Laboratory demonstration of geopotential measurement using transportable optical clocks

We report an experimental demonstration of geopotential difference measurement using a pair of transportable ⁴⁰Ca ⁺ optical clocks (TOC-729-1 and TOC-729-3) in the laboratory, each of them has an uncertainty of 1.3 × 10 ⁻¹⁷ and an instability of $4.8\times {10}^{-15}/\sqrt{\tau }$ . Referenced to a stationary clock of TOC-729-1, the geopotential difference measurements are realized by moving TOC-729-3 to three different locations and the relevant altitude differences are measured with uncertainties at the level of 20 cm. After correcting the systematic shifts (including gravitational red shift), the two-clock frequency difference is measured to be –0.7(2.2) × 10 ⁻¹⁷, considering both the statistic (1.0 × 10 ⁻¹⁷) and the systematic (1.9 × 10 ⁻¹⁷) uncertainties. The frequency difference between these two clocks is within their respective uncertainties, verifying the reliability of transportable ⁴⁰Ca ⁺ optical clocks at the low level of 10 ⁻¹⁷.