Controllable quantum walks, gravitational constant, and Casimir energy in one-dimensional three-boson systems with on-site interactions

Abstract

This study scrutinizes one-dimensional three-boson systems with on-site interactions, delving into perturbation theory, continuous-time quantum walks, and quantum Fisher information (QFI), among other areas. Notably, two critical on-site interaction strength points emerge. At these specific locations, the QFI reaches its zenith, exhibiting a proportionality to $t^4$. This substantively amplifies the precision in measuring both the Newtonian constant of gravitation and the Eötvös parameter. The improvement surpasses models devoid of on-site interactions by 6 orders of magnitude. The methodology used to measure big $G$ can be adapted to quantify the Casimir energy of a many-particle system.