Nonlinear and nonlinear-linear hybrid interferometers using coherent and squeezed vacuum states

Classical and quantum states working in concert play an essential role in high-precision interferometry. In this regard, coherent combined with squeezed vacuum states are the most promising candidate. Here we complement this subject by comparing nonlinear and nonlinear-linear hybrid interferometers with homodyne detection as a readout strategy. For a high-photon coherent state, either of the two interferometers can provide the phase sensitivity approaching the quantum Cramer-Rao bound. Additionally, we discuss the impacts of photon loss during the transmission and readout stages. We find that a nonlinear interferometer is advantageous over a nonlinear-linear hybrid interferometer. With increasing photon number of the coherent state, the maximal tolerable lossy rate ensuring phase sensitivity beyond the shot-noise limit is close to 50%. Our work may deepen the understanding of quantum-enhanced interferometry using nonlinear dynamics.