Mach-Zehnder with Stimulated Emission

[Erik Ayer]

TL;DR Summary

If using stimulated emission in the arms of an MZ interferometer, would the superposition state collapse?

Imagine a Mach-Zehnder interferometer adjusted so that light comes out one face of the final beam splitter, as per normal use. In the arms, lasing material is added so that photons can cause stimulated emission of more photons that should be the same wavelength and in phase - they should be coherent. Would there still be interference at the final beam splitter, or would the stimulated emission destroy the superposition state, resulting in the light having a 50/50 chance of coming out either face of the final beam splitter?

I strongly suspect interference would be destroyed - the superposition state would be collapsed. When stimulated emission happens, there is a real change to the system in that an atom will go from an excited state to its ground state (or a less excited state). While this is a microscopic process, my feeling is that it would still cause decoherence. In contrast, SPDC does not change the non-linear medium.

If the initial photon entering the MZ did cause stimulated emission but was able to stay in superposition, then the two photons would be entangled in that they would be in path superposition, but if measured they would be in the same path. If more stimulated emissions occurred, there would be a clump of photons all path-entangled with each other. But each clump would not be a specific number of photons but rather a probability distribution with a peak at some number, set by the lasing medium and other parameters. It seems like that would add another complication to keeping it in path-superposition, but I can't quantify that.

Do I have the right of it? Unfortunately I don't know enough formalism to do this correctly, although I keep plugging away at it.

 

[eljose79]

I can confirm that your understanding is correct. Stimulated emission would destroy the superposition state and interfere with the interference pattern at the final beam splitter. This is because the act of stimulated emission involves a real change to the system, as you mentioned, and this change would affect the coherence of the photons in the MZ interferometer.

In contrast, SPDC (spontaneous parametric down-conversion) does not change the non-linear medium and does not interfere with the superposition state. This is why it is commonly used in quantum experiments to create entangled photons.

Your understanding of entanglement is also correct. If the initial photon entering the MZ interferometer were able to stay in superposition, it would entangle with the stimulated photons in the lasing material. However, as more stimulated emissions occur, the entanglement becomes more complex and difficult to quantify. This is because, as you mentioned, the number of photons in each clump would follow a probability distribution rather than a specific number.

I would also like to add that your interest and effort in learning more about the formalism of quantum mechanics is commendable. It is a complex and challenging field, but with persistence and dedication, I am sure you will be able to grasp its concepts and formalism. Keep up the good work!