sigma }_{\mathrm{H}}=6.3\times {10}^{-15}{\mathrm{yr}}^{-1}$ and ${\sigma }_{\mathrm{Hg}}=7\times {10}^{-15}{\mathrm{yr}}^{-1}$.