Zeptometer displacement sensing using a superconducting nonlinear interferometer

We propose a design for a superconducting nonlinear interferometer operating at microwave frequencies which allows the measurement of the optical nonlinearity \eta, with a precision which scales better than the Heisenberg-like limit as \delta \eta similar to R^{-3/2}, with R the quantification of resources. By designing the nonlinear optical element to possess physically moving parts we are able to use the superconducting nonlinear interferometer to measure the physical displacement r, of the moving parts to a spatial precision of \delta (rt) on the order of 10^{-21}m/Hz