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Day 2.7
Quantum Polarization and Entanglement
1) You are wearing a pair of 3-D glasses. How much light gets through?
A) exactly 50% because of symmetry
B) exactly 50% because cos2 (45o) = ½
C) around 50% because the filters are not perfect
D) around 50% because of human error
Explain:
Both classical wave theory and quantum theory predict 50%, because of A) and B). However the actual
value will vary from 50% because the filters are not perfect. If the light is very intense, more than 50% of the
light will get through. In that case there is too much light for the filter to handle and it becomes transparent
to the remaining light which will pass through unpolarized. You can demonstrate this using two
perpendicular filters and a laser pointer or by having the participants use crossed polarizers to look directly
at a bright light. No light should get through, but some does. With a less intense source, less than 50% will
get through. Some of the light will be absorbed by the plastic - regardless of polarization. This can be seen
by looking at many filters oriented the same way. Each successive filter will make the light slightly dimmer,
when there should be no effect after the first one. Each filter absorbs around an additional 10% of light.
Good quality (more expensive!) filters will be a closer match to theory and the equipment used for research
with individual photons is much better. For the following questions, assume that the filters are perfect.
2) Suppose a single, vertically polarized photon is heading toward the filter in front of your right eye. The
filters in the glasses are at 45o to vertical. What will get through the filter?
A) half a photon
B) a photon with half the energy
C) a photon
D) no photon
Explain:
From our experiences with many photons, we know that half of the light should get through. However, you
can’t have half a photon. You can have a photon with half the energy - but then it is a very different colour
because E = hf. We don’t see any colour change, so it can’t be a photon with half the energy. You will either
get a photon or no photon, but you can’t know which you will get.
How does this illustrate quantum uncertainty?
We know that this is a vertically polarized photon and that it will go through a vertical polarizer and not
through a horizontal polarizer. However, we are uncertain of what will happen in any other polarization
basis. In this specific case, the quantum model says that this vertical photon can be considered to be in a
superposition of the +45 o and -45o states. This is similar to what happens in the two-slit experiment where
we are uncertain about which slit the photon went through.
3) Suppose 100 vertically polarized photons are heading toward the filter in front of your right eye. What
will get through the filter?
A) exactly 50 photons
B) at least 50 photons
C) around 50 photons
Explain:
The math of both the classical model and quantum models predict that half the light will get through.
However, only the quantum predicts that the value will vary from this amount - even with ideal filters.
How does this illustrate intrinsic randomness?
Quantum randomness is more fundamental than the pseudo-randomness of flipping a coin. The randomness
of a coin flip is due to our ignorance of existing information. If we had a high speed camera, we could use it
to say which way the coin will land. However, in this situation, quantum physics says that there is no
missing information that we could discover with better technology. In fact, the better the technology gets –
the clearer we see the intrinsic randomness because we can detect individual photons.
4) Suppose a vertically polarized photon is heading toward a filter at 45o and then toward a horizontally
polarized filter. What is the chance that a photon will make it through both filters?
A) 25%
B) 12.5 %
C) 6.25%
D) 0%
Explain:
The photon has a 50% chance of passing through each filter, so the combine probability is 50% x 50% = 25
%. The math is the same as for the wave model and is fairly easy. However, how do you explain this
behaviour? When you first see this demonstration, you are amazed that adding a third filter increases the
amount of light that gets through. It doesn’t make sense until you go through the classical wave explanation
where each filter is absorbing one component of the light and transmitting the other. The surprising result is
just a matter of finding the component of a component. However, does this explanation make sense for a
photon? A filter can’t select a component or part of a photon. You either get a photon or you don`t.
How does this demonstrate measurement-disturbance?
The quantum explanation says that the filters do not just measure the polarization; they also set the
polarization. We start out with a vertical photon, which has a 0% chance of getting through the horizontal
filter. Adding the middle filter at 45o means that the photon has a chance to pass through the diagonal filter
and if it does pass, it becomes a diagonally polarized photon. This photon now has a non-zero chance to pass
through the filter because the measurement changed it.
5)
How do these various thought experiments illustrate wave-particle duality?
In each experiment, the particle nature was evident because whenever we detected light it was at a specific
place (detector). You either got a photon or you did not. However, the wave nature is shown by the way we
can use Malus’ Law for polarized waves to calculate the probabilities that a photon will pass. When we do
the experiment with billions of individual photons, we find that over time we get the intensities we would
expect for a wave.
Next we will explore what happens when you put polarization and interference together.
6) Light passes through two thin slits that are very close together and then hits a screen. What will you see?
A)
B)
C)
Explain:
The pattern that you get depends on how thin the slits are and how close they are to each other. If they are
too wide and/or far apart, you will see B) which shows a small amount of diffraction, but not enough to
overlap. If the slits are thin enough and close enough together, then the light will diffract enough that each
slit will individually produce the image in C). The overlapping light interferences and produces the pattern
as seen in A).
7) Light heads toward two slits that will normally produce the pattern shown in answer A) above. However,
one slit is covered by a vertical polarizer and the other by a horizontal polarizer. What will you see now?
A)
B)
C)
Explain:
The polarizers will dim the image because they will block half the light. All three answers show this.
Vertically polarized light passes through one slit and horizontally polarized light passes through the other.
These cannot form an interference pattern, because light with ‘up/down’ polarization cannot destructively
interfere with ‘right/left’. The interference pattern will disappear, so A) is wrong. These slits previously
produced an interference pattern and so we know that the light diffracted enough to overlap. This means you
will see the diffraction shown by C) and not two separate shadows like B). This shows the diffraction of
each slit, overlapped but not interfering. The centers of each will be separated by the separation of the slits –
a tiny amount and will not be niticable.
8) The set up is the same as the last question. In addition, a third polarizer is placed in between the slits and
the screen. What will you see?
A)
B)
C) it depends on_______
Explain:
It depends on the orientation of the third filter. If the polarizer is vertical, we will see the diffraction from
just the one slit that had the vertical polarizer over it and the horizontal light will be blocked. You will see
B). It will just be a dimmer version of what we saw in the last question. The same will happen if the filter is
horizontal. However, if the filter is at 45o, only the 45o component of the light from each slit will pass
through it. Now the light from each slit has the same polarization and interference is possible. The set-up
will produce the interference pattern seen in A.
9) Suppose that the third filter was at 45o and the experiment was done with only one photon at a time. If the
image was allowed to build up slowly over time you would see
A)
B)
C)
Explain:
You will get the same result whether this is done one photon at a time or with many. This experiment has
been done with single photons and you can read more about it in http://arxiv.org/abs/1304.4943. This means
that we need a quantum explanation. But what is it? Quantum physics tells us that after the slits, the photon
is in a superposition of two states – going through one slit or going through the other. In this experiment, this
means that it is in a superposition of being vertically or horizontally polarized and each of those states is a
superposition of diagonal components. Put all together, the photon has a 50% chance to be part of the inphase interference pattern and a 50% chance to be part of the out of phase pattern.
10) Polarization can be explained by classical waves and by quantum physics. Which is most fundamental?
A) Quantum
B) Classical Waves
C) Neither
D) Both
Explain:
When there are many photons the classical model works just as well as the quantum model of light and it is
much simpler to understand. However, when they light is very faint and we are able to detect the light as
individual photons, only the quantum model works. Since high intensity light is just a large collection of
individual photons, the more fundamental explanation is the one that works whether there are many or just a
few photons.
Certain crystals can take one photon and produce two photons with half the energy. These photon pairs are
said to be entangled because they have identical - but still random - polarization. If you measure the
polarization of one of them, you immediately know the polarization of its partner.
11) Modelling Entanglement with concrete objects
a) Explain how entangled gloves work.
You know that a pair of glove has a right hand glove and a left hand glove. Therefore, once you know what
glove you have, you also know what glove the other one has. No surprise.
b) Explain how entangled coins work.
This demonstration only works if you cheat or if you have a quantum system.
12) One of a pair of entangled photons is sent toward double slits that normally produce an interference
pattern. These slits are covered with horizontal and vertical polarizing filters. The partner photon is sent off
in a completely different direction - it never goes near the slits. This is repeated many times and the number
of photons (vertical) vs. detector location is graphed.
a) Which of the following graphs shows what you will get if you graph the number of photons (vertical) vs.
detector location?
A)
B)
C)
Explain:
There is no interference pattern because vertical photons cannot interfere with
horizontal photons. Note: The build-up can be viewed as a sum
of the =45 and -45 interference patterns. For more details, see below*.
b) The experiment is repeated, but now the photon that does not go near the slits is sent thorough a third
polarizing filter which is at 45o to vertical. Which of the above graphs shows what you will get? Explain:
Measuring the partner, sets the polarization of each photon, but it does not change the total pattern that we
see. It looks like the measurement had no effect.
c) The experiment is repeated, but we only keep the data for photons whose partners made it through the
filter. Which of the above graphs shows what you will get? Explain:
A or B: Measuring the photon that does not go through the slits does affect its entangled partner. It
determines whether the photon will be found in the +45 or -45 pattern. This effect is instantaneous. This
experiment and others with single photons is discussed in more detail in Fig. 4 of
http://arxiv.org/abs/1304.4943
13) Entanglement is a key aspect of quantum computing. To get a sense of how these are different from
classical computers go to Quantum Tic-Tac-Toe. http://countergram.com/qtic/
a) How is it quantum Tic-Tac-Toe different from the regular game?
b) How does it demonstrate the key concepts of quantum physics, including entanglement?
*Extra Information: The interference pattern with the third filter at +45o is similar to the one with filter at 45o. If you look at the center of the pattern you will see that one looks like this
and the other looks like this.
Explain why this happens.
The third filter works by allowing us to see one of the underlying interference patterns by removing the
complementary pattern. The vertical slit lets vertical photons through, which can be broken into +/- 45
components. The horizontal filter passes horizontal photons, which can be broken into +/- 45 components.
If the filter is at +45o, you will get a standard interference pattern, formed from the two dashed components.
However, if the filter is at -45o you will get the complementary pattern because the dotted components are
180o out of phase. (Notice how the arrows above are in opposite directions.) These will produce a pattern
with a node in the middle. This shows that the third filter is not creating order from disorder. Both patterns
were there all along and the filter just removes one pattern to reveal the other.