The impact of parametric amplifiers on the phase sensitivity for an unbalanced interferometer

This paper provides a theoretical analysis of a Mach–Zehnder interferometer (MZI) enhanced by optical parametric amplifiers (OPA) placed inside its arms and fed by a coherent input source. Contrary to most cases found in literature, we perform a wider analysis by considering the MZI unbalanced and two internal phase shifts. We discuss the theoretical best-case phase sensitivity of this setup via the quantum Cramér–Rao bound (QCRB) and we consider scenarios having – or not – access to an external phase reference. We also assess the realistic performance of the OPA-enhanced MZI by employing a balanced homodyne detection (asymmetric and symmetric phase shifts) scheme and a difference-intensity detection scheme. We are thus able to find the optimum beam splitter (BS) transmissivity (transmission coefficient) of the first BS via the quantum Fisher information (QFI), while for the second one, we need to take the detection scheme into account. We are able to find these optimal values for all considered scenarios and thus assess the best-case phase sensitivity provided by this setup.