Frequency comparisons and absolute frequency measurements of 171Yb+ single-ion optical frequency standards

We describe experiments with an optical frequency standard based on a laser cooled $^{171}$Yb$^+$ ion confined in a radiofrequency Paul trap. The electric-quadrupole transition from the $^2S_{1/2}(F=0)$ ground state to the $^2D_{3/2}(F=2)$ state at the wavelength of 436 nm is used as the reference transition. In order to compare two $^{171}$Yb$^+$ standards, separate frequency servo systems are employed to stabilize two probe laser frequencies to the reference transition line centers of two independently stored ions. The experimental results indicate a relative instability (Allan standard deviation) of the optical frequency difference between the two systems of $\sigma_y(1000 {\rm s})=5\cdot 10^{-16}$ only, so that shifts in the sub-hertz range can be resolved. Shifts of several hertz are observed if a stationary electric field gradient is superimposed on the radiofrequency trap field. The absolute optical transition frequency of Yb$^+$ at 688 THz was measured with a cesium atomic clock at two times separated by 2.8 years. A temporal variation of this frequency can be excluded within a $1\sigma$ relative uncertainty of $4.4\cdot 10^{-15}$ yr$^{-1}$. Combined with recently published values for the constancy of other transition frequencies this measurement provides a limit on the present variability of the fine structure constant $\alpha$ at the level of $2.0\cdot 10^{-15}$ yr$^{-1}$.Comment: 12 pages, 5 figures, Proceedings of MPLP'04, Novosibirsk, August 22.-27., 200

Coulomb energy contribution to the excitation energy in 229^{229}Th and enhanced effect of α\alpha variation

We calculated the contribution of Coulomb energy to the spacing between the ground and first excited state of $^{229}$Th nucleus as a function of the deformation parameter $\delta$. We show that despite the fact that the odd particle is a neutron, the change in Coulomb energy between these two states can reach several hundreds KeV.This means that the effect of the variation of the fine structure constant $\alpha=e^2/\hbar c$ may be enhanced $\Delta U_C/E \sim 10^4$ times in the $E=$7.6 eV "nuclear clock" transition between the ground and first excited states in the $^{229}$Th nucleus.Comment: 6 pages,2 figure