We report on the design and performance of a cryogenic (300 mK) near-field scanning microwave microscope. It uses a microwave resonator as the near-field sensor, operating at a frequency of 6 GHz and microwave probing amplitudes down to 100 μV, approaching low enough photon population (N ∼ 1000) of the resonator such that coherent quantum manipulation becomes feasible. The resonator is made out of a miniaturized distributed fractal superconducting circuit that is integrated with the probing tip, micromachined to be compact enough such that it can be mounted directly on a quartz tuning-fork, and used for parallel operation as an atomic force microscope (AFM). The resonator is magnetically coupled to a transmission line for readout, and to achieve enhanced sensitivity we employ a Pound-Drever-Hall measurement scheme to lock to the resonance frequency. We achieve a well localized near-field around the tip such that the microwave resolution is comparable to the AFM resolution, and a capacitive sensitivity down to 6.4 × 10(-20) F/Hz, limited by mechanical noise. We believe that the results presented here are a significant step towards probing quantum systems at the nanoscale using near-field scanning microwave microscopy.
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