Molecular hydrogen and its isotopic and ionic species are benchmark systems for testing quantum chemical theory. Advances in molecular energy structure calculations enable the experimental verification of quantum electrodynamics and potentially a determination of the proton charge radius from H_{2} spectroscopy. We measure the ground state energy in ortho-H_{2} relative to the first electronically excited state by Ramsey-comb laser spectroscopy on the EF^{1}Σ_{g}^{+}-X^{1}Σ_{g}^{+}(0,0) Q1 transition. The resulting transition frequency of 2 971 234 992 965(73) kHz is 2 orders of magnitude more accurate than previous measurements. This paves the way for a considerably improved determination of the dissociation energy (D_{0}) for fundamental tests with molecular hydrogen.

High-precision spectroscopy in systems such as molecular hydrogen and helium ions is very interesting in view of tests of quantum electrodynamics and the proton radius puzzle. However, the required deep ultraviolet and shorter wavelengths pose serious experimental challenges. Here we show Ramsey-comb spectroscopy in the deep ultraviolet for the first time, thereby demonstrating its enabling capabilities for precision spectroscopy at short wavelengths. We excite ^{84}Kr in an atomic beam on the two-photon 4p^{6}→4p^{5}5p[1/2]_{0} transition at 212.55 nm. It is shown that the ac-Stark shift is effectively eliminated, and combined with a counterpropagating excitation geometry to suppress Doppler effects, a transition frequency of 2 820 833 101 679(103) kHz is found. The uncertainty of our measurement is 34 times smaller than the best previous measurement, and only limited by the 27 ns lifetime of the excited state.

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 → 5p 5 8s 2 [3/2]1 transition at 110 nm in 132 Xe. We improve its relative accuracy 10 4 times to a value of 2.3 × 10 −10 . This is 3.6 times better than shown before involving HHG, and promising to enable 1S − 2S spectroscopy of He + for fundamental tests.High-precision spectroscopy in calculable atomic and molecular systems is at the heart of the most precise tests of bound-state quantum electrodynamics (QED) and searches for new physics beyond the Standard Model [1][2][3][4][5][6]. Instrumental in this development was the invention of the optical frequency comb (FC) [7,8] which enables precise optical frequency measurements referenced to an atomic clock. However, uncertainties in finite nuclearsize effects are hampering further progress [9]. Instead, spectroscopy has been used to measure the proton size in atomic and muonic hydrogen, but with partly conflicting results [10][11][12][13][14][15][16]. High-precision spectroscopy of the 1S − 2S transition in He + would provide new possibilities for fundamental tests as the uncertainty there is less dominated by nuclear size effects [17]. Combined with muonic He + spectroscopy [18,19] one can extract e.g. the alpha particle radius or the Rydberg constant. A major experimental challenge arises from the requirement of extreme ultraviolet (XUV) light at 60 nm (or shorter), to excite the transition. A similar challenge exist for spectroscopy of highly-charged ions [5], or the Thorium nuclear clock transition near 150 nm in the vacuum ultraviolet (VUV) [20,21]. At those wavelengths a relative accuracy of 0.1 ppm has been achieved with Fouriertransform spectroscopy techniques [22], and 0.03 ppm with low harmonics from nanosecond pulsed lasers [23]. A higher accuracy can be reached with light from highharmonic generation (HHG), induced by focusing ultrafast high-energy laser pulses in a noble gas at intensities of ∼ 10 14 W/cm 2 . The process can be understood using the three-step model [24,25], involving tunnel-ionization and recollision of an electron. This highly coherent process leads to the generation of a series of odd harmonics, which are tightly linked to the fundamental wave [26][27][28][29][30]. In combination with frequency-comb lasers, it has been used to achieve a spectroscopic accuracy of about 1 ppb at VUV and XUV wavelengths [31,32]. To improve on this we recently developed the Ramseycomb spectroscopy (RCS) method [33,34], based on pairs of powerful amplified FC pulses in a Ramsey-type [35] excitation scheme. Using only two pulses can compro-mise the accuracy provided by the FC laser [31], but th...

High-precision laser spectroscopy of atomic hydrogen has led to an impressive accuracy in tests of bound-state quantum electrodynamics (QED). At the current level of accuracy many systematics have to be studied very carefully and only independent measurements provide the ultimate cross-check. This has been proven recently by measurements in muonic hydrogen, eventually leading to a significant shift of the CODATA recommended values of the proton charge radius and the Rydberg constant. We aim to contribute to tests of fundamental physics by measuring the 1S-2S transition in the He + ion for the first time. Combined with measurements in muonic helium ions this can probe the value of the Rydberg constant, test higher-order QED terms, or set benchmarks for ab initio nuclear polarizability calculations. We extend the Ramsey-comb spectroscopy method to the XUV using high-harmonic generation in order to excite a single, trapped He + ion.

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