Mach-Zehnder interferometer

A Mach-Zehnder interferometer splits an incident wave into two arms and recombines them at a second beam splitter. A relative quantum phase changes the interference at its output ports. With symmetric lossless 50:50 splitters, the ports can be calibrated to have detection probabilities ${\cos }^2(\theta /2)$ and ${\sin }^2(\theta /2)$.

// Target: optics.bigb

An output port whose ideal probability amplitude vanishes by destructive interference for a specified coherent input and calibration. Changing a relative wave phase, losing quantum coherence or changing the input can brighten it.

For two identical mixers $U=R_x(\beta )$ with a lower-arm phase shifter $P(\varphi )=\mathrm{diag}(1,e^{i\varphi })$, the upper-input state evolves asThe upper-output interferometric visibility is ${\sin }^2\beta /(1+{\cos }^2\beta )$ and reaches one exactly at $\beta =\pi /2(\mathrm{mod}\pi )$. Replacing the second mixer by its inverse changes the port convention and phase dependence; it is a different specified network.