Enhancing the sensitivity of quantum optomechanical gyroscope by optical Kerr effect

We propose a theoretical scheme to enhance the sensitivity of a quantum optomechanical gyroscope (QOMG) by optical Kerr effect. We utilize quantum Fisher information (QFI) to evaluate the metrological potential of the QOMG scheme. It is found that the Kerr interaction can significantly enhances the sensitivity of the QOMG. We observe the super-Hesenberg scaling of parameter estimation precision. Furthermore, we also evaluate the performance of QOMG for the quadrature measurement. It is indicated that the sensitivity in the quadrature measurement scheme can saturate the quantum Crmam\'{e}r-Rao bound. We study the effect of the driving and dissipation of the optical cavity on the QFI, and find that the sensitivity can be manipulated by changing the driving while dissipation decreases the sensitivity. The work shows that the photon nonlinear interaction can improve sensitivity of QOMG, and demonstrates a valuable quantum resource for the QOMG. These results could have a wide-ranging impact on developing high-performance QOMG in the future.