Randolf Pohl

• Dr. sc. nat.
• Professor at Johannes Gutenberg University Mainz

Muonic atom spectroscopy is a method that can determine absolute nuclear charge radii with typical relative precision of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$...

With the recent update of the SI system, all but one of the units are now based on defining the values of some fundamental constants. This development began in 1983 when the speed of light was assigned an exact fixed value. The advantage of this method is that it separates the definition from the realization, allowing new realizations to be introdu...

Muonic atom spectroscopy is a method that can determine absolute nuclear charge radii with typical relative precision of 10-3. Recent developments have enabled to extend muonic atom spectroscopy to microscopic target quantities as low as 5 µg. This substantial reduction from the traditional limit of the order of 100 mg is based on a transfer mechan...

The QUARTET collaboration aims to significantly improve the precision of the absolute nuclear charge radii of light nuclei from Li to Ne by using an array of metallic magnetic calorimeters to perform high-precision X-ray spectroscopy of low-lying states in muonic atoms. A proof-of-principle measurement with lithium, beryllium and boron is planned f...

We, the QUARTET Collaboration, propose an experiment to measure the nuclear charge radii of light elements with up to 20 times higher accuracy. These are essential both for understanding nuclear physics at low energies, and for experimental and theoretical applications in simple atomic systems. Such comparisons advance the understanding of bound-st...

A comprehensive theory of the Lamb shift in light muonic atoms such as μH, μD, μ3He+, and μ4He+ is presented, with all quantum electrodynamic corrections included at the precision level constrained by the uncertainty of nuclear structure effects. This analysis can be used in the global adjustment of fundamental constants and in the determination of...

We report on an Yb:YAG thin-disk multipass amplifier delivering 100 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 21.7, and the gain at 330 mJ was measured to be 6.9. The 20-pass amplifier...

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...

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...

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ( \mu μ p) with 1 ppm accuracy by means of pulsed laser spectroscopy. In the proposed experiment, the \mu μ p atom is excited by a laser pulse from the singlet to the triplet hyperfine sub-levels, and is quenched back to the singlet st...

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 l...

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 l...

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 l...

Hydrogen-like light muonic ions, in which one negative muon replaces all the electrons, are extremely sensitive probes of nuclear structure, because the large muon mass increases tremendously the wave function overlap with the nucleus. Using pulsed laser spectroscopy we have measured three 2S-2P transitions in the muonic helium-3 ion ($\mu^3$He$^+$...

Muonic atom spectroscopy–the measurement of the x rays emitted during the formation process of a muonic atom–has a long standing history in probing the shape and size of nuclei. In fact, almost all stable elements have been subject to muonic atom spectroscopy measurements and the absolute charge radii extracted from these measurements typically off...

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 fre...

We present a comprehensive theory of the Lamb shift in light muonic atoms, such as $\mu$H, $\mu$D, $\mu^3$He$^+$, and $\mu^4$He$^+$, with all quantum electrodynamic corrections included at the precision level constrained by the uncertainty of nuclear structure effects. This analysis can be used in the global adjustment of fundamental constants and...

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ($\mu$p) with 1 ppm accuracy by means of pulsed laser spectroscopy. In the proposed experiment, the $\mu$p atom is excited by a laser pulse from the singlet to the triplet hyperfine sub-levels, and is quenched back to the singlet state...

Recent progress in laser and x-ray spectroscopy of muonic atoms offers promising long-term possibilities at the intersection of atomic, nuclear and particle physics. In muonic hydrogen, laser spectroscopy measurements will determine the ground-state hyperfine splitting (HFS) and additionally improve the Lamb shift by a factor of 5. Precision spectr...

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 fre...

Muonic atom spectroscopy -- the measurement of the x rays emitted during the formation process of a muonic atom -- has a long standing history in probing the shape and size of nuclei. In fact, almost all stable elements have been subject to muonic atom spectroscopy measurements and the absolute charge radii extracted from these measurements typical...

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ( \mu μ p) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with 2\times10^{-4} 2 × 10 − 4 relative accuracy. In the proposed experiment, the \mu μ p atom undergoes a laser exc...

The toolbox for material characterization has never been richer than today. Great progress with all kinds of particles and interaction methods provide access to nearly all properties of an object under study. However, a tomographic analysis of the subsurface region remains still a challenge today. In this regard, the Muon Induced X-ray Emission (MI...

In Sec. 6 (polarization monitor) of our recent publication [Opt. Express 29(5), 7024 (2021)10.1364/OE.417455], we assumed a small value of δ. This is however incorrect. The correct approximation for small β leads to the updated Eqs. (10)–(11), resulting in a corrected Fig. 12.

The toolbox for material characterization has never been richer than today. Great progress with all kinds of particles and interaction methods provide access to nearly all properties of an object under study. However, a tomographic analysis of the subsurface region remains still a challenge today. In this regard, the Muon-Induced X-ray Emission (MI...

The CREMA collaboration is pursuing a measurement of the ground-state hyperfine splitting (HFS) in muonic hydrogen ($\mu$p) with 1 ppm accuracy by means of pulsed laser spectroscopy to determine the two-photon-exchange contribution with $2\times10^{-4}$ relative accuracy. In the proposed experiment, the $\mu$p atom which undergoes a laser excitatio...

The energy levels of hydrogen-like atomic systems are shifted slightly by the complex structure of the nucleus, in particular by the finite size of the nucleus. These energy shifts are vastly magnified in muonic atoms and ions, i.e. the hydrogen-like systems formed by a negative muon and a nucleus. By measuring the 2S-2P energy splitting in muonic...

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

We present an improved active fiber-based retroreflector (AFR) providing high-quality wavefront-retracing anti-parallel laser beams in the near UV. We use our improved AFR for first-order Doppler-shift suppression in precision spectroscopy of atomic hydrogen, but our setup can be adapted to other applications where wavefront-retracing beams with de...

The energy levels of hydrogen-like atomic systems can be calculated with great precision. Starting from their quantum mechanical solution, they have been refined over the years to include the electron spin, the relativistic and quantum field effects, and tiny energy shifts related to the complex structure of the nucleus. These energy shifts caused...

Testing physics using the hydrogen atom Discrepancy between the proton radius determined from hydrogen and muonic hydrogen spectroscopy data, the so-called “proton radius puzzle,” has been a focus of the physics community for more than a decade now. Using two-photon ultraviolet frequency comb spectroscopy below 1 kilohertz, Grinin et al. report a h...

The hyperfine splitting of the 5g→4f transitions in muonic Re185,187 has been measured using high resolution high purity germanium detectors and compared to state-of-the-art atomic theoretical predictions. The spectroscopic quadrupole moment has been extracted using modern fitting procedures and compared to the values available in literature obtain...

The hyperfine splitting of the 5g -> 4f transitions in muonic 185,187-Re has been measured using high resolution HPGe detectors and compared to state-of-the-art atomic theoretical predictions. The spectroscopic quadrupole moment has been extracted using modern fitting procedures and compared to the values available in literature obtained from muoni...

High‐resolution laser spectroscopy serves the purpose of determining the energy difference between states of atoms and molecules with the best possible accuracy. Therefore, one may face the problem of finding the center of a symmetric line within a small fraction of the line width, or one needs to extract the energy difference from an asymmetric li...

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 t...

We present a multi-pass amplifier which passively compensates for distortions of the spherical phase front occurring in the active medium. The design is based on the Fourier transform propagation which makes the output beam parameters insensitive to variation of thermal lens effects in the active medium. The realized system allows for 20 reflection...

The stability properties of Fourier-based multipass amplifier to misalignments (tilts) of its optical components has 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 on the tilt stability by more than an order of...

Testing theories means to compare precise measurements with theoretical predictions. I will describe where we stand with quantum electrodynamics by verifying calculations of energy levels in atomic hydrogen.

We present an architecture for a multipass 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 -based amplifiers. We found that the proposed multipass amplifier is robust to variations of the active medium dioptric power....

Precision spectroscopy of light muonic atoms provides unique information about the atomic and nuclear structure of these systems and thus represents a way to access fundamental interactions, properties and constants. One application comprises the determination of absolute nuclear charge radii with unprecedented accuracy from measurements of the 2S...

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 dioptr...

An up to date review of the theoretical contributions to the $2S\rightarrow{}2P$ Lamb shift and the fine structure of the $2P$-state in the $(\mu^4\mathrm{He})^+$ ion is given. This summary will serve as the basis for the extraction of the alpha particle charge radius from the muonic helium Lamb shift measurements at the Paul Scherrer Institute Swi...

Precision spectroscopy of light muonic atoms provides unique information about the atomic and nuclear structure of these systems and thus represents a way to access fundamental interactions, properties and constants. One application comprises the determination of absolute nuclear charge radii with unprecedented accuracy from measurements of the 2S$...

Spatial hole burning prevents single-frequency operation of thin-disk lasers when the thin disk is used as a folding mirror. We present an evaluation of the saturation effects in the disk for disks acting as end mirrors and as folding mirrors, explaining one of the main obstacles toward single-frequency operation. It is shown that a twisted-mode sc...

The core of the “proton radius puzzle” is the discrepancy of four standard deviations between the proton root mean square charge radii (rp) determined from regular hydrogen (H), and the muonic hydrogen atom (μp). We have measured the 2S-4P transition frequency in H, utilizing a cryogenic beam of H and directly demonstrate that quantum interference...

The double response of a large area avalanche photodiode, a planar RMD model S1315, to 6-keV x-rays was investigated as a function of APD biasing voltage and for different operating temperatures. Our data are consistent with the interpretation that the dissimilar APD response is due to x-ray interactions in the different APD-layer structures; inter...

Muonic atoms have been used to extract the most accurate nuclear charge radii based on the detection of X-rays from the muonic cascades. Most stable and a few unstable isotopes have been investigated with muonic atom spectroscopy techniques. A new research project recently started at the Paul Scherrer Institut aims to extend the highresolution muon...

Spatial hole burning prevents single-frequency operation of thin-disk lasers when the thin disk is used as a folding mirror. We present an evaluation of the saturation effects in the disk for disks acting as end-mirrors and as folding-mirrors explaining one of the main obstacles towards single-frequency operation. It is shown that a twisted-mode sc...

The present knowledge of Lamb shift, fine-, and hyperfine structure of the 2S and 2P states in muonic helium-3 ions is reviewed in anticipation of the results of a first measurement of several $\mathrm{2S\rightarrow2P}$ transition frequencies in the muonic helium-3 ion, $\mathrm{\mu^3He^+}$. This ion is the bound state of a single negative muon $\m...

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 wa...

How big is the proton? The discrepancy between the size of the proton extracted from the spectroscopy of muonic hydrogen and the value obtained by averaging previous results for “regular” hydrogen has puzzled physicists for the past 7 years. Now, Beyer et al. shed light on this puzzle (see the Perspective by Vassen). The authors obtained the size o...

High-precision measurements of the proton radius from laser spectroscopy of muonic hydrogen demonstrated up to six standard deviations smaller values than obtained from electron-proton scattering and hydrogen spectroscopy. The status of this discrepancy, which is known as the proton radius puzzle will be discussed in this paper, complemented with t...

High-precision measurements of the proton radius from laser spectroscopy of muonic hydrogen demonstrated up to six standard deviations smaller values than obtained from electron-proton scattering and hydrogen spectroscopy. The status of this discrepancy, which is known as the "proton radius puzzle" will be discussed in this paper, complemented with...

The present knowledge of Lamb shift, fine-, and hyperfine structure of the 2S and 2P states in muonic helium-3 ions is reviewed in anticipation of the results of a first measurement of several $\mathrm{2S\rightarrow2P}$ transition frequencies in the muonic helium-3 ion, $\mathrm{\mu^3He^+}$. This ion is the bound state of a single negative muon $\m...

We give a pedagogical description of the method to extract the charge radii and Rydberg constant from laser spectroscopy in regular hydrogen (H) and deuterium (D) atoms, that is part of the CODATA least-squares adjustment (LSA) of the fundamental physical constants. We give a deuteron charge radius rd from D spectroscopy alone of 2.1415(45) fm. Thi...

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 simplifie...

Seit einigen Jahren gibt es eine dramatische Diskrepanz bei der Bestimmung der Größe des Protons. Während Elektron-Proton-Streuung und Laserspektroskopie von atomarem Wasserstoff einen Ladungsradius von 0,88 fm liefern, ergab unsere Messung im exotischen myonischen Wasserstoff nur 0,84 fm – 7 Standardabweichungen kleiner als der Mittelwert aller bi...

Laser spectroscopy of muonic hydrogen atoms, μp, has revealed a proton root-mean-square (rms) charge radius rE that is an order of magnitude more accurate than the CODATA world average from elastic electron-proton scattering and precision spectroscopy of regular (electronic) hydrogen. Interestingly, though, the value of rE from μp is 4%, or 7 combi...

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 wa...

The deuteron is the simplest compound nucleus, composed of one proton and one neutron. Deuteron properties such as the root-mean-square charge radius rd and the polarizability serve as important benchmarks for understanding the nuclear forces and structure. Muonic deuterium μd is the exotic atom formed by a deuteron and a negative muon μ–. We measu...

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 consis...

We present an obstacle in power scaling of thin-disk lasers related with 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 o...

We present an active fiber-based retroreflector providing high quality phase-retracing anti-parallel Gaussian laser beams for precision spectroscopy of Doppler sensitive transitions. Our design is well-suited for a number of applications where implementing optical cavities is technically challenging and corner cubes fail to match the demanded requi...

We give a pedagogical description of the method to extract the charge radii and Rydberg constant from laser spectroscopy in regular hydrogen (H) and deuterium (D) atoms, that is part of the CODATA least-squares adjustment (LSA) of the fundamental physical constants. We give a deuteron charge radius Rd from D spectroscopy alone of 2.1415(45) fm. Thi...

We report the first laser spectroscopy of muonic deuterium. At the Paul Scherrer Institute, we have measured the frequency of the 2S-2P Lamb shift in muonic deuterium. As in the case of the muonic hydrogen, the observed lines are shifted from the theoretical predictions. Thanks to improved new QED and nuclear structure calculations, an accurate det...

We provide an up to date summary of the theory contributions to the 2S-2P Lamb shift and the fine structure of the 2P state in the muonic helium ion $(\mathrm{\mu^4He})^+$. This summary serves as the basis for the extraction of the alpha particle charge radius from the muonic helium Lamb shift measurements at the Paul Scherrer Institute, Switzerlan...

We identify a systematic present in two-photon direct frequency comb spectroscopy (DFCS) which is a result of chirped laser pulses and is a manifestation of the first-order Doppler effect. We carefully analyze this systematic and propose methods for its mitigation within the context of our measurement of the hydrogen 1S−3S transition. We also repor...

We investigate the quantum interference shifts between energetically close states, where the state structure is observed by laser spectroscopy. We report a compact and analytical expression that models the quantum interference induced shift for any admixture of circular polarization of the incident laser and angle of observation. An experimental sc...

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 mi...

Precision measurements of transition frequencies in atomic hydrogen provide important input for a number of fundamental applications, such as stringent tests of QED and the extraction of fundamental constants. Here we report on precision spectroscopy of the 2S–4P transition in atomic hydrogen with a reproducibility of a few parts in 10 12 . Utilizi...

In the context of the Lamb shift measurement in muonic helium we developed a thin-disk laser composed of a Q-switched oscillator and a multi-pass amplifier delivering pulses of 150 mJ at a pulse duration of 100 ns. Its peculiar requirements are stochastic trigger and short delay time (< 500 ns) between trigger and optical output. The concept of the...

We review the status of the proton charge radius puzzle. Emphasis is given to the various experiments initiated to resolve the conflict between the muonic hydrogen results and the results from scattering and regular hydrogen spectroscopy.

Quantum interference between energetically close states is theoretically investigated, with the state structure being observed via laser spectroscopy. In this work, we focus on hyperfine states of selected hydrogenic muonic isotopes, and on how quantum interference affects the measured Lamb shift. The process of photon excitation and subsequent pho...

A precision measurement of the 2S-4P transition in atomic hydrogen, when combined with the precisely known 1S-2S transition frequency\footnote{C. G. Parthey et al., PRL 107, 203001 (2011)}, can be used to determine the value of the r.m.s. proton charge radius r p . We report on our progress towards an absolute frequency measurement, using a cryogen...

Precision spectroscopy of atomic hydrogen has long been successfully used to provide stringent tests on fundamental theories and precisely determine physical constants. The current limit originates from the uncertainty in the value of the proton r.m.s. charge radius r p . Moreover, the value of r p extracted from laser spectroscopy of muonic hydrog...

The present knowledge of Lamb shift, fine- and hyperfine structure of the $\mathrm{2S}$ and $\mathrm{2P}$ states in muonic deuterium is reviewed in anticipation of the results of a first measurement of several $\mathrm{2S-2P}$ transition frequencies in muonic deuterium ({\mu}d). A term-by-term comparison of all available sources reveals reliable va...

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 photo absorption in the various APD 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 corr...

Laser spectroscopy of muonic atoms, where a nucleus is orbited by one negative muon, is a novel tool for tests of quantum electrodynamics and the Standard Model, determination of fundamental physical constants, and for nuclear physics.

Reach-through avalanche photodiodes (RT-APDs) from Hamamatsu Photonics, with different active areas, $5 times 5$ and $3 times 5$ mm$^2$, were investigated to evaluate their suitability for the muonic helium Lamb shift experiment. The gain has been determined as a function of voltage and temperature for both prototypes. As expected, it increases wit...

The recent measurement of the Lamb shift in muonic hydrogen resulted in a tenfold improved value of the rms charge radius of the proton. The value is, however, 7 standard deviations discrepant from the world average of this quantitiy which is obtained from elastic electron-proton scattering and precision spectroscopy of hydrogen and deuterium. New...

A multipass laser cavity is presented which can be used to illuminate an elongated volume from a transverse direction. The illuminated volume can also have a very large transverse cross section. Convenient access to the illuminated volume is granted. The multipass cavity is very robust against misalignment, and no active stabilization is needed. Th...