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We report on the design and performance of a cryogenic (300 mK) near-fieldscanning microwave microscope. It uses a microwave resonator as the near-fieldsensor, operating at a frequency of 6 GHz and microwave probing amplitudes downto 100 uV, approaching low enough photon population (N~1000) of the resonatorsuch that coherent quantum manipulation becomes feasible. The resonator is madeout of a miniaturized distributed fractal superconducting circuit that isintegrated with the probing tip, micromachined to be compact enough such thatit can be mounted directly on a quartz tuning-fork, and used for paralleloperation as an atomic force microscope (AFM). The resonator is magneticallycoupled to a transmission line for readout, and to achieve enhanced sensitivitywe employ a Pound-Drever-Hall measurement scheme to lock to the resonancefrequency. We achieve a well localized near-field around the tip such that themicrowave resolution is comparable to the AFM resolution, and a capacitivesensitivity down to 6.4x10^-20 F/rtHz, limited by mechanical noise. We believethat the results presented here are a significant step towards probing quantumsystems at the nanoscale using near-field scanning microwave microscopy.

A near-field scanning microwave microscope based on a superconducting resonator for low power measurements