Demonstration of Ramsey-Comb Precision Spectroscopy in Xenon at Vacuum Ultraviolet Wavelengths Produced with High-Harmonic Generation

The remarkable progress in the field of laser spectroscopy induced by the invention of the frequency-comb laser has enabled many new high-precision tests of fundamental theory and searches for new physics. Extending frequency-comb based spectroscopy techniques to the vacuum (VUV) and extreme ultraviolet (XUV) spectral range would enable measurements in e.g. heavier hydrogen-like systems and open up new possibilities for tests of quantum electrodynamics and measurements of fundamental constants. The main approaches rely on high-harmonic generation (HHG), which is known to induce spurious phase shifts from plasma formation. After our initial report (Physical Review Letters 123, 143001 (2019)), we give a detailed account of how the Ramsey-comb technique is used to probe the plasma dynamics with high precision, and enables accurate spectroscopy in the VUV. A series of Ramsey fringes is recorded to track the phase evolution of a superposition state in xenon atoms, excited by two up-converted frequency-comb pulses. Phase shifts of up to 1 rad induced by HHG were observed at ns timescales and with mrad-level accuracy at \(110\) nm. Such phase shifts could be reduced to a negligible level, enabling us to measure the \(5p^6 \rightarrow 5p^5 8s~^2[3/2]_1\) transition frequency in \(^{132}Xe\) at 110 nm (seventh harmonic) with sub-MHz accuracy. The obtained value is \(10^4\) times more precise than the previous determination and the fractional accuracy of \(2.3 \times 10^{-10}\) is \(3.6\) times better than the previous best spectroscopic measurement using HHG. The isotope shifts between \(^{132}Xe\) and two other isotopes were determined with an accuracy of \(420\) kHz. The method can be readily extended to achieve kHz-level accuracy, e.g. to measure the \(1S-2S\) transition in \(He^+\). Therefore, the Ramsey-comb method shows great promise for high-precision spectroscopy of targets requiring VUV and XUV wavelengths.