Enhancement of charge sensitivity by nonlinear optomechanics

Quantum estimation of electrical charge is investigated by using nonlinear optomechanical interaction. Due to the light-matter decoupling at one mechanical period, we need to consider only the cavity state, meaning that no direct access to the oscillator state is required. It is shown that the charge sensitivity can be greatly improved by enhancing optomechanical coupling. Further, we find that our theoretical result can surpass the sensitivity obtained from electrical measurements.