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Hyperfine splittings in muonic atoms and laser technology

Periodic Reporting for period 3 - HyperMu (Hyperfine splittings in muonic atoms and laser technology)

Reporting period: 2020-10-01 to 2022-03-31

Highly accurate measurements of atomic transitions can be used as precise probes of low-energy properties of the nuclei. As the Bohr radius of hydrogen-like atoms decreases with increasing orbiting particle mass, muonic hydrogen, a hydrogen-like atom formed by a negative muon and a proton, has enhanced sensitivity to the proton structure. The objective of this project is to measure, for the first time, the ground-state hyperfine splitting (HFS) in muonic hydrogen (μp) with 1 ppm relative accuracy. From this measurement information about the magnetic structure of the proton can be extracted.
More precisely, by comparing the measured HFS transition frequency with the corresponding theoretical prediction based on bound-state QED calculations, the Two-Photon-Exchange (TPE) contribution can be extracted with 200 ppm relative accuracy. The extracted TPE contribution can be compared to predictions from chiral perturbation theory (chPT) or from data-driven (proton structure functions and form factors) dispersion relations. Because the TPE contribution can be expressed as the sum of a finite-size part proportional to the Zemach radius and a polarizability part, its determination can be used to extract the two parts: the Zemach radius can be extracted when the polarizability contribution is assumed from theory and the polarizability contribution can be extracted when taking the Zemach radius from e-p scattering or H laser spectroscopy. The Zemach radius extracted from μp can be compared with the determinations from electron-proton scattering and H spectroscopy to expose a possible violation of lepton flavor and will serve as a benchmark for modelling the proton, for constraining the scattering data and for lattice QCD calculations. The polarizability contribution will be a benchmark for chiral perturbation theory and dispersion-based predictions.

Our experimental method follows this sequence: Low energy muons (μ−) are stopped in a cryogenic H2 gas of 1 mm length and 1 bar pressure forming μp. An on-resonance laser pulse at a wavelength of 6.8 μm excites the muonic hyperfine transition from the singlet to the triplet hyperfine sublevels. The subsequent collisionally-induced quenching from the triplet back to the singlet state imparts an average kinetic energy of 0.1 eV to the μp atom, so that it can quickly diffuse in the hydrogen gas reaching efficiently (before muon decay) one of the target walls coated with gold. At the target wall the muon is transferred from μp to a gold atom forming muonic gold in an excited state (μAu∗) that de-exciting (atomic cascade) emits X-rays. The resonance curve is retrieved by plotting the number of cascade signals measured in the surrounding scintillators shortly after the laser excitation versus the laser frequency.

This experiment at the intersection between particle, atomic and nuclear physics requires the development of cutting-edge laser technologies especially in the thin-disk laser and the mid-infrared laser domains. The mid infrared source needed for this experiment is realized starting from a single-frequency thin-disk laser operating in the 500 mJ regime and down-converting its pulses in a cascade of nonlinear processes to produce single-frequency pulses of 5 mJ energy tunable around a wavelength of 6.8 μm with a bandwidth < 100 MHz within 1 μs after a laser trigger.
In the last decades, thin-disk lasers have become workhorses in the high-power industrial laser sector, while the field of mid-infrared laser sources has a number of applications including spectroscopy, remote sensing and numerous bio-medical applications, such as surgery. In this project, we focus on energy-scaling of these lasers and operating them in single-frequency and fundamental transverse mode. There is an excellent potential for technology transfer.
We have addressed various developments needed for the measurement of the hyperfine splitting (HFS) in μp:

1. Laser-induced excitation probability: We computed the laser-induced excitation probability by integrating numerically the Optical Bloch Equation including collisional effects, Doppler broadening, laser bandwidth and a simplified treatment of the cavity.

2. μp diffusion: The μp thermalisation, de-excitation after laser excitation, and diffusion in the hydrogen gas were simulated using a Monte Carlo code and various μp-H2 cross sections to optimise the target (pressure, temperature, length) minimising background and maximising the probability that a laser- excited μp atom is reaching the target walls.

3. Muon beam: We have measured muon rates and electron contaminations at low momentum using three different beamlines. We found muon rates fulfilling our requirements but some improvements are needed to suppress the electron contamination. We also measured the probability that a muon is stopping in our 1 mm long hydrogen gas target.

4. Detection system: We simulated, developed and qualified in a beamtime using muons a prototype detection system (including DAQ) that fulfils our requirements: we measured 75% detection efficiency for μAu cascade events and suppression of the false identification of the decay-electrons to the few % level.

5. Background studies: We quantified using simulations and measurements the various background sources: (a) related to the diffusion of non-laser excited μp atoms to the target walls; (b) related to Bremsstrahlung produced by electrons from “regular” muon decays; (c) originating from energy depositions in the X-ray detectors uncorrelated with the muons (natural radioactivity, beam electrons etc).

6. Design of the laser system: We finalised the design of the complex laser system for the μp measurement that has to deliver pulses of at least 5 mJ energy tunable around a wavelength of 6.8 μm with a bandwidth < 100 MHz, having a good transverse profile and a short delay (< 1 μs) upon stochastic trigger. The laser system consists of a single-frequency high-energy thin-disk laser in oscillator - multipass amplifier configuration at 1030 nm, followed by a complex nonlinear down-conversion based on a cascade of optical parametric oscillators (OPOs) and optical parametric amplifiers (OPAs). The pulses at 6.8 μm delivered by this down-conversion process are eventually injected into a multi- pass cavity placed inside the cryogenic hydrogen target to enhance the laser fluence in the μp region. The frequency control of the laser system is obtained by performing injection seeding of the thin-disk oscillator and of two OPOs using three cw seed lasers.

7. Thin-disk laser: We have realized a thin-disk laser oscillator with a Q-switched control, a Pound- Drewer-Hall locking scheme for injection seeding and another loop to stabilize the circulating intensity prior to trigger. Presently we are optimising these control loops. We are also developing a thin-disk multipass amplifier based on a hybrid propagation scheme of Fourier transforms and 4f-imaging sustaining a large number of passes in a compact layout. The amplifier has shown a small-signal gain of 30 for 20 passes. Improvement of the active medium by mitigating amplified spontaneous emission effects are ongoing.

8. OPO lasers: We designed two OPO prototypes apt for injection seeding and featuring a tunable out-coupling.

9. Optical multipass cavity: We have designed and simulated several multipass cavities to enhance the laser fluence in the μp region. Production of various cavity prototypes is ongoing including the development of a dedicated process for coating dielectric layers on “internally-oriented” surfaces withstanding cryogenic temperatures.
Until the end of the project we expect to conclude the development of the experimental setup needed for the measurement of the hyperfine splitting in muonic hydrogen. This includes the complex laser system, the multipass optical cavity, the detection system, the target region, the cryogenic system, the data acquisition system and the muon beamline. Several technological innovations are needed to meet the challenging requirements related to the spectroscopy of this weak transition in muonic hydrogen, especially in the domain of thin-disk and mid infrared lasers. Eventually, in the last part of the project, we will search for the muonic resonance.