K. S. E. Eikema

Extreme-ultraviolet (XUV) spectroscopy represents an important new direction in precision physics, with potential applications ranging from the metrology of fundamental constants to tests of physics beyond the Standard Model. However, the application of quantum control methods for precision spectroscopy remains an open challenge in the XUV range. Here we present a novel quantum logic (QL) spectroscopy method for precision spectroscopy of weak XUV transitions, and numerically validate its feasibility for the $1S-2S$ transition at 40.81\,eV in singly-ionized helium (He$^{+}$). We propose a scheme based on a single He$^{+}$ ion co-trapped with a Be$^{+}$ ion in a Paul trap, and He$^{+}$ excitation with pairs of frequency-comb (FC) laser pulses upconverted to the XUV via High-Harmonic Generation (HHG). We investigate a nondestructive QL scheme to detect $1S-2S$ excitation, and compare its performance with a destructive readout based on state-selective ionization. Phase coherence of the XUV light is modelled and an optical cavity is used to filter the FC pulses prior to HHG. We model the motional excitation dynamics of trapped ions outside the Lamb-Dicke regime, and numerically validate a scheme we proposed in \cite{Grundeman} to cancel the first-order Doppler broadening and the recoil shift by synchronizing the ion's secular period with the time delay between the two excitation pulses. We show that precision spectroscopy of the $1S-2S$ transition in He$^{+}$ at the 10 kHz level is feasible, for improved tests of quantum electrodynamics (QED), a measurement of the Rydberg constant $R_{\infty}$ independent of hydrogen measurements, or an improved determination of the alpha particle and helion charge radii. The proposed method may also be applied to XUV spectroscopy of other ions outside the Lamb-Dicke regime.

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.

Recently we reported a high precision optical frequency measurement of the (v,L):(0,2)->(8,3) vibrational overtone transition in trapped deuterated molecular hydrogen (HD+) ions at 10 mK temperature. Achieving a resolution of 0.85 parts-per-billion (p.p.b.) we found the experimental value ($ν_0= 383,407,177.38(41)$ MHz) to be in agreement with the value from molecular theory ($ν_\text{th}=383,407,177.150(15)$ MHz) within 0.6(1.1) p.p.b. [Biesheuvel et al., Nat. Commun. 7, 10385 (2016)]. This enabled an improved test of molecular theory (including QED), new constraints on the size of possible effects due to 'new physics', and the first determination of the proton-electron mass ratio from a molecule. Here, we provide the details of the experimental procedure, spectral analysis, and the assessment of systematic frequency shifts. Our analysis focuses in particular on deviations of the HD+ velocity distribution from thermal (Gaussian) distributions under the influence of collisions with fast ions produced during (laser-induced) chemical reactions, as such deviations turn out to significantly shift the hyperfine-less vibrational frequency as inferred from the saturated and Doppler-broadened spectrum, which contains partly unresolved hyperfine structure.

Direct frequency comb spectroscopy of trapped ions is demonstated for the first time. It is shown that the 4s^2S_(1/2)-4p^2P_(3/2) transition in calcium ions can be excited directly with a frequency comb laser that is upconverted to 393 nm. Detection of the transition is performed using a shelving scheme to suppress background signal from non-resonant comb modes. The measured transition frequency of f=761 905 012.7(0.5) MHz presents an improvement in accuracy of more than two orders of magnitude.

High accuracy frequency metrology on the 4s 2S1/2 - 4p 2P1/2 transition in calcium ions is performed using laser cooled and crystallized ions in a linear Paul trap. Calibration is performed with a frequency comb laser, resulting in a transition frequency of f=755222766.2(1.7) MHz. The accuracy presents an improvement of more than one order of magnitude, and will facilitate a comparison with quasar data in a search for a possible change of the fine structure constant on a cosmological time scale.