Precision Spectroscopy of Atomic Hydrogen and Variations of Fundamental Constants

Abstract

In 2003 we have measured the absolute frequency of the $(1S,F=1,m_F=\pm 1)\leftrightarrow (2S,F^{\prime }=1,m_F^{\prime }=\pm 1)$ two-photon transition in atomic hydrogen. We observed a variation of $(-29\pm 57)$ Hz over a 44 months interval separating this measurement from the previous one performed in 1999. We have combined this result with recently published results of optical transition frequency measurement in the ${}^{199}$Hg${}^{+}$ ion and and comparison between clocks based on ${}^{87}$Rb and ${}^{133}$Cs. From this combination we deduce the stringent limits for fractional time variation of the fine structure constant $\partial /\partial t(\ln \hat{I}\pm )=(-0.9\pm 4.2)\times 10^{-15}$ yr${}^{-1}$ and for the ratio of ${}^{87}$Rb and ${}^{133}$Cs spin magnetic moments $\partial /\partial t(\ln [\hat{I}{¼}_{\mathrm{Rb}}/\hat{I}{¼}_{\mathrm{Cs}}])=(0.5\pm 2.1)\times 10^{-15}$ yr${}^{-1}$. This is the first precise restriction for the fractional time variation of $\hat{I}\pm$ made without assumptions about the relative drifts of the constants of electromagnetic, strong and weak interactions.

18 pages, 10 figures, invited talk