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This thesis was written in the context of the HyperMu experiment being performed at the Paul Scherrer Institut (PSI), Switzerland, aiming at laser spectroscopy of muonic hydrogen (μp), the hydrogen-like bound state of a negative muon and a proton. The goal of the experiment is to measure the ground-state hyperfine splitting (HFS) of μp at a relative precision of 1 parts-per-million (ppm). Since the muon is ~200 times heavier than the electron, it orbits the proton much closer than the electron of a regular hydrogen atom. This makes μp an exquisite system to investigate the proton structure. In particular, the HFS is sensitive to the two-photon exchange contribution that can be related to the polarized structure functions of the proton and the Zemach radius, which depends on the electric and magnetic form factors of the proton. The precise result of the HyperMu measurement, will thus serve as a benchmark for future precision calculations of the proton structure. The experiment is based on the measurement of the \left(1S,\,F=0\right)\rightarrow\left(1S,\,F=1\right) transition in μp using a pulsed, tuneable laser, at a wavelength around 6.8 μm. Negative, low momentum muons, arriving at a rate of ca. 500\,\text{s}^{-1}, are stopped in a short (~1 mm), \text{H}_{2} gas-target at cryogenic temperature (~22 K), where they form μp in a highly excited state. After de-exciting to the ground state \left(1S,\,F=0\right) and thermalizing in 1 μs to the \text{H}_{2} gas temperature, a laser pulse illuminates the μp atom. If the laser is on resonance, the μp atom is excited to the \left(1S,\,F=1\right). A subsequent inelastic collision with an \text{H}_{2} molecule from the surrounding gas, de-excites the μp atom back to F=0. In this process the μp atom gains kinetic energy. This makes the μp atom quickly diffuse to the gold coated target wall, where the muon is transferred from the proton to a gold atom, forming μAu in an excited state. The subsequent de-excitation of μAu that results in the emission of several MeV X-rays heralds a successful laser excitation of the hyperfine transition. The resonance is obtained by scanning the laser frequency and counting the number of X-rays versus laser frequency. The laser system for the HyperMu experiment is based on the creation of high energy pulses in the near IR which are converted to the target wavelength of 6.8 μm in the mid IR, by a series of non-linear frequency conversion stages. The near-IR pulses are created by a single-frequency thin-disk oscillator/amplifier system running at 1030 nm wavelength. The pulses are split into two independent branches where optical parametric oscillators and amplifiers create ~2 μm and ~3 μm radiation, respectively. A single-pass difference frequency generation stage is then used to obtain the radiation at 6.8 μm with a bandwidth 300 mJ) needed because of the small hyperfine transition matrix-element, and single-frequency operation at bandwidth |
