Amplification of gravitational motion via quantum weak measurement. (28th April 2019) - Kawana, Kiyoharu; Ueda, Daiki
Abstract: We investigate a new experimental possibility of measuring the Newtonian gravitational constant $G$ by using weak measurement. Amplification via weak measurement is an interesting phenomenon of quantum mechanics. In this letter, we consider it in a system consisting of many cold atoms that are gravitationally interacting with an external macroscopic source and show that it is possible to obtain ${\cal{O}}(10^{3})$ amplification of their relative motion compared with the classical motion when the number of atoms is ${\cal{O}}(10^{15})$ 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 setup for determining $G$ . In addition, our study indicates that the gravitational force can behave as a repulsive force because of the weak measurement.