Amplification of gravitational motion via Quantum weak measurement

TL;DR

This paper proposes using quantum weak measurement with cold atoms to amplify gravitational signals, potentially enabling more precise measurement of the gravitational constant G and revealing that gravity can exhibit repulsive behavior under certain quantum conditions.

Contribution

It introduces a novel experimental setup employing weak measurement to amplify gravitational effects in cold atom systems for measuring G.

Findings

Achieves approximately 10^3 amplification of relative motion

Potential to measure G with higher precision using this method

Suggests gravity can act as a repulsive force due to weak measurement effects

Abstract

We investigate a new experimental possibility of measuring the Newtonian gravitational constant $G$ by using the weak measurement. Amplification via weak measurement is one of the interesting phenomena of quantum mechanics. In this letter, we consider it in a system consisting of many cold atoms which are gravitationally interacting with an external macroscopic source and show that it is possible to obtain ${\mathcal{O}}(10^{3})$ amplification of their relative motion compared with the classical motion when the number of atoms are ${\mathcal{O}}(10^{15})$ and the observing time is $\sim 0.5$s. This result suggests that it might be possible to use this system as a new experimental set up for determining $G$. Besides, our study indicates that the gravitational force can behave as a repulsive force because of the weak measurement.