Quantum-based Mechanical Force Realization in Pico-Newton Range

We propose mechanical force realization based on flux quantization in the pico-Newton range. By controlling the number of flux quantum in a superconducting annulus, a force can be created as integer multiples of a constant step. For a 50 nm-thick Nb annulus with the inner and outer radii of 5 $\mu$m and 10 $\mu$m, respectively, and the field gradient of 10 T/m the force step is estimated to be 184 fN. The stability against thermal fluctuations is also addressed.