Alice and Bob are best friends. But recently, Alice moved to Mars and when they are talking over Facetime, the delay between them is sooo long. Light takes 4.3 minutes to travel from Earth to Mars. Wouldn't be nice for them to have instant communication, a communication faster than light? Quantum entanglment may seems like a great option. Entanglement means that you have 2 particles that shares a property called state. Some exemple of properties that can be entangled are the position, the spin, the polarization, the shape, etc. An example could be that I have two particle and I now for sure that the have inverted spin. If I can know that the first one is up, I know instantly the other is down, whereever the aprticle is. So if I entangle a bunch of photon, send one of each pair to Alice and the one to Bob, could they use a kinda morse code by alternating between up and down photons to communicate? And because both photons are linked, they instantly switch, witch mean instant communication? There is actualy one experiment that can help us figure out what truly happens with entanglement and show if faster then light communication is possible in that scenario. It is called the delayed-choice quantum eraser and it raises many questions about what is happening. Is consciousness a part of the solution? What is knowing and who needs to know. Can we unknow or erase something we did know. Can we change the behavior of a photon in the past. Can information travels faster then light?
Let's start with the basic slit experiment and work our way up.
The single slit experiment and the double slit experiment are super simple: we send particles through one or two thin openings in a wall and we look at the pattern created on a screen or a detector behind the slits. If we use classical particles, like sand, and send them through only one slit, we will see one pile of sand, higher near the center of the slit (like a pyramid shape, but round). Then we add the second slit: each particles will go through either one of the slit. The pattern will look exactly like the first pile of sand, but bigger. This bigger pile is actually the sum of two smaller pile, but because the slit are so close, you cannot distinguish them and you only see one big pile of send
The experiment becomes way more intersesting when we move from classical particle to wuantum particle. Let's do the same experiement with photon.
When using quantum particles (particles that can behaves like waves) like photons or small atoms, we find a different result. If we send the particles through only one slit, we see a blob of intensity on the screen. The blob is brighter in the center and the intensity decrease near the edge. We could say the blob is the 2D version of the sand pile, because theparticle won't stack up on the detector. When we talk about intensity, we mean the number of photon detect at one spot on the detector. If we change for a double slit, we don't get a bigger blob like with the sand, but we get an interference pattern. Each photons will go through either one of the slits and interfere with photons that went through the other slit. When a maximum of the wave meets a maximum, they add up and form a bright spot. When a maximum meets a minimum, they cancel each other out and form a dark spot. The most confusing aspect of this experiment is that, despite allowing only a single photon at a time to pass through the slits, the interference pattern persists. This experiment proves that even a single particle can behaves like a wave.
Hypothetically, if we can detect in which slit the photon went through, we would loose the interference. When you don't know in which slit the photon went, we say the photon is in a superposition of both case. This is moment were the photon act like a wave. Whenever we detect a photon, it stops acting like a wave and is detected as a particle, which means it went though one and one only slit. So we retrieve the same pattern as a photon going through only one slit. As mentioned before, if you have only one slit, you get a small blob, called a diffraction pattern. Both slits acts like a single slit and then add up to get a bigger blob. It sure seems weird an observation can change the results of an experiement, but we will get to it.
A "detector" that lets you know where the photon went is tricky to get. If you put a detector or your own eye, you will absorb the photon. You will never be able to see anything on the screen because you've blocked it. That is why Scenario 1 doesn't make sens in real life. But we can be more resourceful and figure a way to realise the experiement. We will use two different methods throughout our experiments. First, we will use polarizers. Polarizers are not detectors, but more like selectors or filters. The second tool we will use is entanglement. By creating two identical particles, we can detect one of them and let the other one go through the double slit. We will explain this in more detail in *** section. For now, let's look at a couple of scenarios with polarizers that will be necessary for later
Polarization is a proprerty of waves. It is direction in which it oscillate. polarization can be linear, circular or elliptic.
Polarizers are optical filters that only lets certain polarizations pass. An incidant beam at 45 degree would totally pass through a 45 degree polarizer, but will not pass at all in a -45 degree polarizer. It would halfly pass through either a 0 or 90 degrees. The choice of passing or not is true randomness. It is still a complet mystery in physics to know whether a photon would pass are not or even to know how it is decided.
Once it is decided that a photon passes through the polarizer, it will exit in the same polarization state as the polarizer.
Our goal with polarizer is to find a way to "detect" in which slit a photon went, with detecting the photon itself. Let's start by inserting one polarizer in front of each slit and try to thing about how it can help us identify the photon's path.
We already know the normal double slit experiment gives an interference pattern, like on the picture on the left, which depends on the width of the slit, the distance between both slits, and a few more parameters. If you put a polarizer in front of each slit separated by an angle of 90 degrees, you will lose the interference pattern because both exiting waves won't be able to interact (they won't oscillate in the same plane). You will find a pattern that is the sum of the diffraction of each slit. If the polarizers aren't perpendicular, you'll still see the interference, but the intensity will depend on the angle between them. It wil be maximum when they are at the same angle and overall proportionnal to the cosinus of the angle between the polarizer.
Now, it is time to detect the photon's path. If we add a third polarizer, P1, that intercept both path, the angle on this polarizer would act as a slit selector.
Start by trying it yourself, all the explaination are coming just after. You can rotate the polarizers P1, using the pink dot and change the slit parameters using the control panel.
It is important to note that the pattern with 45 and -45 degrees are not the same. They are actually opposite. Wherever one as a minimum, the other is a maximum. If you sum them both, you recreate the diffraction pattern.This is why we say polarizers are selectors and detectors. The same thing happens with the poalrizer at 0 degree and 90 degree. Because the slit will act as a single slit, we get a diffraction pattern in front of the right slit. If we sum both pattern, you will find a bigger diffraction pattern, centered in the middle of the two slits. The polarizer lets you choose what you want to see, but they don't change what is really happening. The intensity will decrease a lot when we add all the polarizer, because, again, you are selecting only on part of the photons. But they still exist, even though you are not looking at them. The same logic can apply to color filter. If you place a blue filter in front of a white light, you are not erasing the fact that the light was white. You are just looking at the blue part of that white light.
The conclusion to undersand on each of the previous exemple is really that filters are not detectors, they just select on part of the data. Polarizers are so helpful, because they give you a way to interact with the photons without stopping them or without detecting them. What would be even better is if we can come up with a way to really detect the photons, but still not catch them. Fortunatelly, we still haven't run out of option yet! Let's talk talk about quantum entanglement.
From now on, we dive into quantum entanglement as our second method for detecting but not detecting photon. I don't want to spoil to much, but keep in mind all the previous double slit and poalrizers experiement if you want to try predicting how we will complet our detection.
Quantum entanglement is the phenomenon where a particles can only be describe in function of some other particles. The entanglement can comes from any physical state, like position, spin, polarization, etc. A basic metaphor of entanglement is if I take two ball (one red and one blue) and put each of them in identical box. I destroy one of the box picked randomly. As soon as I open the untouched box and see that the blue ball is inside, I know for a fact that the one destroyed is red. The two balls where entangled by color.
At this point, it is completly normal to have a lot of question about quantum entanglement. Can information travel faster than light? If knowing the path creates interference, aren't we changing the past? Does photons has conciousness? Are we living in a virtual reality? We will try to answer most of them in the next section, and some more in the FAQ.
We will entangle the photon by position and polarization at the same time. To create entangled photon, we will use two BBO crystals. How it works is weshoot a beam of photons. Once in a very while, the BBO will convert one photon into two. They will quit the crystal at the same time and at the same angle. That is the position entanglement, saying if there is on photon that is produce, a second one will also be produce. Plus,both photons will be entangled by polarization (that happens because we have not one, but two BBo). The polarization will be in one of the Bell state depending on the BBO orientation. In our case, the polarization state is $\ket{\psi^+} = \frac{1}{\sqrt{2}} ( \ket{\updownarrow} \ket{\updownarrow} + \ket{\leftrightarrow} \ket{\leftrightarrow})$. It means that if the first photon has an horizontal polarization, the second will also be horizontal, and if it is vertical, the same goes for the second photon. It is completly random in which state the photon is.
Quantum is a rare case in which true randomness is believed to exist. For example, tossing a coin: the result is not actually random. Even though you have 50-50 chance, the result could be predict by knowing the force and rotation it was tossed at. It would be truly complecated to calculate because of so many factors, wind, dust, imperfection and so one. But in quantum, be cannot have access to those factors, is it because we don't have the technologies to predict the result and true randomness doesn't exist, it has yet to be discovered.
$\begin{equation*}
\color{blue}{\ket{\psi^+} = \frac{1}{\sqrt{2}} ( \ket{\updownarrow} \ket{\updownarrow} + \ket{\leftrightarrow} \ket{\leftrightarrow})}
\end{equation*}$
$\begin{equation*}
\ket{\psi^-} = \frac{1}{\sqrt{2}} ( \ket{\updownarrow} \ket{\updownarrow} - \ket{\leftrightarrow} \ket{\leftrightarrow})
\end{equation*}$
$\begin{equation*}
\ket{\phi^+} = \frac{1}{\sqrt{2}} ( \ket{\updownarrow} \ket{\leftrightarrow} + \ket{\leftrightarrow} \ket{\updownarrow})
\end{equation*}$
$\begin{equation*}
\ket{\phi^-} = \frac{1}{\sqrt{2}} ( \ket{\updownarrow} \ket{\leftrightarrow} - \ket{\leftrightarrow} \ket{\updownarrow})
\end{equation*}$
Let's jump right into the experiment we wanted to acheive. Note that in the lab, we added one componant at the time, juste checkout experiemnt 4 and 5 for more detail.
Now, howcanwe use entanglement to detect in which slit the photon went? Well, it create two photon. Let's detect the polarization of one and let the second one go through the double slit with polarizer experiment.
Again, before telling you too much, try it yourself and try to understand when their is interference and when it is only diffraction. (Checkout the preset, they are the most intersting angles).
So, when do we see interference? The question has already be answered a few time, there is interference only when we cannot know which path the photon took.
Keep in mind weare in the poalrization state |↕⟩|↕⟩+|↔⟩|↔⟩. If P2 is at 0 degree, then we know for sure that both photons were horizontaly polarized an therefore, the second photon reached the upper slit. If the polarizator P2 is at 90 degree, everything is the same, but the photon want through to the bottom slit. If the polarizator P2 is at 45 or -45 degrees, we again have a scenario where we cannot know in which slit the photon want. Again, whenever we know the path (0 or 90 degreee), we loose all interference on the screen. If we don't know the path (45 or -45 degrees) we see interference.
Dans le dernier paragraph, je parle pas trop de coincidence, je sais pas si c'est mélangeant?
parler du measuring problem
parler de l'expérience 7
