The quantum optical description of a double Mach-Zehnder interferometer

In this paper we describe within the formalism of Quantum Optics (QO) a double Mach-Zehnder interferometer (MZI). For single photon Fock states this experimental setup is shown to exhibit a counter-intuitive behavior: for certain values of the path length difference of the first MZI, the singles photon-count statistics at the output detectors does not change, whatever the difference in path length for the second MZI. For simultaneously impinging light quanta, we show that this setup is able to show the same HOM antibunching effect previously obtained with a beam splitter. However, by adding substantial delays in each MZI, we can obtain the same effect even if the "photon wave packets" do not overlap at the second beam splitter.