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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 by an inelastic collision with a H$_2$ molecule. The resulting increase of kinetic energy after this cycle modifies the $\mu$p atom diffusion in the hydrogen gas and the arrival time of the $\mu$p atoms at the target walls. This laser-induced modification of the arrival times is used to expose the atomic transition. In this paper we present the simulation of the $\mu$p diffusion in the H$_2$ gas which is at the core of the experimental scheme. These simulations have been implemented with the Geant4 framework by introducing various low-energy processes including the motion of the H$_2$ molecules, i.e. the effects related with the hydrogen target temperature. The simulations have been used to optimize the hydrogen target parameters (pressure, temperatures and thickness) and to estimate signal and background rates. These rates allow to estimate the maximum time needed to find the resonance and the statistical accuracy of the spectroscopy experiment., Comment: Submission to SciPost

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 undergoes a laser excitation from the singlet hyperfine state to the triplet hyperfine state, {then} 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 $\mu$p 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 decoherence effects caused by {the laser bandwidth and }collisions would overestimate the transition probability by more than a factor of two in the experimental conditions. Moreover, we also account for Doppler effects and provide the matrix element, the saturation fluence, the elastic and inelastic collision rates for the singlet and triplet states, and the resonance linewidth. This calculation thus quantifies one of the key unknowns of the HFS experiment, leading to a precise definition of the requirements for the laser system and to an optimization of the hydrogen gas target where $\mu$p is formed and the laser spectroscopy will occur., Comment: 21 pages, 4 figures

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 reflections on the active medium and delivers a small signal gain of 30 with M$^2$ = 1.16. Its novel geometry combining Fourier transform propagations with 4f-imaging stages as well as a compact array of adjustable mirrors allows for a layout with a footprint of 400 mm x 1000 mm., Comment: 7 pages, 6 figures

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$\,$-$\,$2P Lamb shift. Here, we review recent results of nuclear charge radii extracted from muonic hydrogen and helium spectroscopy and present experiment proposals to access light muonic atoms with $Z \geq 3$. In addition, our approaches towards a precise measurement of the Zemach radii in muonic hydrogen ($\mu$p) and helium ($\mu$$^{3}$He$^{+}$) are discussed. These results will provide new tests of bound-state quantum-electrodynamics in hydrogen-like systems and can be used as benchmarks for nuclear structure theories., Comment: 17 pages, 8 figures

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 new insights obtained from spectroscopy of muonic deuterium., Comment: Moriond 2017 conference, 8 pages, 4 figures

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., Comment: 11 pages, 8 figures

Novel thin-disk laser pump layouts are proposed yielding an increased number of passes for a given pump module size and pump source quality. These novel layouts result from a general scheme which bases on merging two simpler pump optics arrangements. Some peculiar examples can be realized by adapting standard commercially available pump optics simply by intro ducing an additional mirror-pair. More pump passes yield better efficiency, opening the way for usage of active materials with low absorption. In a standard multi-pass pump design, scaling of the number of beam passes brings ab out an increase of the overall size of the optical arrangement or an increase of the pump source quality requirements. Such increases are minimized in our scheme, making them eligible for industrial applications, Comment: 16 pages, 9 figures

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 thin-disk laser allows for energy and power scaling with high efficiency. However the single pass gain is small (about 1.2). Hence a multi-pass scheme with precise mode matching for large beam waists (w = 2 mm) is required. Instead of using the standard 4f design, we have developed a multi-pass amplifier with a beam propagation insensitive to thermal lens effects and misalignments. The beam propagation is equivalent to multiple roundtrips in an optically stable resonator. To support the propagation we used an array of 2 x 8 individually adjustable plane mirrors. Astigmatism has been minimized by a compact mirror placement. Precise alignment of the kinematic array was realized using our own mirror mount design. A small signal gain of 5 for 8 passes at a pump power of 400 W was reached. The laser was running for more than 3 months without the need of realignment. Pointing stability studies is also reported here., Comment: 11 pages, 14 figures

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., Comment: 9 pages, Few Body Systems FB21 conference