Bringing near-field scanning microwave microscopy into the quantum regime

Near-field scanning microwave microscopy (NSMM) is a widely used scanning probe microscopy (SPM) technique. It can non-intrusively probe the material properties of a sample at the nano-scale using microwave frequency radiation. The rapid development of nanotechnology, materials and surface science underpinned by scanning probe techniques drives the demand for ever more versatile and non-invasive nano-scale analysis tools. Specifically, the development of solid-state quantum technologies has created a need for nano-scale measurement techniques that operate in the same regime as these quantum devices. However, there are very few nano-scale characterisation tools that are capable of quantum coherent interaction with samples. In particular, all NSMMs so far operate in the 'classical' regime, at high powers. To reach the quantum limit for NSMM we require (i) temperatures that are lower than the photon energy, kbT << hω and (ii) ultra-low power such that the average photon number (n) ~ 1, as is necessary for coherent interaction with a quantum system without saturating it. This work presents an ultra-low power cryogenic NSMM integrated with an atomic force microscope (AFM), to enable precise distance control. A high-quality 6 GHz superconducting resonator is used as the microwave probe. This resonator is micro-machined so that it also forms the scanning tip of the AFM. We show that the microscope is capable of obtaining nano-scale dielectric contrast down to the single microwave photon regime, up to 109 times lower power than in typical NSMMs. The microscope was designed in-house in a dilution refrigerator operating at 10 mK with a customised suspension system to minimise the effects of external mechanical vibrations. In this thesis, we evaluate the performance of this NSMM. We also discuss the remaining challenges towards developing an NSMM capable of quantum coherent interaction, an enabling tool for the development of quantum technologies in the microwave regime.