Membrane-based scanning force microscopy and strong parametric coupling*

We report the development of a scanning force microscope based on an ultrasensitive silicon nitride membrane optomechanical transducer and strong parametric coupling of the membrane modes. Our development is made possible by inverting the standard microscope geometry—in our instrument, the substrate is vibrating and the scanning tip is at rest. We present topography images of samples placed on the membrane surface. Our measurements demonstrate that the membrane retains an excellent force sensitivity when loaded with samples and in the presence of a scanning tip. The flexible parametric coupling method can potentially be useful for rapid state control and transfer between modes, and is an important step towards parametric spin sensing experiments with membrane resonators. We discuss the prospects and limitations of our instrument as a quantum-limited force sensor and imaging tool.