Microwave Optomechanics with a Carbon Nanotube Quantum Dot

This thesis deals with the implementation and demonstration of an optomechanical system that is composed of a superconducting microwave resonator and a suspended carbon nanotube (CNT). This is of particular interest, as CNTS - being macromolecules - have outstanding electronic and mechanical properties. Single electron effects combined with large mechanical resonance frequencies, quality factors, and zero-point motion amplitudes make possible promising applications in the field of quantum information processing or fundamental research, e.g. the synthesis of arbitrary quantum states. Besides the assembly of a high frequency measurement setup for cryogenic temperatures in the millikelvin range, introductory chapters discuss electronic and mechanical characteristics of carbon nanotubes. Here, two different fabrication techniques are described, the overgrowth and the fork transfer process. The physics of superconducting microwave resonators in coplanar waveguide geometry is introduced. Their high frequency behaviour at low temperatures is described by a transition from Mattis-Bardeen to two-level system theory. This serves as a means to investigate the high frequency material properties of a molybdenum/rhenium alloy, which is particularly suitable for the overgrowth process. Device design adjustments and considerations are described that were necessary for the integration of CNTs into hybrid geometries using the fork transfer process. Through this, the (previously demonstrated) electronic coupling of a carbon nanotube to a microwave resonator could be successfully experimentally demonstrated. There, the transmission of the resonator is sensitive to single electron tunneling processes in the CNT. The central point of this thesis is the introduction to the field of dispersive optomechanics. Here, the interaction of a vibrating carbon nanotube and a microwave field is investigated. A mechanism based on the quantum capacitance enhances this otherwise negligible coupling by orders of magnitude. Through an optomechanically induced transparency experiment, this coupling was experimentally quantified. A comparison to the beforehand deduced theory shows a very good agreement. In conclusion, subsequent prospective experiments towards optomechanical cooling and motion manipulation are explained and preliminary experimental data are discussed