[Paper Review] Improved tests of Local Position Invariance using 87Rb and 133Cs fountains

Jocelyne Guéna, Michel Abgrall+6 more|UWA Profiles and Research Repository (University of Western Australia)|May 18, 2012

Radioactive Decay and Measurement Techniques4 citations

TL;DR

This study presents improved laboratory tests of Local Position Invariance using 87Rb and 133Cs atomic fountain clocks over 14 years, achieving a time variation limit of $ d\ln(\nu_{\text{Rb}}/\nu_{\text{Cs}})/dt = (-1.39 \pm 0.91) \times 10^{-16}\ \text{yr}^{-1} $, a 7.7-fold improvement over prior work, and setting the first constraint on gravitational potential dependence at $ c^2 d\ln(\nu_{\text{Rb}}/\nu_{\text{Cs}})/dU = (0.11 \pm 1.04) \times 10^{-6} $. These results constrain variations in the fine-structure constant $\alpha$ and other fundamental constants with high precision.

ABSTRACT

We report tests of local position invariance based on measurements of the ratio of the ground state hyperfine frequencies of 133Cs and 87Rb in laser-cooled atomic fountain clocks. Measurements extending over 14 years set a stringent limit to a possible variation with time of this ratio: d ln(nu_Rb/nu_Cs)/dt=(-1.39 +/- 0.91)x 10-16 yr-1. This improves by a factor of 7.7 over our previous report (H. Marion et al., Phys. Rev. Lett. 90, 150801 (2003)). Our measurements also set the first limit to a fractional variation of the Rb/Cs ratio with gravitational potential at the level of c^2 d ln(nu_Rb/nu_Cs)/dU=(0.11 +/- 1.04)x 10^-6, providing a new stringent differential redshift test. The above limits equivalently apply to the fractional variation of the quantity alpha^{-0.49}x(g_Rb/g_Cs), which involves the fine structure constant alpha and the ratio of the nuclear g-factors of the two alkalis. The link with variations of the light quark mass is also presented together with a global analysis combining with other available highly accurate clock comparisons.

Motivation & Objective

• To test Local Position Invariance (LPI) by measuring the ratio of hyperfine frequencies in 87Rb and 133Cs atomic fountain clocks over 14 years.
• To set stringent limits on the time variation of the Rb/Cs frequency ratio, improving upon previous results by a factor of 7.7.
• To establish the first experimental limit on the variation of the Rb/Cs frequency ratio with gravitational potential, enabling a differential redshift test.
• To link the measured frequency ratio variations to fundamental constants such as the fine-structure constant $\alpha$, the electron-to-proton mass ratio $\mu$, and the ratio $m_q/\Lambda_{\text{QCD}}$ via atomic and nuclear structure calculations.
• To perform a global analysis combining this result with other high-precision clock comparisons to update constraints on temporal and gravitational potential variations of fundamental constants.

Proposed method

• The experiment uses a dual-fountain clock (FO2) at LNE-SYRTE that simultaneously cools, launches, probes, and detects 87Rb and 133Cs atoms in a single vacuum chamber using the Ramsey interrogation method.
• The clocks operate with a common ultra-low-noise cryogenic oscillator, enabling precise comparison of the Rb and Cs hyperfine frequencies over long integration times.
• Systematic shifts are corrected using detailed uncertainty budgets, and data are averaged over 864-second intervals to minimize noise and remove common-mode oscillator drifts.
• The fractional frequency instability of the Rb/Cs comparison is limited by quantum projection noise, reaching $ 2 \times 10^{-16} $ resolution after a few days of averaging.
• The time variation of the Rb/Cs frequency ratio is determined by fitting the long-term data series, with uncertainties dominated by systematic effects after the noise floor.
• A global least-squares fit is performed using results from multiple clock comparisons to constrain the temporal and gravitational potential variations of $\alpha$, $\mu$, and $m_q/\Lambda_{\text{QCD}}$.

Experimental results

Research questions

• RQ1 What is the most stringent laboratory limit on the time variation of the Rb/Cs hyperfine frequency ratio?
• RQ2 How sensitive is the Rb/Cs frequency ratio to gravitational potential, and what is the first experimental constraint on its differential redshift dependence?
• RQ3 To what extent do the measured frequency ratio variations constrain possible temporal variations of the fine-structure constant $\alpha$ and the electron-to-proton mass ratio $\mu$?
• RQ4 How do the results from this Rb/Cs comparison contribute to disentangling the contributions of $\mu$ and $m_q/\Lambda_{\text{QCD}}$ in global analyses of fundamental constant variations?
• RQ5 What are the updated constraints on the coupling of fundamental constants to gravity, based on a global analysis including this experiment?

Key findings

• The time variation of the Rb/Cs frequency ratio is measured as $ d\ln(\nu_{\text{Rb}}/\nu_{\text{Cs}})/dt = (-1.39 \pm 0.91) \times 10^{-16}\ \text{yr}^{-1} $, representing a 7.7-fold improvement over the previous best result.
• The first experimental limit on the gravitational potential dependence of the Rb/Cs frequency ratio is $ c^2 d\ln(\nu_{\text{Rb}}/\nu_{\text{Cs}})/dU = (0.11 \pm 1.04) \times 10^{-6} $, providing a stringent differential redshift test.
• The results constrain the time variation of the fine-structure constant as $ d\ln\alpha/dt = (-0.25 \pm 0.26) \times 10^{-16}\ \text{yr}^{-1} $, consistent with no variation.
• The electron-to-proton mass ratio $\mu = m_e/m_p$ is constrained to $ d\ln\mu/dt = (1.5 \pm 3.0) \times 10^{-16}\ \text{yr}^{-1} $, with no evidence for variation.
• The ratio $ m_q/\Lambda_{\text{QCD}} $ is constrained to $ d\ln(m_q/\Lambda_{\text{QCD}})/dt = (71 \pm 44) \times 10^{-16}\ \text{yr}^{-1} $, indicating no significant time variation.
• The coupling of $ m_e/\Lambda_{\text{QCD}} $ to gravity is found to be $ c^2 d\ln(m_e/\Lambda_{\text{QCD}})/dU = (-4 \pm 17) \times 10^{-6} $, consistent with zero.