High-harmonic generation (HHG) is widely used for up-conversion of amplified (near) infrared ultrafast laser pulses to short wavelengths. We demonstrate that Ramsey-comb spectroscopy, based on two such pulses derived from a frequency-comb laser, enables us to observe phase effects in this process with a few mrad precision. As a result, we could perform the most accurate spectroscopic measurement based on light from HHG, illustrated with a determination of the $5p^6\to 5p^{5}8s{}^2[3/2{]}_1$ transition at 110 nm in ${}^{132}\mathrm{Xe}$. We improve its relative accuracy $10^4$ times to a value of $2.3\times {10}^{-10}$. This is 3.6 times better than shown before involving HHG, and promising to enable $1S\text{−}2S$ spectroscopy of ${\mathrm{He}}^{+}$ for fundamental tests.

• Received 17 May 2019

DOI:https://doi.org/10.1103/PhysRevLett.123.143001