Phase Sensitivity Optimization For a Hybrid Mach‐Zehnder Interferometer With Internal Parametric Amplifiers and One Input in the Vacuum State

In this work, we address the problem of phase sensitivity optimization for a hybrid interferometer. The device we consider is composed of a usual Mach–Zehnder interferometer (MZI), however with parametric amplifiers (PA) inserted in each of its arms. We consider a generic pure input having one port in the vacuum state, and the MZI is assumed to be unbalanced. We address this optimization problem for both detection schemes having access – or not – to an external phase reference. As applications, we discuss a number of input states showing a potential interest in quantum metrology and thoroughly evaluate their performance. We discuss both the QFI and phase sensitivity scaling in respect with the average number of PA photons. We show that the PA‐enhanced MZI can outperform both the usual Mach–Zehnder and also the standard SU(1,1) interferometer having the same input resources. We also address the effect of both internal and external losses on the performance of the hybrid interferometer.