New Limits on Coupling of Fundamental Constants to Gravity Using $^{87}$Sr Optical Lattice Clocks

Abstract: The $^1\mathrm{S}_0$-$^3\mathrm{P}_0$ clock transition frequency $\nu_\text{Sr}$ in neutral $^{87}$Sr has been measured relative to the Cs standard by three independent laboratories in Boulder, Paris, and Tokyo over the last three years. The agreement on the $1\times 10^{-15}$ level makes $\nu_\text{Sr}$ the best agreed-upon optical atomic frequency. We combine periodic variations in the $^{87}$Sr clock frequency with $^{199}$Hg$^+$ and H-maser data to test Local Position Invariance by obtaining the strongest limits to date on gravitational-coupling coefficients for the fine-structure constant $\alpha$, electron-proton mass ratio $\mu$ and light quark mass. Furthermore, after $^{199}$Hg$^+$, $^{171}$Yb$^+$ and H, we add $^{87}$Sr as the fourth optical atomic clock species to enhance constraints on yearly drifts of $\alpha$ and $\mu$.

• The paper demonstrates 87Sr clock frequencies measured across labs with 1×10⁻¹⁵ level agreement, supporting its role in redefining the SI second.
• It constrains gravitational coupling coefficients for the fine-structure constant, electron-proton mass ratio, and light quark mass using cross-comparisons with Cs, Hg⁺, and H-maser data.
• By testing Local Position Invariance, the results indicate no significant long-term drift in fundamental constants, reinforcing established physical models.

Analysis of the Coupling of Fundamental Constants to Gravity via $^{87}$Sr Optical Lattice Clocks

This paper presents a detailed investigation into the measurement of the $^1\mathrm{S}_0$-$^3\mathrm{P}_0$ clock transition frequency in neutral $^{87}$Sr, comparing it against the Cs standard at three independent laboratories located in Boulder, Paris, and Tokyo. The reported measurements achieve consensus at the $1\times10^{-15}$ level, which positions $\nu_\text{Sr}$ as the most consistently agreed-upon optical atomic frequency measured to date.

The study explores the implications of these measurements for testing fundamental physics, focusing on two areas: Local Position Invariance (LPI) and potential drifts in fundamental constants. By integrating periodic variations in the $^{87}$Sr clock frequency with data from $^{199}$Hg$^+$ and H-masers, the authors obtain strong constraints on gravitational-coupling coefficients for the fine-structure constant $\alpha$, the electron-proton mass ratio $\mu$, and the light quark mass. Additionally, they assess the strontium frequency relative to Cs standards to place bounds on yearly variations of these fundamental constants.

Results and Analysis

• Agreement in Frequency Measurements: These data, especially the remarkable consensus on the frequency $\nu_\text{Sr}$ at a level of 1.7 Hz, suggest the $^{87}$Sr optical lattice clock as a contender for future redefinition of the SI second. The precision and agreement achieved are crucial for pushing the boundaries of high-accuracy frequency standards.
• Implications for Fundamental Constants: An analysis on the dataset suggests no significant long-term drift in fundamental constants, displayed in fractional frequency drift constraints:
  • $$\delta\alpha/\alpha = (-3.3 \pm 3.0)\times 10^{-16}/\text{yr}$$
  • $$\delta\mu/\mu = (1.6 \pm 1.7)\times 10^{-15}/\text{yr}$$
• Testing of Local Position Invariance: This is tested by estimating the coupling of fundamental constants to the gravitational potential. The ellipticity of Earth’s orbit results in annual variations that are significant for these measurements.
  • The paper reports $k_\alpha = (2.5 \pm 3.1)\times 10^{-6}$, $k_\mu = (-1.3 \pm 1.7)\times 10^{-5}$, and $k_q = (-1.9 \pm 2.7)\times 10^{-5}$, suggesting no detected coupling at current limits.

Theoretical and Practical Implications

From the theoretical standpoint, this research provides a robust platform for testing the invariance of fundamental constants under varying gravitational fields, supporting the LPI component of the Einstein Equivalence Principle. The constraints on possible variations in constants provide empirical support to numerous cosmological models postulating that these quantities might remain constant over time.

Practically, the precision and consistency of the $^{87}$Sr system enhance the reliability of optical frequency standards for timekeeping, suggesting a pathway for refining or redefining temporal measurement units. Continued improvements in clock stability and accuracy will facilitate further empirical tests over extended time periods.

Speculations on Future Developments

Further advancements in atomic clock technology, possibly incorporating deep-space missions or establishing new terrestrial infrastructural setups to reduce systematic uncertainties, could tighten constraints on variations in fundamental constants even further. Additionally, as other optical atomic species are examined with similar rigor, a more comprehensive understanding of potential variations will emerge.

The continued development of these precise atomic systems will likely play a significant role in extending the parameters of current Physical theories, potentially hinting at new interactions or dimensions that lay beyond the established framework of General Relativity and the Standard Model of particle physics. Thus, this research not only anchors current models but also serves as a pivotal step towards their evolution.