What is Mach-Zehnder interferometer and what is it used for?

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What exactly is the purpose of this interferometer? And what does splitting a light into two paths exactly do anything? From what I’ve heard so far it’s to prove that electrons are quantum objects, but not much more.

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You take a beam of coherent (all the same) light with an amplitude of 2. You split it into two paths with amplitudes of 1. When recombined, they have amplitude of 2. Now imagine that I n one path, you can flip the wave (or phase shift it 180degrees) to give it an amplitude of -1. Now, when you recombine the paths, you end up with amplitude 1-1=0.

If you can control the phase shift on one arm with respect to the other, you can change the output strength from the original beam to no beam. This is called a modulator and is a key component of an optical communication systems (eg the internet, cellular networks, optical links in data centers, etc).

This is just one application. They’re very sensitive to changes in one light path with respect to the other so they can be used in sensing of distances, temperature, pressure, etc.