Probing new forces with nuclear-clock quintessometers

Abstract: Clocks based on nuclear isomer transitions promise exceptional stability and precision. The low transition energy of the Thorium-229 isomer makes it an ideal candidate, as it may be excited by a vacuum-ultraviolet laser and is highly sensitive to subtle interactions. This enables the development of powerful tools for probing new forces, which we call quintessometers. In this work, we demonstrate the potential of nuclear clocks, particularly solid-state variants, to surpass existing limits on scalar field couplings, exceeding the sensitivity of current fifth-force searches at submicron distances and significantly improving equivalence-principle tests at kilometer scales and beyond. Additionally, we highlight the capability of transportable nuclear clocks to detect scalar interactions at distances beyond $10\,$km, complementing space-based missions.