Phase sensitivity approaching the quantum Cramér-Rao bound in a modified SU(1,1) interferometer

SU(1,1) interferometers, based on the usage of nonlinear elements, are superior to passive interferometers in phase sensitivity. However, interferometer cannot make full use photons carrying information as second element annihilates some inside. Here, we focus improving sensitivity and propose a new protocol modified interferometer, where is replaced by beam splitter. We utilize two coherent states inputs implement balanced homodyne measurement at output. Our analysis suggests that can achieve sub-shot-noise-limited robust against photon loss background noise. work important for practical quantum metrology using interferometers.