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

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 $^{2S_{1/2}\rightarrow} {<sup>2F_{7/2}}$ electric octupole (E3) transition in $<sup>{171}$Yb$<sup>+$ against two caesium fountain clocks as $f(E3) = 642\,121\,496\,772\,645.36(25)$~Hz with an improved fractional uncertainty of $3.9\times 10<sup>{-16}$. This transition frequency shows a strong sensitivity to changes of $\alpha$. Together with a number of previous and recent measurements of the $^{2S_{1/2}\rightarrow} {<sup>2D_{3/2}}$ electric quadrupole transition in $<sup>{171}$Yb$<sup>+$ and with data from other elements, a least-squares analysis yields $$(1/\alpha)(d\alpha/dt)=-0.20(20)\times 10<sup>{-16}/\mathrm{yr}$$ and $$(1/\mu)(d\mu/dt)=-0.5(1.6)\times 10<sup>{-16}/\mathrm{yr}$$, confirming a previous limit on $d\alpha/dt$ and providing the most stringent limit on $d \mu/dt$ from laboratory experiments.

• The paper demonstrates improved constraints on the temporal variation of the proton-to-electron mass ratio, reporting dμ/dt = -0.5(1.6)×10⁻¹⁶/yr.
• It employs high-precision frequency measurements of the Yb⁺ electric octupole transition compared to Cs fountain clocks with a fractional uncertainty of 3.9×10⁻¹⁶.
• The findings provide stringent laboratory benchmarks that support theoretical unification efforts and motivate further advances in optical clock technology.

Improved Limit on Temporal Variation of $m_p/m_e$ from Atomic Clock Comparisons

The paper "Improved limit on a temporal variation of $m_p/m_e$ from comparisons of Yb$^+$ and Cs atomic clocks" by Huntemann et al. presents an empirical investigation into the potential temporal variations of the fine structure constant $\alpha$ and the proton-to-electron mass ratio $\mu$, through high-precision frequency measurements using atomic clocks based on ytterbium ions ($^{171}$Yb$^+$) and caesium (Cs).

Summary of Methods and Results

The study employs accurate measurements of the $^2S_{1/2} \rightarrow {^2F_{7/2}$ electric octupole (E3) transition frequency in $^{171}$Yb$^+$ ions measured against two caesium fountain clocks. The reported frequency for this transition is 642,121,496,772,645.36(25) Hz, with a considerably improved fractional uncertainty of $3.9 \times 10^{-16}$. This measurement derives its significance from the strong sensitivity of this transition to variations in the fine structure constant $\alpha$.

The results were analyzed together with previous measurements of the $^2S_{1/2} \rightarrow {^2D_{3/2}$ electric quadrupole transition in the same ion and data from other atomic species. A least-squares analysis performed on these measurements yields $$(1/\alpha)(d\alpha/dt) = -0.20(20) \times 10^{-16}/\mathrm{yr}$$ and $$(1/\mu)(d\mu/dt) = -0.5(1.6) \times 10^{-16}/\mathrm{yr}$$. These results confirm previously set limits on $d\alpha/dt$ and represent the most precise constraint on $d\mu/dt$ obtained from laboratory measurements to date.

Implications and Future Directions

The investigation into constants $\alpha$ and $\mu$ is driven by theoretical efforts aimed at unifying the fundamental forces, which suggest that these constants might exhibit temporal variations over cosmological timescales. Laboratory constraints of this nature provide insights at the intersection of quantum mechanics, atomic physics, and cosmology, potentially informing theories beyond the Standard Model of particle physics.

The results discussed in this paper highlight the capability of atomic clocks not only as tools for precision timekeeping but also as instruments for probing the fundamental constants of nature. With ongoing improvements in clock technology and methodologies, future investigations will likely yield even tighter bounds on the variations of these constants. Direct optical frequency comparisons, benefiting from lower systematic uncertainties than cesium-referenced measurements, will be particularly promising for further progress.

Conclusion

This paper substantiates the current understanding of fundamental constants' immutability at the temporal resolution offered by state-of-the-art atomic clocks. The technical advances showcased in this study exemplify the role of precision metrology in foundational physics research, setting a benchmark for future experimental efforts to explore the temporal stability of nature’s constants.