Tests of local position invariance using continuously running atomic clocks

Tests of local position invariance (LPI) made by comparing the relative redshift of atomic clocks based on different atoms have been carried out for a variety of pairs of atomic species. In most cases, several absolute frequency measurements per year are used to look for an annual signal, resulting in tests that can span on order of a decade. By using the output of continuously running clocks, we carry out LPI tests with comparable or higher precision after less than 1.5 years. These include new measurements of the difference in redshift anomalies $\beta$ for hyperfine transitions in ${}^{87}\mathrm{Rb}$ and ${}^{133}\mathrm{Cs}$ and in ${}^1\mathrm{H}$ and ${}^{133}\mathrm{Cs}$ and a measurement comparing ${}^{87}\mathrm{Rb}$ and ${}^1\mathrm{H}$, resulting in a stringent limit on LPI, ${\beta }_{\mathrm{Rb}}-{\beta }_{\mathrm{H}}=\left(-2.7\pm 4.9\right)\times {10}^{-7}$. The method of making these measurements for continuous clocks is discussed.

Figure 1

LPI tests for various pairs of atomic species in terms of the difference in anomalous redshift parameters, $\Delta \beta ={\beta }_1-{\beta }_2$. (a) Dark data points are previous measurements: (i) neutral strontium optical transition against cesium standard, carried out over 2.5 years [9, 11]; (ii) mercury ion optical transition against cesium standard, carried out over 5 years [7]; (iii) hydrogen hyperfine transition against cesium standard, carried out over 7 years [8]; and (iv) rubidium-87 hyperfine transition against cesium standard, carried out over 14 years [10]. Light data points are results presented in this work. (b) A more detailed look at the shaded region in (a).

Figure 2

(a) Frequency difference of rubidium-fountain average and cesium ensemble over 1.5 years. Fit to a linear drift is shown. (b) Residuals after removing drift, along with the fit to an LPI-violating signal, amplified $\times$20. MJD stands for modified Julian day.

Figure 3

Frequency comparison for one hydrogen maser and (a) the cesium ensemble and (b) the rubidium-fountain average. Each point is a 2-day average, and linear drifts have been removed. Fits to LPI-violating signals are amplified by the factors shown.

Figure 4

Constraints on coupling of $\alpha$, $m_e/m_p$, and $m_q/{\Lambda }_{\mathrm{QCD}}$ to gravitational potential characterized by the dimensionless parameters $k_{\alpha }$, $k_{m_e/m_p}$, and $k_{m_q/{\Lambda }_{\mathrm{QCD}}}$. Gray bands show constraints imposed by previous measurements, compiled from Refs. [7, 8, 9, 10] and presented in [10]. Diamonds show the tighter constraints that result when our measurements are included in the analysis. Squares represent the values for $k_{\alpha }$ and $k_{m_q/{\Lambda }_{\mathrm{QCD}}}$ that are derived using only the results presented here.