Hydrogen-like light muonic ions, in which one negative muon replaces all of the electrons, are extremely sensitive probes of nuclear structure. Using pulsed laser spectroscopy, we have measured three 2S-2P transitions in the muonic helium-3 (μ3He+) ion, an ion formed by a negative muon and bare helium-3 nucleus. This allowed us to extract the Lamb shift, the 2P fine structure splitting, and the 2S-hyperfine splitting in μ3He+. Comparing these measurements with theory, we determined the root-mean-square charge radius of the helion (3He nucleus) to be rh = 1.97007(94) fm, in good agreement with the value from elastic electron scattering but a factor 15 more accurate. Our results represent benchmarks for few-nucleon theories and open the way for precision quantum electrodynamics tests in He atoms and ions.

Optical multipass cells are used in photochemical reactors and laser excitation of weak transitions. In these applications, estimation of the radiation dose in a volume of interest allows us to assess the performance and optimize the design of the cell. We adopt radiant fluence as the figure of merit and employ the radiative transfer equation to derive analytical expressions for average radiant fluence in a given volume of interest. These expressions involve quantities that are either obtained with Monte Carlo ray tracing methods or approximated on the grounds of geometry arguments. Furthermore, we compute the spatial distribution of fluence by applying either of the two methods to individual volume elements in a rectangular voxel grid. Ray tracing is performed with Zemax OpticsStudio 18.9.

We report on an Yb:YAG thin-disk multipass amplifier delivering 50 ns long pulses at a central wavelength of 1030 nm with an energy of 330 mJ at a repetition rate of 100 Hz. The beam quality factor at the maximum energy was measured to be M² = 1.17. The small signal gain is 20, and the gain at 330 mJ was measured to be 6.9. The 20-pass amplifier is designed as a concatenation of stable resonator segments in which the beam is alternately Fourier transformed and relay-imaged back to the disk by a 4f-imaging optical scheme stage. The Fourier transform propagation makes the output beam robust against spherical phase front distortions, while the 4f-stage is used to compensate the thermal lens of the thin-disk and to reduce the footprint of the amplifier.

We demonstrate an injection-seeded thin-disk Yb:YAG laser at 1030 nm, stabilized by the Pound-Drever-Hall (PDH) method. We modified the PDH scheme to obtain an error signal free from Trojan locking points, which allowed robust re-locking of the laser and reliable long-term operation. The single-frequency pulses have 50 mJ energy (limited to avoid laser-induced damage) with a beam quality of M2 < 1.1 and an adjustable length of 55-110 ns. Heterodyne measurements confirmed a spectral linewidth of 3.7 MHz. The short pulse build-up time (850 ns) makes this laser suitable for laser spectroscopy of muonic hydrogen, pursued by the CREMA collaboration.

The Pound-Drever-Hall (PDH) technique is a popular method for stabilizing the frequency of a laser to a stable optical resonator or, vice versa, the length of a resonator to the frequency of a stable laser. We propose a refinement of the technique yielding an "infinite" dynamic (capture) range so that a resonator is correctly locked to the seed frequency, even after large perturbations. The stable but off-resonant lock points (also called Trojan operating points), present in conventional PDH error signals, are removed by phase modulating the seed laser at a frequency corresponding to half the free spectral range of the resonator. We verify the robustness of our scheme experimentally by realizing an injection-seeded Yb:YAG thin-disk laser. We also give an analytical formulation of the PDH error signal for arbitrary modulation frequencies and discuss the parameter range for which our PDH locking scheme guarantees correct locking. Our scheme is simple as it does not require additional electronics apart from the standard PDH setup and is particularly suited to realize injection-seeded lasers and injection-seeded optical parametric oscillators.

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen (µp) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with 2 × 10 -4 relative accuracy.In the proposed experiment, the µp atom that undergoes a laser excitation from the singlet hyperfine state to the triplet hyperfine state, is quenched back to the singlet state by an inelastic collision with a H 2 molecule.The resulting increase of kinetic energy after the collisional deexcitation is used as a signature of a successful laser transition between hyperfine states.In this paper, we calculate the combined probability that a µp atom initially in the singlet hyperfine state undergoes a laser excitation to the triplet state followed by a collisional-induced deexcitation back to the singlet state.This combined probability has been computed using the optical Bloch equations including the inelastic and elastic collisions.Omitting the

A Correction to this paper has been published: https://doi.org/10.1038/s41586-021-03360-2.

In experiments at the Paul Scherrer Institute PSI, an international research collaboration has measured the radius of the atomic nucleus of helium five times more precisely than ever before. With the aid of the new value, fundamental physical theories can be tested and natural constants can be determined even more precisely. For their measurements, the researchers needed muons—these particles are similar to electrons but are around 200 times heavier. PSI is the only research site in the world where enough so-called low-energy muons are produced for such experiments. The researchers are publishing their results today in the journal Nature.

For spectroscopy on muonic helium, we developed a thin-disk laser with an output pulse energy of 147 mJ capable of stochastic triggering (< 500 Hz) with a beam quality of M² = 1.04. We reached these values by implementing Fourier transform propagation from disk to disk. This architecture is passively compensating for phase front distortions caused by thermal lensing in the thin disk. The amplifier was not only very stable against thermal lens effects but was also forgiving misalignment of the disk. Indeed, it was operated for 3 months without realignment. Our design utilizes the gain profile of the active medium (effective soft aperture) to provide transversal mode filtering. As a result, the beam remains in the TEM00 mode during propagation in the amplifier. This implies that modeling of its propagation does not require techniques for higher-order mode propagation. Soft apertures can simply be modeled as lenses with imaginary focal length. We modeled the misalignment related losses for two different multi-pass amplifier designs reproducing the measured behavior. We also realized a simple control system to correct for tilt misalignment of the active medium. Only two servo-controlled folding mirrors inside the amplifier were sufficient to stabilize the beam position of all (eight) passes on the active medium. This active stabilization reduced the sensitivity (decrease of output energy) to tilts of the active medium by a factor of 10 compared to the multi-pass amplifier without active stabilization.

This study investigates the stability to tilts (misalignments) of Fourier-based multipass amplifiers, i.e., amplifiers where a Fourier transform is used to transport the beam from pass to pass. Here, the stability properties of these amplifiers to misalignments (tilts) of their optical components have been investigated. For this purpose, a method to quantify the sensitivity to tilts based on the amplifier small-signal gain has been elaborated and compared with measurements. To improve tilt stability by more than an order of magnitude, a simple auto-alignment system has been proposed and tested. This study, combined with other investigations devoted to the stability of the output beam to variations in aperture and thermal lens effects of the active medium, qualifies the Fourier-based amplifier for the high-energy and high-power sectors.

We present a frequency selective optical setup based on a Gires-Tournois interferometer suitable to enforce single-frequency operation of high power lasers. It is based on a birefringent Gires-Tournois interferometer combined with a λ/4 plate and a polarizer. The high-reflective part of the Gires-Tournois interferometer can be contacted to a heat sink to obtain efficient cooling (similar cooling principle as for the active medium in thin-disk lasers) enabling power scaling up to output powers in the kW range.

We present a novel architecture for a multi-pass amplifier based on a succession of optical Fourier transforms and short propagations that shows a superior stability for variations of the thermal lens compared to state-of-the-art 4f-based amplifiers. We found that the proposed multi-pass amplifier is robust to variations of the active medium dioptric power. The superiority of the proposed architecture is demonstrated by analyzing the variations of the size and divergence of the output beam in form of a Taylor expansion around the design value for variations of the thermal lens in the active medium. The dependence of the output beam divergence and size is investigated also for variations of the number of passes, for aperture effects in the active medium and as a function of the size of the beam on the active medium. This architecture makes efficient use of the transverse beam filtering inherent in the active medium to deliver a beam with excellent quality (TEM00) without additional losses.

The deuteron is too small, too The radius of the proton has remained a point of debate ever since the spectroscopy of muonic hydrogen indicated a large discrepancy from the previously accepted value. Pohl et al. add an important clue for solving this so-called proton radius puzzle. They determined the charge radius of the deuteron, a nucleus consisting of a proton and a neutron, from the transition frequencies in muonic deuterium. Mirroring the proton radius puzzle, the radius of the deuteron was several standard deviations smaller than the value inferred from previous spectroscopic measurements of electronic deuterium. This independent discrepancy points to experimental or theoretical error or even to physics beyond the standard model. Science , this issue p. 669

A novel optical layout for a multi-pass resonator is presented paving the way for pulse energy scaling of mode-locked thin-disk lasers. The multi-pass resonator we are proposing consists of a concatenation of nearly identical optical segments. Each segment corresponds to a round-trip in an optically stable cavity containing an active medium exhibiting soft aperture effects. This scheme is apt for energy and power scaling because the stability region of this multi-pass resonator contrarily to the 4f-based schemes does not shrink with the number of passes. Simulation of the eigen-mode of this multi-segment resonator requires considering aperture effects. This has been achieved by implementing effective Gaussian apertures into the ABCD-matrix formalism as lenses with imaginary focal length. We conclude proposing a simple way to double the stability region of the state-of-the-art layouts used in industry achievable by a minimal rearrangement of the used optical components.

We present a fundamental obstacle in power scaling of thin-disk lasers related to self-driven growth of misalignment due to thermal lens effects. This self-driven growth arises from the changes of the optical phase difference at the disk caused by the excursion of the laser eigen-mode from the optical axis. We found a criterion based on a simplified model of this phenomenon, which can be applied to design laser resonators insensitive to this effect. Moreover, we propose several resonator architectures that are not affected by this effect.

Laser spectroscopy of the Lamb shift (2S-2P energy difference) in light muonic atoms or ions, in which one negative muon $\mu^-$ is bound to a nucleus, has been performed. The measurements yield significantly improved values of the root-mean-square charge radii of the nuclei, owing to the large muon mass, which results in a vastly increased muon wave function overlap with the nucleus. The values of the proton and deuteron radii are 10 and 3 times more accurate than the respective CODATA values, but 7 standard deviations smaller. Data on muonic helium-3 and -4 ions is being analyzed and will give new insights. In future, the (magnetic) Zemach radii of the proton and the helium-3 nuclei will be determined from laser spectroscopy of the 1S hyperfine splittings, and the Lamb shifts of muonic Li, Be and B can be used to improve the respective charge radii.

Thin-disk laser pump layouts yielding an increased number of passes for a given pump module size and pump source quality are proposed. These layouts result from a general scheme based on merging two simpler pump optics arrangements. Some peculiar examples can be realized by adapting standard, commercially available pump optics with an additional mirror pair. More pump passes yield better efficiency, opening the way for the usage of active materials with low absorption. In a standard multipass pump design, scaling of the number of beam passes brings about an increase in the overall size of the optical arrangement or an increase in the pump source quality requirements. Such increases are minimized in our scheme, making them eligible for industrial applications.

Avalanche photodiodes are commonly used as detectors for low energy x-rays. In this work, we report on a fitting technique used to account for different detector responses resulting from photoabsorption in the various avalanche photodiode layers. The use of this technique results in an improvement of the energy resolution at 8.2 keV by up to a factor of 2 and corrects the timing information by up to 25 ns to account for space dependent electron drift time. In addition, this waveform analysis is used for particle identification, e.g., to distinguish between x-rays and MeV electrons in our experiment.