Phase estimation by photon counting measurements in the output of a linear Mach -Zehnder interferometer

Photon counting measurements are analyzed for obtaining a classical phase parameter in a 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 into the other input port, and (d) exchanging the first beam splitter of an MZI by a nonlinear system that inserts a NOON (representing a superposition of N particles in the first mode with zero particles in the second mode, and vice versa) 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. (c) 2012 Optical Society of America