Entanglement based tomography to probe new macroscopic forces

Quantum entanglement provides a novel way to test short distance physics in the nonrelativistic regime. We will provide a protocol to potentially test new physics by bringing two charged massive particle interferometers adjacent to each other. Being charged, the two superpositions will be entangled via electromagnetic interactions mediated by the photons, including the Coulomb and the Casimir-Polder potential. We will bring a method of entanglement based tomography to seek time evolution of very small entanglement phases to probe new physical effects mediated by hitherto unknown macroscopic force which might be responsible for entangling the two charged superpositions modeled by the Yukawa type potential. We will be able to constrain the Yukawa couplings α ≥10^-35 for r ≥10^-6 m for new physics occurring in the electromagnetic sector, and in the gravitational potential α_g≥10^-8 for r ≥10^-6 m . Furthermore, our protocol can also constrain the axionlike particle mass and coupling, which is complimentary to the existing experimental bounds.