How is superposition demonstrated?

[Halc]

TL;DR Summary

How is superposition demonstrated for 'spin' and for larger cases?

I just wanted to know how they go about demonstrating a particle being in superposition of both spin up and down relative to some axis. OK, it probably cannot be done with just one any more than you get an interference pattern by sending a single photon through the slits. I get that much. I have 10000 particles and I want to generate some sort of interference based on spin. How is that done? A link to a topic already answering this will suffice, but I couldn't find one.

Secondly, a very similar question about something macroscopic. They've apparently taken a piezoelectric tuning fork large enough (1/25th of a mm long) to see unaided, and by isolating it sufficiently from its environment (putting it in Schrodinger's box so to speak), managed to put it in superposition (for around 6 nanoseconds) of vibrating and not vibrating. The pop article was Scientific American: https://www.scientificamerican.com/article/quantum-microphone/
I cannot find a link to the actual paper referenced, by apparently Aaron O'Connell
Again, how is that sort of superposition demonstrated? The SA article wasn't particularly clear on that point, but I think it might be detected via the same circuitry by which the superposition was set up in the first place.

 

[PeterDonis]

I just wanted to know how they go about demonstrating a particle being in superposition of both spin up and down relative to some axis.

"They" don't. Superposition is basis dependent; it's an artifact of how the system is represented in math. It's not something that can be demonstrated physically.

What can be demonstrated physically is that, for example, if a large number of particles are prepared with their spins all up about one axis, measuring the spin about a different axis will have some nonzero probability of each result (spin-up or spin-down about the different axis).

I have 10000 particles and I want to generate some sort of interference based on spin. How is that done?

Look up "Mach-Zehnder interferometer".

superposition (for around 6 nanoseconds) of vibrating and not vibrating

That's not really a good way of describing the state, per my remarks above. A better way would be that, if you measured the "is it vibrating?" observable of the tuning fork, you would have a nonzero probability of each result ("yes, it's vibrating" or "no, it's not vibrating").

 

[Halc]

It's not something that can be demonstrated physically.

That makes sense since I think FTL communication could be implemented if there was a physical way to demonstrate it. Forgive my naive usage of the terminology.

What can be demonstrated physically is that, for example, if a large number of particles are prepared with their spins all up about one axis, measuring the spin about a different axis will have some nonzero probability of each result (spin-up or spin-down about the different axis).

That sounds classical. If a large number of shoes are prepared all with holes in them, measuring their color will have some nonzero probability of black or white. There's more to it than that.
They often use spin to demonstrate entangled correlation, implying that the state is more than just a classical unknown one. I'm also sure I'm wording things wrong again.

Look up "Mach-Zehnder interferometer".

I checked wiki and a few other places. Seems to have to do with light and no mention of spin measurement.

That's not really a good way of describing the state, per my remarks above. A better way would be that, if you measured the "is it vibrating?" observable of the tuning fork, you would have a nonzero probability of each result ("yes, it's vibrating" or "no, it's not vibrating").

Again, how does that differ from just not knowing what the classical coin flip was until you check? The crazy lengths taken to isolate the setup would not be necessary otherwise.

 

[renormalize]

I checked wiki and a few other places. Seems to have to do with light and no mention of spin measurement.

Maybe you want to look at the Stern–Gerlach experiment instead.

 

[Nugatory]

I just wanted to know how they go about demonstrating a particle being in superposition of both spin up and down relative to some axis. OK, it probably cannot be done with just one any more than you get an interference pattern by sending a single photon through the slits. I get that much. I have 10000 particles and I want to generate some sort of interference based on spin.

we don’t need interference to demonstrate superposition (or more precisely and as @PeterDonis pointed out above, to demonstrate that the mathematical formalism of vector spaces, which includes superposition, is an accurate description of reality).

Violations of Bell’s inequality show that the states described as superpositions of A and B are not just A or B like a classical coin toss.
The recombination observed in a Mach-Zehnder interferometer can only be explained in terms of superposition. The analogous result for spins would use multiple Stern-Gerlach devices - googling for “Stern-Gerlach recombination” will get you a bunch of good links including some to threads here.

You will find that most experiments use photons instead of electrons or other spin-1/2 particles, but that’s for logistical reasons. The mathematical principles of superposition are the same in both cases and photons are incomparably easier to work with, so that’s what the experimentalists do.

 

[PeterDonis]

That sounds classical.

In a simple experiment with just one particle's spins, yes, you can't really show non-classical phenomena like violation of the Bell inequalities. But you can with spin measurements on two entangled particles.

I checked wiki and a few other places. Seems to have to do with light and no mention of spin measurement.

It has to do with the polarization of light, which is the equivalent of spin for light.

You can also, in principle, set up a similar interferometer using, say, the spin of an electron--for example, by using Stern-Gerlach magnets in place of the polarizing beam splitters; it's just much, much harder in practice.