Precision Atomic Spectroscopy for Improved Limits on Variation of the Fine Structure Constant and Local Position Invariance

We report tests of local position invariance and the variation of fundamental constants from measurements of the frequency ratio of the 282-nm ${}^{199}\mathrm{Hg}^{+}$ optical clock transition to the ground state hyperfine splitting in ${}^{133}\mathrm{Cs}$. Analysis of the frequency ratio of the two clocks, extending over 6 yr at NIST, is used to place a limit on its fractional variation of $<5.8\times {10}^{-6}$ per change in normalized solar gravitational potential. The same frequency ratio is also used to obtain 20-fold improvement over previous limits on the fractional variation of the fine structure constant of $|\frac{\dot{\alpha }}{\alpha }|<1.3\times {10}^{-16}{\mathrm{yr}}^{-1}$, assuming invariance of other fundamental constants. Comparisons of our results with those previously reported for the absolute optical frequency measurements in H and ${}^{171}\mathrm{Yb}^{+}$ vs other ${}^{133}\mathrm{Cs}$ standards yield a coupled constraint of $-1.5\times {10}^{-15}<\dot{\alpha }/\alpha <0.4\times {10}^{-15}{\mathrm{yr}}^{-1}$ and $-2.7\times {10}^{-15}<\frac{d}{dt}\ln \frac{{\mu }_{\mathrm{Cs}}}{{\mu }_B}<8.6\times {10}^{-15}{\mathrm{yr}}^{-1}$.