Realization of a highly sensitive mass sensor in a quadratically coupled optomechanical system

We propose and analyze an efficient scheme for realizing high-sensitive mass sensor in a quadratically coupled optomechanical system via nonlinear second-order sideband process. This is achieved by exploiting a well-established optomechanical circumstance, where a degenerate parametric amplifier (DPA) is embedded into a membrane-in-the-middle cavity driven by a strong control field and a weak probe pulse. Beyond the conventional linearized approximation, we derive analytical expressions for the efficiency of a second-order sideband and the sensitivity of a mass sensor by using a perturbation method. In this scheme, an added mass deposited on the dielectric membrane can be measured by monitoring the efficiency variation of second-order sideband generation. Using experimentally achievable parameters, we identify the conditions under which nonlinear gain of DPA allows us to enhance the efficiency of a second-order sideband and improve the sensitivity of a mass sensor beyond what is achievable in the linearly coupled optomechanical system based on the detection of mechanical frequency shift. More importantly, we also find that the maximum efficiency of a second-order sideband and the optimum sensitivity of a mass sensor simultaneously serve as an efficient detection for the added mass of a membrane when a control field and nonlinear gain of DPA become strong. The present proposal offers a practical opportunity to design an all-optical nonlinear mass sensor at the picogram level.