Generation and application of squeezed states of light in higher-order spatial laser modes

The next generation of gravitational-wave detectors (GWD), formed by the Einstein Telescope (ET) and Cosmic Explorer (CE), aims for improving the currently achieved sensitivities by one order of magnitude which requires significant progress in the overall noise reduction. In this regard, one discussed option for a thermal noise mitigation beyond the current ET and CE baselines is the replacement of the fundamental Gaussian TEM00 laser mode by a higher-order spatial mode. To justify this approach it is crucial to investigate whether these modes comply with the targets for all other noise sources. In this thesis, this question is investigated with respect to the quantum noise and its reduction via squeezed states of light. Cavity-enhanced second harmonic generation (SHG) is the first nonlinear process in every GWD squeezed light source. Based on the initial ET design study, the performance of the Laguerre-Gaussian LG33 mode in this process was analysed first. A numerical model for the LG33 SHG was developed and showed a good agreement with a corresponding experiment where a conversion efficiency of 45% could be achieved. However, astigmatism strongly limited the conversion efficiency as well as the output mode purity and the focus then switched to Hermite-Gaussian (HG) modes which are less sensitive in this respect. The theory on the generation of squeezed states in a type-I optical parametric amplifier was applied to higher-order HG modes, yielding that a TEM00 SHG in combination with a subsequent spatial light modulator can generate an efficient pump field in a single higher-order mode. Based on these findings, bright squeezed states at a wavelength of 1064nm in the TEM00, HG11, HG22 and HG33 mode were generated and characterised via a balanced homodyne detector in the measurement frequency range of 1MHz to 20MHz. The achieved benchmark of a quantum noise reduction of 10dB in the HG11 mode is a substantial improvement compared to previously published results. 7.5dB and 4.5dB in the HG22 and HG33 mode, respectively, were primarily limited by the available pump power. Finally, the shot-noise limited sensitivity of a tabletop Michelson interferometer with balanced homodyne detection, which is the planned readout-scheme topology for future GW detectors, was improved via the generated squeezed states in the frequency range of 1MHz to 20MHz. In this thesis, the first successful 10dB quantum noise reduction in a Michelson interferometer could be demonstrated with the TEM00 mode at 5MHz. Moreover, comparable levels of quantum noise reduction, unprecedented for any measurement application, could be achieved for the HG11 and HG22 operation at 4MHz: 8.8dB and 7.5dB, respectively. These results were mainly limited by optical loss in the squeezed light injection stage including a Faraday rotator whose aperture caused additional clipping loss for the higher-order modes. At frequencies below 4MHz, technical laser noise was the main limitation. These findings are a highly promising step in the feasibility demonstration for an improved thermal noise reduction in gravitational-wave detectors via higher-order spatial modes