The weak Coulomb force estimation via an optomechanical system

This study presents an effective scheme for estimating the weak Coulomb force through a hybrid optomechanical system. In this scheme, information regarding the weak Coulomb force can be transferred to the cavity field through the coupling between the cavity field and the mechanical oscillator, and it can be fully extracted from the cavity field when the cavity field and the mechanical oscillator are disentangled. We employed the quantum Fisher information and the error propagation formula to analyze the effects of the coupling strength, the cavity average photon number and the Coulomb force on the estimation precision. We observed that the estimation precision can be improved by increasing the coupling strength. In addition, when choosing the proper value of average photon number and the proper range of the Coulomb force, we can approach the theoretical-attainable precision determined by quantum Fisher information. Particularly, the magnitude of the estimated weak Coulomb force in this scheme is up to 10⁻¹⁰ N or even smaller, which is better than the results obtained from previously conducted studies. Moreover, the decoherence of the mechanical oscillator and that of the cavity field are considered by solving the master equation. We show that the leakage of photons from the cavity greatly influences the measurement precision. (paper)