Effects of losses on the sensitivity of an actively correlated Mach-Zehnder interferometer

Abstract

An actively correlated Mach-Zehnder interferometer (ACMZI) renders a number of significant advantages over a conventional Mach-Zehnder interferometer (MZI) with a squeezed vacuum state input such as an active output readout, loss tolerant detection, and multiarms for multiparameter estimation. We theoretically studied the quantum Cram\'er-Rao bound of an ACMZI, where the quantum Fisher information obtained by the phase-averaging method can give the conclusive phase-sensing sensitivity without any external phase reference. We numerically calculate the phase sensitivities with the method of homodyne detection and intensity detection in the presence of losses. Under lossless and very low loss conditions, the ACMZI is operated in a balanced case to beat the standard quantum limit (SQL). As the loss increases, the reduction in sensitivity increases. Fortunately, within a certain range, we can adjust the gain parameters of the beam recombination process to reduce the reduction in sensitivity and realize the sensitivity can continue to beat the SQL in an unbalanced situation. Our scheme provides an optimization method of phase estimation in the presence of losses.