Where does the Quantum Interference effect show up?
The Quantum Interference effect (QIE) shows up when you are observing the particle wave duality properties of an electron or of a photon.
Imagine the following experiment:
We have a machine gun firing bullets randomly at a wall. This wall has two holes in it (H1 and H2) and occasionally, the bullet goes in. On the other side we have another wall, but with no holes (W). In front of this wall we have a bullet-detector. When we place this bullet detector at a position on the x-axis of W. We let the gun fire for 1 minute, and the amount of bullets that hit the detector is the probability of a bullet hitting that point on the x-axis of W. We increase the x-value and repeat this process. When we have done enough x-axis points, we get a graph of the probabilities (P12). Here it is:
You may see, that it is the sum of the graphs produced, when you cover one of the holes up. The graph made when H2 is covered is P1, and when H1 is covered you get P2. The sum of the two graphs is P12, which is the probability graph when both holes are open.
Now let's change it up:
Instead of a machine gun we now have a water wave-maker. We sill have two holes (H1' and H2') and a wall (W') and a wave detector. Unlike the bullet example, where either a bullet is detected or not, we always detect a wave no matter where we place the detector. So The graph would be a straight line. Instead, let's measure the intensity of the wave at the given x-points. Once we have measured the intensity of the wave at the x-axis points, we make another graph (I3). Here it is:
The graph I3 looks rather strange. Let's do the same thing we did with the first example and cover up one of the holes. When we cover up H2 we get the graph I1, and when we cover up H1 we get the graph I2. The sum of these two graphs, however does NOT equal I3. This is called quantum interference. At some spots the graph is bigger that the sum of I1 and I2, which is called Constructive Interference. at other points it is the exact opposite, i.e. it is less less that the sum of I1 and I2. This is called Destructive Interference. What happens is that I1 and I3 add up at some points, and cancel each other out at other points. That is the simple description, however. The mathematical explanation is quite complicated (I might make a separate post about that). This is the characteristic of a wave.
Particle-Wave duality
Now for a last example:
You have an electron emitter and a wall with two holes (H1 and H2) in front of the emitter. Behind the holes you have another wall (W) with an electron-multiplier in front of it. You place the EM on an x position in front of W. The EM clicks every time it detects an electron. There are no half-clicks or partial-clicks, just whole electrons. So the electron is perceived as a particle..for now. The amount of clicks per minute is the probability for that point on the x-axis. This seems simple so far. Since that electron seems to be behaving like a particle, we should expect the same result as with the machine gun example, right? I mean, they are basically like bullets, i.e. they have mass, are small and are going very quickly, right? Nope. When we graph out the probabilities we get the same graph as in the wave example, I3. We get interference.
But why, the electrons are behaving like particles? That's the magic of quantum mechanics. It behaves like a particle in some instances and like a wave in other instances. This is called particle-wave duality and this is the case for ALL subatomic particles. All of them.
Now lets look at something interesting. If it behaves like a particle, then it either goes through H1 or H2, right? Let's find out.
Imagine the following extension to our experiment:
We place a light source behind the H1 and H2 wall, just between the two holes. We should observe a flash on the H1 side when the electron goes through H1 and a flash near H2 when the electron goes through H2. So we can observe where it goes through. We should be able to observe if the electron goes through both holes at the same time, which should be the case if we are observing interference. But no. We observe, that it either goes through H1 or H2. Not both. Well then, let's make another probability graph. We make the graph and observe this:
The interference is gone.
It is as if the electron knew that we were observing it and the interference disappeared.
How is this possible? It's simple:
The photons coming from the light source are altering the path of the electron. We can not observe it without changing it. This is a nightmare.
what if we lower the intensity of the light, i.e. the amount of photons. Well, we still don't observe the interference, but something else happens. What is supposed to happen is that we see a flash and the here a click. Because the electron is being detected by the light and then the EM. But sometimes we only hear a click. How is this. Well, because there are less photons, occasionally there is no photon present to detect the electron and it passes through undisturbed. This particular electron will then be detected according to the interference effect. Since there is no photon to observe it, it continues on it's original trajectory. Well, let's keep the original intensity and just increase the wave length. This way the frequency of photons is different, not the amount. The light is therefore softer than shorter wave lengths. What do we observe? Well, the light still interferes with the electrons. So lets keep increasing the wave length (f.e. microwaves) and simply detect the flashes with the appropriate camera. Well now that the wavelength is longer than the space between the holes H1 and H2, we only get one flash. So we can't see which hole it went through. But the interference is back. This is a nightmare.
It's not a nightmare, it's the uncertainty principle, which governs the subatomic world. The more we try to measure the position, the less we can measure the velocity and vice versa. In this case, the more we try to see which hole, the less interference and the more we try to measure the interference, the less we know the hole the electron went through.
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Cheers :D
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