Phase estimation by photon counting measurements in the output of a linear Mach Zehnder (MZI) interferometer

TL;DR

This paper investigates photon counting measurements for phase estimation in a Mach-Zehnder interferometer across various input states, analyzing their effectiveness and minimal phase uncertainties, including non-linear modifications with NOON states.

Contribution

It provides a detailed analysis of phase estimation using photon counting in MZI with different input states and introduces a non-linear system with NOON states for improved phase measurement.

Findings

Photon counting achieves minimal phase uncertainties with coherent states.

Fock states and squeezed-vacuum states enhance phase sensitivity.

Non-linear system with NOON states improves phase estimation accuracy.

Abstract

Photon counting measurements are analyzed for obtaining a classical phase parameter in linear Mach Zehnder interferometer (MZI), by the use of phase estimation theories. The detailed analysis is made for four cases: a) Coherent states inserted into the interferometer. b) Fock number state inserted in one input port of the interferometer and the vacuum into the other input port. c) Coherent state inserted into one input port of the interferometer and squeezed-vacuum state in the other input port. d) Exchanging the first beam-splitter (BS1) of a MZI by a non-linear system which inserts a NOON state into the interferometer and by using photon counting for parity measurements. The properties of photon counting for obtaining minimal phase uncertainties for the above special cases and for the general case are discussed.