Dual cavity quantum enhanced optomechanical force sensor

Force sensors, used as accelerometers and gravimeters, are useful in a number of applications including inertial navigation and geodesy. Here, we explore a force sensing configuration in which the quantum correlations of a two-mode squeezed state can be exploited in order to improve sensitivity and allow for the use of intensity detection instead of the more complex homodyne detection without a significant reduction in sensitivity. We theoretically study a double ring cavity system where an optomechanical system based on a membrane is used as a shared movable mirror for both cavities. Each of the modes of the two-mode squeezed state couples to one of the two cavities and reflect on opposite sides of the reflective membrane. We rotate the angle of squeezing, the direction the quadrature noise is below the classical limit, between the amplitude or phase difference quadratures as this reduces the back-action noise or readout noise, respectively. We show that the optimal squeezing angle is frequency dependent and often not along the amplitude or phase difference squeezing as one would expect. We also explore off cavity resonance force sensitivity as the phase shift between the carrier and sidebands make it possible to extract the relevant information of external forces via the amplitude quadrature, thus enabling intensity detection when using bright states of light. For both on and off resonance, we show a quantum enhancement to the force sensitivity and a reduction in the optimal power needed for maximum sensitivity as compared to a classical, single cavity systems.