Improved limit on a temporal variation of $m_p/m_e$ from comparisons of Yb$^+$ and Cs atomic clocks

TL;DR

This paper reports a highly precise measurement of the $^{171}$Yb$^+$ electric octupole transition frequency, leading to improved laboratory limits on the temporal variation of the proton-to-electron mass ratio and the fine structure constant.

Contribution

The study provides the most stringent laboratory limit on the time variation of the proton-to-electron mass ratio using advanced atomic clock measurements.

Findings

No significant variation of $eta$ over time within measurement uncertainty.

Improved fractional uncertainty of the Yb$^+$ transition frequency to $3.9 imes 10^{-16}$.

Established tighter constraints on fundamental constant variations.

Abstract

Accurate measurements of different transition frequencies between atomic levels of the electronic and hyperfine structure over time are used to investigate temporal variations of the fine structure constant $\alpha$ and the proton-to-electron mass ratio $\mu$. We measure the frequency of the $^2S_{1/2}\rightarrow {^2F_{7/2}}$ electric octupole (E3) transition in $^{171}$Yb$^+$ against two caesium fountain clocks as $f(E3) = 642\,121\,496\,772\,645.36(25)$~Hz with an improved fractional uncertainty of $3.9\times 10^{-16}$. This transition frequency shows a strong sensitivity to changes of $\alpha$. Together with a number of previous and recent measurements of the $^2S_{1/2}\rightarrow {^2D_{3/2}}$ electric quadrupole transition in $^{171}$Yb$^+$ and with data from other elements, a least-squares analysis yields $(1/\alpha)(d\alpha/dt)=-0.20(20)\times 10^{-16}/\mathrm{yr}$ and $(1/\mu)(d\mu/dt)=-0.5(1.6)\times 10^{-16}/\mathrm{yr}$, confirming a previous limit on $d\alpha/dt$ and providing the most stringent limit on $d \mu/dt$ from laboratory experiments.