Proposal for measuring Newtonian constant of gravitation at an exceptional point in an optomechanical system

TL;DR

This paper proposes a quantum optomechanical method to measure the Newtonian gravitational constant G using a system operating at an exceptional point, which enhances measurement sensitivity.

Contribution

It introduces a novel EP-assisted optomechanical setup for precise measurement of G, leveraging eigenfrequency shifts at exceptional points.

Findings

Operating at EP amplifies eigenfrequency shifts due to gravity.

Derived the relationship between EP-induced shifts and G.

Demonstrated potential for enhanced precision in G measurement.

Abstract

We develop a quantum mechanical method of measuring the Newtonian constant of gravitation, G. In this method, an optomechanical system consisting of two cavities and two membrane resonators is used. The added source mass would induce the shifts of the eigenfrequencies of the supermodes. Via detecting the shifts, we can perform our measurement of G. Furthermore, our system can features exceptional point (EP) which are branch point singularities of the spectrum and eigenfunctions. In the paper, we demonstrate that operating the system at EP can enhance our measurement of G. In addition, we derive the relationship between EP enlarged eigenfrequency shift and the Newtonian constant. This work provides a way to engineer EP-assisted optomechanical devices for applications in the field of precision measurement of G