Proposal for constraining non-Newtonian gravity at nm range via criticality enhanced measurement of resonance frequency shift
We propose a quantum mechanical method of constraining non-Newtonian gravity at the nanometer range. In this method, a hybrid electro-optomechanical system is employed. Applying a strong driving field, we can obtain normal mode splitting of the electromechanical subsystem which is related to the resonance frequency of the mechanical oscillator. Moreover, we investigate the relationship between the variance of normal mode splitting and the resonance frequency shift induced by the gradient of exotic forces provided that our system is operated at critical points. Furthermore, via suppressing the Casimir background, we set a constraint on the non-Newtonian gravity which improves the previous bounds by about a factor of 7 at 1 nanometer range. Our results indicate that our method could be put into consideration in relevant experimental searches.