Measuring the α-particle charge radius with muonic helium-4 ions.

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 by the nuclear structure are vastly magnified in hydrogen-like systems formed by a negative muon and a nucleus, so spectroscopy of these muonic ions can be used to investigate the nuclear structure with high precision. Here we present the measurement of two 2S-2P transitions in the muonic helium-4 ion that yields a precise determination of the root-mean-square charge radius of the α particle of 1.67824(83) femtometres. This determination from atomic spectroscopy is in excellent agreement with the value from electron scattering1, but a factor of 4.8 more precise, providing a benchmark for few-nucleon theories, lattice quantum chromodynamics and electron scattering. This agreement also constrains several beyond-standard-model theories proposed to explain the proton-radius puzzle2-5, in line with recent determinations of the proton charge radius6-9, and establishes spectroscopy of light muonic atoms and ions as a precise tool for studies of nuclear properties.

Compact 20-pass thin-disk multipass amplifier stable against thermal lensing effects and delivering 330 mJ pulses with M2 < 1.17.

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 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.

Injection-seeded high-power Yb:YAG thin-disk laser stabilized by the Pound-Drever-Hall method.

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.

Improved active fiber-based retroreflector with intensity stabilization and a polarization monitor for the near UV: erratum.

In Sec. 6 (polarization monitor) of our recent publication [Opt. Express29(5), 7024 (2021)10.1364/OE.417455], we assumed a small value of δ. This is however incorrect. The correct approximation for small ß leads to the updated Eqs. (10)-(11), resulting in a corrected Fig. 12.

Improved active fiber-based retroreflector with intensity stabilization and a polarization monitor for the near UV.

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 defined laser polarization are important. We demonstrate how weak aberrations produced by the fiber collimator may remain unobserved in the intensity of the collimated beam but limit the performance of the AFR. Our general results on characterizing these aberrations with a caustic measurement can be applied to any system where a collimated high-quality laser beam is required. Extending the collimator design process by wave optics propagation tools, we achieved a four-lens collimator for the wavelength range 380-486 nm with the beam quality factor of M2 ≃ 1.02, limited only by the not exactly Gaussian beam profile from the single-mode fiber. Furthermore, we implemented precise fiber-collimator alignment and improved the collimation control by combining a precision motor with a piezo actuator. Moreover, we stabilized the intensity of the wavefront-retracing beams and added in-situ monitoring of polarization from polarimetry of the retroreflected light.

Passive alignment stability and auto-alignment of multipass amplifiers based on Fourier transforms.

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.

Multipass amplifiers with self-compensation of the thermal lens.

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 4f-based amplifiers. We found that the proposed multipass 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 the 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).

The size of the proton.

The proton is the primary building block of the visible Universe, but many of its properties-such as its charge radius and its anomalous magnetic moment-are not well understood. The root-mean-square charge radius, r(p), has been determined with an accuracy of 2 per cent (at best) by electron-proton scattering experiments. The present most accurate value of r(p) (with an uncertainty of 1 per cent) is given by the CODATA compilation of physical constants. This value is based mainly on precision spectroscopy of atomic hydrogen and calculations of bound-state quantum electrodynamics (QED; refs 8, 9). The accuracy of r(p) as deduced from electron-proton scattering limits the testing of bound-state QED in atomic hydrogen as well as the determination of the Rydberg constant (currently the most accurately measured fundamental physical constant). An attractive means to improve the accuracy in the measurement of r(p) is provided by muonic hydrogen (a proton orbited by a negative muon); its much smaller Bohr radius compared to ordinary atomic hydrogen causes enhancement of effects related to the finite size of the proton. In particular, the Lamb shift (the energy difference between the 2S(1/2) and 2P(1/2) states) is affected by as much as 2 per cent. Here we use pulsed laser spectroscopy to measure a muonic Lamb shift of 49,881.88(76) GHz. On the basis of present calculations of fine and hyperfine splittings and QED terms, we find r(p) = 0.84184(67) fm, which differs by 5.0 standard deviations from the CODATA value of 0.8768(69) fm. Our result implies that either the Rydberg constant has to be shifted by -110 kHz/c (4.9 standard deviations), or the calculations of the QED effects in atomic hydrogen or muonic hydrogen atoms are insufficient.

Thin-disk laser scaling limit due to thermal lens induced misalignment instability.

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.

Thin-disk laser pump schemes for large number of passes and moderate pump source quality.

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.

Multipass laser cavity for efficient transverse illumination of an elongated volume.

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. The scheme is suitable for example in beam experiments, where the beam path must not be blocked by a laser mirror, or if the illuminated volume must be very large. This cavity was used for the muonic-hydrogen experiment in which 6 µm laser light illuminated a volume of 7 × 25 × 176 mm3, using mirrors that are only 12 mm in height. We present our measurement of the intensity distribution inside the multipass cavity and show that this is in good agreement with our simulation.

Pound-Drever-Hall locking scheme free from Trojan operating points.

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.

Improved measurement of the hydrogen 1S-2S transition frequency.

We have measured the 1S-2S transition frequency in atomic hydrogen via two-photon spectroscopy on a 5.8 K atomic beam. We obtain f(1S-2S) = 2,466,061,413,187,035 (10)  Hz for the hyperfine centroid, in agreement with, but 3.3 times better than the previous result [M. Fischer et al., Phys. Rev. Lett. 92, 230802 (2004)]. The improvement to a fractional frequency uncertainty of 4.2 × 10(-15) arises mainly from an improved stability of the spectroscopy laser, and a better determination of the main systematic uncertainties, namely, the second order Doppler and ac and dc Stark shifts. The probe laser frequency was phase coherently linked to the mobile cesium fountain clock FOM via a frequency comb.

Precision measurement of the hydrogen-deuterium 1S-2S isotope shift.

Measuring the hydrogen-deuterium isotope shift via two-photon spectroscopy of the 1S-2S transition, we obtain 670,994,334,606(15) Hz. This is a 10-times improvement over the previous best measurement [A. Huber, Phys. Rev. Lett. 80, 468 (1998)] confirming its frequency value. A calculation of the difference of the mean square charge radii of deuterium and hydrogen results in d - p =3.82007(65) fm2, a more than twofold improvement compared to the former value.

Two-photon frequency comb spectroscopy of atomic hydrogen.

We have performed two-photon ultraviolet direct frequency comb spectroscopy on the 1S-3S transition in atomic hydrogen to illuminate the so-called proton radius puzzle and to demonstrate the potential of this method. The proton radius puzzle is a significant discrepancy between data obtained with muonic hydrogen and regular atomic hydrogen that could not be explained within the framework of quantum electrodynamics. By combining our result [f 1S-3S = 2,922,743,278,665.79(72) kilohertz] with a previous measurement of the 1S-2S transition frequency, we obtained new values for the Rydberg constant [R ∞ = 10,973,731.568226(38) per meter] and the proton charge radius [r p = 0.8482(38) femtometers]. This result favors the muonic value over the world-average data as presented by the most recent published CODATA 2014 adjustment.

The Rydberg constant and proton size from atomic hydrogen.

At the core of the "proton radius puzzle" is a four-standard deviation discrepancy between the proton root-mean-square charge radii (rp) determined from the regular hydrogen (H) and the muonic hydrogen (µp) atoms. Using a cryogenic beam of H atoms, we measured the 2S-4P transition frequency in H, yielding the values of the Rydberg constant R∞ = 10973731.568076(96) per meterand rp = 0.8335(95) femtometer. Our rp value is 3.3 combined standard deviations smaller than the previous H world data, but in good agreement with the µp value. We motivate an asymmetric fit function, which eliminates line shifts from quantum interference of neighboring atomic resonances.

Laser spectroscopy of muonic deuterium.

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 measured three 2S-2P transitions in µd and obtain r(d) = 2.12562(78) fm, which is 2.7 times more accurate but 7.5σ smaller than the CODATA-2010 value r(d) = 2.1424(21) fm. The µd value is also 3.5σ smaller than the r(d) value from electronic deuterium spectroscopy. The smaller r(d), when combined with the electronic isotope shift, yields a "small" proton radius r(p), similar to the one from muonic hydrogen, amplifying the proton radius puzzle.