Interferometers with unequal arm lengths

[alanf]

One arm of a Michelson interferometer is one light second long, the other is one light minute long. We run photons through it one at a time. Do we see interference? And if so, when? After one second? One minute? Some other time?

I've been reading a number (too many!) "layman's" books on quantum mechanics, and each time I read about the double slit experiment this question nags at me. (Certainly the slits aren't at precisely equivalent distances from the light source.) And I'm still unable to answer it. But I'm sure you folks can. I hope you all won't mind an inquiry from an amateur. :)

 

[DrChinese]

Welcome to PhysicsForums, alanf!

The interference from an interferometer involves mixing 2 beams so there is constructive or destructive interference at a particular place at the same time. This is similar, but a little different from, what you get with a double slit setup.

Since you mixed references to these, is there any chance you might clarify your question?

 

[alanf]

Hi Dr. C! I only brought up the double slit experiment because the issue seems similar to me. If the slits aren't the same distance from the light source, simply by measuring the time from emission to detection, an observer should be able to determine which slit - and similarly, which arm of the interferometer - each photon passed through, destroying the interference. But I'm guessing it's more complicated than that.

 

[DrChinese]

Hi Dr. C! I only brought up the double slit experiment because the issue seems similar to me. If the slits aren't the same distance from the light source, simply by measuring the time from emission to detection, an observer should be able to determine which slit - and similarly, which arm of the interferometer - each photon passed through, destroying the interference. But I'm guessing it's more complicated than that.

Yes, you are correct. For the double slit, any technique that yields which path information will eliminate the interference. And that can be done a variety of ways, including timing/path length. I think one of the best to picture the situation is this:

Take a double slit setup using light. Place one polarizer over the left slit at angle L, another over the right slit at angle R. When L-R=0, there IS interference. When L-R=90 degrees, there is NO interference. Obviously, the presence or absence of a polarizer does not change anything unless which slit information is gained. That becomes progressively more feasible as L-R goes from 0 to 90 degrees. In other words: you *could* know which path (100%) certain) by checking the polarization of the detected photon when L-R=90 (crossed), even if you didn't.

 

[alanf]

That's a clever experiment, one which I've never seen described in any of the lay discussions of the subject. So you don't actually have to check the polarity of the arriving photon. It's enough simply that you *could* check?

So how can the double slit experiment work? Is there some quantum mechanical issue preventing us from measuring each photon's flight time, and thus determining the route? And if so, what about the interferometer? No interference fringes there because we actually can measure the flight time? And would the interference fringes show up when we make the variance in distance small enough that the quantum issue - whatever it is - prevents us from measuring the flight time?

 

[Misericorde]

That's a clever experiment, one which I've never seen described in any of the lay discussions of the subject. So you don't actually have to check the polarity of the arriving photon. It's enough simply that you *could* check?

So how can the double slit experiment work? Is there some quantum mechanical issue preventing us from measuring each photon's flight time, and thus determining the route? And if so, what about the interferometer? No interference fringes there because we actually can measure the flight time? And would the interference fringes show up when we make the variance in distance small enough that the quantum issue - whatever it is - prevents us from measuring the flight time?

"...That you could check" is exactly right. When people talk about observers, it's the "could" that really matters, not that a real person or cat or atom is around to do it.

 

[alanf]

Thanks Misericorde. So to go back to the double slit experiment, what is it that prevents us from measuring the flight time of the photon, and thus determining which slit it went through (assuming the source-slit-detector distance is not precisely the same for each slit), and destroying the interference?

 

[DrChinese]

Thanks Misericorde. So to go back to the double slit experiment, what is it that prevents us from measuring the flight time of the photon, and thus determining which slit it went through (assuming the source-slit-detector distance is not precisely the same for each slit), and destroying the interference?

Nothing, really. Although that is more easily said than done. When was it emitted? How do you know there was only one?

Here is an interesting fact: entangled particles do NOT* exhibit interference effects! Because then you could determine the answers to the above questions!

*with a minor exception: when which path information is fully erased.

 

[alanf]

So to take the easier case - the interferometer with widely differing arm lengths - no interference, because we could easily determine the path the photon took with a simple stopwatch? What prevents us from doing the same with the double slit experiment? Of course we'd need something more sophisticated than a stopwatch, but I take it from what you said earlier that the measuring equipment isn't the issue - it's whether the time could ever be determined, or whether some quantum effect prevents us from doing so. If that's right, what is that quantum effect? Thanks for all the info so far. I'm learning much more here than with the "quantum mechanics for amateurs" books.

 

[Misericorde]

Can you gain information that a pair of particles is entangled by running this test, or would the test lead to decoherence?