Tripartite loss model for Mach-Zehnder interferometers with application to phase sensitivity

Abstract

An analytical loss model for Mach-Zehnder interferometers (MZIs) is developed and used to provide a general phase sensitivity expression for arbitrary photon input states. The model takes into account phase regime, regional losses, and regional internal “environmental” conditions and is therefore useful for understanding the relationships among these factors and phase sensitivity. The ground state MZI is also defined and the associated model’s formalism is used to deduce several well established MZI phase sensitivity performance characteristics. It is shown that this ground state model represents nonideal MZIs for a wide range of operational frequencies and environmental conditions. This model also predicts that Heisenberg limited phase sensitivity cannot be achieved by a lossy MZI. Rather, for large input photon number and instrument efficiency η, the limiting phase sensitivity is the associated shot-noise limit scaled by the factor 21−η.