# What are the similarities between a beam splitter and a double-slit?

More generally, my question is about the similarity between an $$N$$-slit and an $$N$$-mode beam splitter. Conceptually speaking, would it be accurate to say that the beam splitter is just the discretized version of the slit? (Let's simplify things and ignore the specific parameters of each such as slit width, transmittance, etc.)

I presume that

a single particle incident on the $$N$$-slit delocalizes into $$N$$ paths just as it would if it were incident on the $$N$$-mode beam splitter. One would therefore conclude that the two have the same effect (with the only difference that the former is continuous whereas the latter is discrete). (*)

Where I'm confused, however, is at the measurement stage. For the slit, the measurement would be the pattern formed on a screen, whereas for the beam splitter it would be the clicks on detectors placed at the output modes. I however fail to see how, in this latter case with be beam splitter, one would witness any kind of interference pattern (as is the case for the slit). To see any kind of interference, the beam splitter needs to be followed by a second beam splitter that would recombine the modes (thereby effectively forming an $$N$$-armed Mach-Zehnder interferometer). Consequently, it would be more accurate to say

that a slit is actually equivalent to a Mach-Zehnder interferometer, and not to a single beam splitter. (†)

Something isn't clear in my head as I fail to reconcile the two heuristics (*) and (†).

• I think you could deflect one of the modes of a 2N beam splitter with a simple mirror .... back thru the beamsplitter ... that would create interference. Commented Jan 6 at 21:27
• @PhysicsDave Isn't it a requirement that the field excitations travel in the same mode to witness interference? With just a mirror, the two modes may technically cross but they wouldn't merge (?) Commented Jan 7 at 10:56