Split-Post Microwave Displacement Transducer with Quadratic Readout

TL;DR

This paper explores a microwave cavity-based displacement sensor with a split-post geometry, demonstrating controllable quadratic and linear responses for potential quantum sensing applications.

Contribution

It introduces a split-post microwave cavity design that enables tunable quadratic and linear displacement readout, advancing quantum transducer development.

Findings

Maximum displacement-to-voltage sensitivity at the centre position.

Transition from quadratic to linear response as membrane moves away from centre.

Significant difference in quadratic and linear coefficients depending on membrane position.

Abstract

We investigate a microwave cavity-based displacement readout employing a split-post geometry for measuring the motion of a dielectric membrane. The cavity response to membrane displacement is predominantly quadratic when the membrane is positioned at the centre of the posts. We characterise this behaviour by driving the membrane piezo electrically at both central and off-centre positions and calibrating the displacement using an independent interferometric measurement. The calibration reveals a linear coupling between the membrane displacement and the applied drive voltage, while the microwave response follows the static displacement dependence. When the membrane is driven at the centre, the system exhibits the highest displacement-to-voltage sensitivity and the largest quadratic output. As the membrane is moved away from the centre, the response gradually transitions from quadratic to linear. There is a difference of ~ 97 $\%$ in the quadratic coefficient from the central position and a difference of ~ 92 $\%$ in the linear coefficient from the off-centre position. This controllable crossover between quadratic and linear coupling is a key requirement for sensors capable of resolving energy quantisation. It establishes this platform as a promising candidate for a microwave-mechanical quantum transducer.