Two Slit Experiment: Detectors

[Tom B]

I understand the two slit experiment and the outcome, but where I am confused is how the detectors work.

It seems to me that a very simple explanation of the result differing due to the presence of the detectors is that somehow the detectors interfere with the path of the electrons. By detecting the electron as it goes through the slit, some variable on it is changed and the place it lands on the screen at the end is then also changed.

How do these detectors work? A simple example: given a microphone, the microphone will pick up a sound, but will also adjust the sound wave slightly (essentially acting as an obstacle for any other detector further away). How do the detectors in the two-slit experiment work? What's to stop them interfering with the electron in some way?

Has it been shown that this doesn't happen? If I had the equipment I'd run the it with a solid object between the two slits and a detector on one side only. If the detector caused interference in the experiment then on the side with the detector we'd see only one line, on the side without the detector we'd see multiple lines.

This likely has a very simple answer and people have probably done this experiment to death, but it's not something I've seen mentioned

 

[DrChinese]

I understand the two slit experiment and the outcome, but where I am confused is how the detectors work.

It seems to me that a very simple explanation of the result differing due to the presence of the detectors is that somehow the detectors interfere with the path of the electrons. By detecting the electron as it goes through the slit, some variable on it is changed and the place it lands on the screen at the end is then also changed.

Welcome to PhysicsForums, Tom!

This is a great question. Anything that allows you to determine in principle the which-slit information will eliminate the interference, regardless of whether you actually look at it or otherwise attempt to measure that. The presence of detectors alone does NOT matter. Although a suitable experiment to demonstrate this for electrons does not immediately come to mind (one in which detectors clearly can't alter anything), there is such for photons.

Photons, like other elementary and quantum particles, exhibit double slit interference patterns. It is possible to place polarizers over the individual slits. So regardless of whether the photon goes left or right, it encounters a detector. Here is the thing: if the photon goes through the left slit, the setting of the polarizer setting on the right should not matter, correct? And vice versa.

However, if the polarizers are parallel, you DO get interference. And if they are perpendicular, you do NOT get interference. So clearly, the detector is not the relevant variable. If not the detector, then what is? Answer goes back to the line highlighted. You must be able to learn the which slit information to eliminate interference. With polarizers perpendicular, it is possible to do just that - although that information is actually ignored in the experiment. That is because when the polarizers are perpendicular, the photon cannot have gone through both slits - the slits are mutually exclusive. When parallel, they are not and interference can occur.

 

[Nugatory]

It seems to me that a very simple explanation of the result differing due to the presence of the detectors is that somehow the detectors interfere with the path of the electrons. By detecting the electron as it goes through the slit, some variable on it is changed and the place it lands on the screen at the end is then also changed.

Yes, that is a very simple explanation, and it's also basically correct. If the particle interacts with something its state may be changed; the particle has to interact with the detector in some way (not all interactions are detections but all detections are interactions); those interactions that could tell us which slit the particle passed through also change the state so that the interference disappears.

When done with electrons, the most interesting and surprising aspect of the experiment is that an interference pattern does appear when both slits are open, so in these experiments the "detector" is often just a barrier that blocks one slit or the other. More sophisticated experiments generally use photons instead of electrons, because the setup is easier and because photons are readily manipulated with polarizers, beam splitters, and the like. In these experiments we can play with the interaction at the detectors (for example, by rotating a polarizer as DrChinese describes above) and watch the interference pattern appear and disappear according to whether the interaction could tell us which slit the particle passed through.

 

[Strilanc]

What's to stop them interfering with the electron in some way?

Has it been shown that this doesn't happen?

In theoretical quantum computing a "detector" is idealized into a controlled gate, something that takes effect in the parts of the superposition where the control qubit is on but not in the parts of the superposition where the control qubit is off. In this abstraction, the controlled gate has no effect on the control qubit. You can even measure the control qubit before or after it is used as a control, without changing the overall expected outcome of a circuit, as long as you weren't going to do any more operations on it.

However, you still get interference-destroying effects. For example, a Hadamard gate is its own inverse. Apply it to a qubit twice, and you've done nothing overall. But if you use the qubit as a control between those two applications, you will instead find that you have effectively randomized the qubit:

The reason this happens comes down to the fact that only entire states interfere. Interference doesn't happen when just the first qubit ends up with same value in two possible paths through the system, the second qubit also has to end up with the same value. By toggling the second qubit, you're making a difference that distinguishes the end states and so they stop interfering.

I made some animations of the state transitions of a Mach-Zehnder Interferometer with and without a detector a long time ago. It shows how the extra state-space of the detector gives the amplitude vector space to spread out instead of being forced back together into interfering:

:

:

Does that make sense? Not sure how clear the diagrams are without more context.

 

[ZapperZ]

I understand the two slit experiment and the outcome, but where I am confused is how the detectors work.

It seems to me that a very simple explanation of the result differing due to the presence of the detectors is that somehow the detectors interfere with the path of the electrons. By detecting the electron as it goes through the slit, some variable on it is changed and the place it lands on the screen at the end is then also changed.

How do these detectors work? A simple example: given a microphone, the microphone will pick up a sound, but will also adjust the sound wave slightly (essentially acting as an obstacle for any other detector further away). How do the detectors in the two-slit experiment work? What's to stop them interfering with the electron in some way?

Has it been shown that this doesn't happen? If I had the equipment I'd run the it with a solid object between the two slits and a detector on one side only. If the detector caused interference in the experiment then on the side with the detector we'd see only one line, on the side without the detector we'd see multiple lines.

This likely has a very simple answer and people have probably done this experiment to death, but it's not something I've seen mentioned

I'm assuming that you are referring to the detector at the slits themselves, rather than the detector/screen that shows the pattern afterwards.

The problem here is that the detector could be the slits themselves (I could easily isolate each slit, make them metallic, and detect the induce current/magnetic field at each slit)! So one can say that the electrons interact with the slits. The question is, why would they act so differently if we were able to know which slit the electrons passed through, when compared to when we don't know. After all, if the slits interact with the electrons when they passed by, why would they interact so differently under those two scenarios?

So yes, they do interact with the "detector", but the interaction gives different outcome depending on the setup. That is the so-called puzzle here.

Zz.