This thesis focuses on the advances and challenges in coupling electromagnetic fields in the microwave and optical domain to soft-clamped membrane mechanical resonators, a promising component in emerging quantum technologies.

Soft-clamped membranes exhibit exceptionally low mechanical damping due to their isolated mechanical modes from their substrate, enabling ground-state cooling and an extraordinary 140 ms coherence time. However, certain limitations must be addressed for their effective implementation in quantum systems.

In electro-mechanical coupling, the coupling strength is constrained by nanofabrication techniques. Microwave resonators and mechanical resonators have to be brought very close to each other for electro-mechanical coupling. We have demonstrated how integrating a piezo actuator might significantly enhance this coupling.

Opto-mechanical coupling presents its own challenges: operating a highfinesse cavity in a dilution refrigerator, optical losses due to the membrane resonator design, and optical absorption heating of the membrane material.

For the first issue, we have devised a new design of a high-finesse cavity that enables operation at milliKelvin temperatures. To tackle optical losses of the membrane design, we have characterized them and derived and implemented design considerations that can minimize these losses. We built a low optical loss, high-finesse cavity with a refined membrane design for the absorption heating effect. We then characterized how optical absorption heating influences the thermal bath temperature and the intrinsic mechanical decay rate.

Our findings offer comprehensive solutions that significantly enhance softclamped membrane resonators’ electro- and optomechanical coupling. This