Early afternoon. The car is packed and you
are waiting on Carol, just like your dad waited on your mother almost every
time both were going in the car according to your sister, Cathy. - Amorella
1315 hours. Strangely this was a good observation on Cathy's part;
however, I didn't appreciate it very much as she quickly became fully aware,
which is why she said it in the first place. In the olden days Dad and I would be waiting in the
car, let's say, to go to an outdoor movie theatre on Friday or Saturday night
in the Summer. We might wait ten to fifteen minutes for Mom, Cathy and Gretchen
to climb in the car. I can still hear Dad swearing a bit. Never fazed Mom,
never that I can remember. He swore anyway, every time she was late.
"Jesus Chriiist, Mary!" Those were the usual first words. I thought it
was funny because he said Mary and I was thinking of Jesus' mother and I was
thinking of Dad starting a prayer unintended. This was very funny to me because
Dad wasn't much for going to church. He liked staying at home with Mom when she
didn't go to church with us. I never figured that out until I was older.
Paul made supper -- chicken and brats on the grill, corn on the cob,
broccoli and baked beans. It was very good. Kim and Carol cleaned up, the boys
are playing outside and Paul is packing for the trip to Charleston in the very
early morning. Kim is going over the three day agenda with Carol. Most of the
trees in the area are in the greening process while Mason is almost fully
leafed. - Amorella
1946 hours. Three of the large deer just crossed the plowed field to the
southeast of the house; I am waiting for the others to follow; very cool as
dusk is approaching. Earlier Paul set our phones for Owen's 'gadget' (watch
with GPS) so we know where he is. We and Owen can text or phone one another. He
also cleaned up Carol's phone electronically and we had a good chat before Kim
came home with the boys after an hour and a half of jujitsu classes.
Earlier Doug sent you a
Wikipedia article his son (who is working on a doctorate in physics) sent him. This
is a good place to post it. - Amorella
2001 hours. I have read it a couple of times but I don't really have an
understanding of the complete article -- the math, no understanding whatsoever.
Anyone curious about the numbers can read the article at Wikipedia.
** **
Quantum eraser
experiment
From Wikipedia, the free encyclopedia
In quantum mechanics, the quantum eraser experiment is an
interferometer experiment that demonstrates several fundamental aspects of
quantum mechanics, including quantum entanglement and complementarity.
The double-slit quantum eraser experiment described in this
article has three stages:
1 First, the
experimenter reproduces the interference pattern of Young's double-slit
experiment by shining photons at the double-slit interferometer and checking
for an interference pattern at the detection screen.
2 Next, the experimenter
marks through which slit each photon went and demonstrates that thereafter the
interference pattern is destroyed. This stage indicates that it is the
existence of the "which-path" information that causes the destruction
of the interference pattern.
3 Third, the
"which-path" information is "erased," whereupon the
interference pattern is recovered. (Rather than removing or reversing any
changes introduced into the photon or its path, these experiments typically
produce another change that obscures the markings earlier produced.)
A key result is that it does not matter whether the eraser
procedure is done before or after the photons arrive at the detection screen.
Quantum
erasure technology can be used to increase the resolution of advanced
microscopes.
Introduction
The
quantum eraser experiment described in this article is a variation of Thomas
Young's classic double-slit
experiment. It establishes that when action is taken to determine which slit a
photon has passed through, the photon cannot interfere with itself. When a
stream of photons is marked in this way, then the interference fringes
characteristic of the Young experiment will not be seen. The experiment
described in this article is capable of creating situations in which a photon
that has been "marked" to reveal through which slit it has passed can
later be "unmarked." A photon that has been "marked" cannot
interfere with itself and will not produce fringe patterns, but a photon that
has been "marked" and then "unmarked" can thereafter
interfere with itself and will cooperate in producing the fringes
characteristic of Young's experiment.
This
experiment involves an apparatus with two main sections. After two entangled photons
are created, each is directed into its own section of the apparatus. Anything
done to learn the path of the entangled partner of the photon being examined in
the double-slit part of the apparatus will influence the second photon, and
vice versa. The advantage of manipulating the entangled partners of the photons
in the double-slit part of the experimental apparatus is that experimenters can
destroy or restore the interference pattern in the latter without changing
anything in that part of the apparatus. Experimenters do so by manipulating the
entangled photon, and they can do so before or after its partner has passed
through the slits and other elements of experimental apparatus between the
photon emitter and the detection screen. So, under conditions where the
double-slit part of the experiment has been set up to prevent the appearance of
interference phenomena (because there is definitive "which path"
information present), the quantum eraser can be used to effectively erase that
information. In doing so, the experimenter restores interference without
altering the double-slit part of the experimental apparatus.
A
variation of this experiment, delayed choice quantum eraser, allows the
decision whether to measure or destroy the "which path" information
to be delayed until after the entangled particle partner (the one going through
the slits) has either interfered with itself or not In delayed-choice experiments quantum
effects can mimic an influence of future actions on past events. However, the
temporal order of measurement actions is not relevant.
The experiment
[Figure does not appear]
Figure 1. Crossed polarizations prevent
interference fringes
First, a photon is shot through a specialized nonlinear optical
device: a beta barium borate (BBO) crystal. This crystal converts the single
photon into two entangled photons of lower frequency, a process known as spontaneous
parametric down-conversion (SPDC). These entangled photons follow separate
paths. One photon goes directly to a detector, while the second photon passes
through the double-slit mask to a second detector. Both detectors are connected
to a coincidence circuit, ensuring that only entangled photon pairs are
counted. A stepper motor moves the second detector to scan across the target
area, producing an intensity map. This configuration yields the familiar
interference pattern.
Figure 2. Introduction of polarizer in upper
path restores interference fringes below
Next, a circular polarizer is placed in front of each slit in
the double-slit mask, producing clockwise circular polarization in light
passing through one slit, and counter-clockwise circular polarization in the
other slit (see Figure 1). This polarization is measured at the detector, thus
"marking" the photons and destroying the interference pattern (see
Fresnel-Arago laws).
Finally, a linear polarizer is introduced in the path of the
first photon of the entangled pair, giving this photon a diagonal polarization
(see Figure 2). Entanglement ensures a complementary diagonal polarization in
its partner, which passes through the double-slit mask. This alters the effect
of the circular polarizers: each will produce a mix of clockwise and
counter-clockwise polarized light. Thus the second detector can no longer
determine which path was taken, and the interference fringes are restored.
A
double slit with rotating polarizers can also be accounted for by considering
the light to be a classical wave. However this experiment uses entangled
photons, which are not compatible with classical mechanics.
Non-locality
A very common misunderstanding about this experiment is that it
may be used to communicate instantaneously information between two detectors.
Imagine Alice on the first detector measuring either linear or circular
polarization and instantaneously affecting the result of Bob's interference
measurement. One could even conceive a situation in which Alice would switch
from a circular polarizer to a linear polarizer on her detector long after Bob
made his measurement: Bob's interference pattern would suddenly change from
interference to a smear, but in the past! Following this train of thought would
lead to an abundance of time paradoxes, like Bob measuring one pattern and
telling Alice to switch her detector in the future to the polarizer that would
cause the opposite pattern. So something must be wrong.
The misunderstanding is that Bob always measures a smear,
never an interference pattern, no matter what Alice does. Non-locality
manifests in a somewhat more subtle way. How? Let's say that the BBO crystal
produces the following state:
[equations]
(Alice's photon has clockwise polarization and Bob's photon has
anti-clockwise polarization) or (Bob's photon has clockwise polarization and
Alice's photon has anti-clockwise polarization)
If Alice places a circular polarizer in front of her detector
that filters out photons with clockwise polarization, then every time Alice
measures a photon, Bob's corresponding photon is sure to have a clockwise
polarization:
[equations]
Since Bob has placed opposite polarization filters on each slit,
we know that these photons can only have passed through (let's say) the first
slit. From that slit, they hit the screen according to the wave-function:
[equations]
where a is the spacing between the slits, d is the
distance from the slits to the screen and x is the distance to the
middle of the screen. The intensity of light on the screen (counts of photons)
will be proportional to the square of the amplitude of this wave, in other
words
[equations]
Likewise, when Alice measures a photon with anti-clockwise
polarization, Bob receives an anti-clockwise polarized photon which can only
pass through the second slit and arrives at the screen with a wave-function
[equations]
Notice that the only difference is the sign of a/2,
because the photon was emitted from another slit. The pattern on the screen is
another smear, but shifted by a. Now, this point is important: if Alice
never tells him directly, then Bob never knows which polarization Alice
measured, since both are produced in equal amounts by the crystal. So what Bob
actually sees on his screen is the sum of the two intensities:
Figure 3. The two intereference patterns and
their sum when Alice measures her photons' polarization with a circular
polarizer.
[equations]
The results of this experiment are summarized in Fig.3. Bob can
only distinguish the two peaks in his data after he got access to Alice's
results: for the set of photons where Alice measured clockwise polarization,
Bob's subset of photons is distributed according to
[equations]
and for the set of
photons where Alice measured anti-clockwise polarization, Bob's subset of
photons is distributed according to
[equations]
Next, let Alice use a linear polarizer instead of a circular
one. The first thing to do is write down the system's wave-function in terms of
linear polarization states:
[equations]
So say Alice measures a horizontally polarized photon. Then the
wave function of Bob's photon is in a superposition of clockwise and
anti-clockwise polarizations, which means indeed it can pass through both
slits! After travelling to the screen, the wave amplitude is
[equations]
and the intensity is
[equations]
is the phase difference
between the two wave function at position x on the screen. The pattern
is now indeed an interference pattern! Likewise, if Alice detects a vertically
polarized photon then the wave amplitude of Bob's photon is
[Figure does not appear]
Figure 4. The two intereference patterns and
their sum when Alice measures her photons' polarization with a linear
polarizer.
[equations]
and
[equations]
and once again an interference pattern appears, but slightly changed
because of the 180º phase difference between the two photons traversing each
slit. So can this be used by Alice to send a message to Bob, encoding her
messages in changes between the two types of patterns? No! Remember that, as
before, if Bob is not told which polarization Alice measured, then all he sees
is the sum of both patterns. The result is therefore,
[equations]
which is again a smudge. The results are given in Fig.4.
So
what's so odd about this experiment? The correlations change according to which
experiment was conducted by Alice. Despite the fact that the total pattern is
the same, the two subsets of outcomes give radically different correlations: if
Alice measured a linear polarization the total smear is subdivided into two
interference patterns whereas if Alice measured a circular polarization the
pattern is the sum of two other Gaussian bell-shapes. How could Bob's photon
know that it could go in the forbidden stripes of the interference pattern when
Alice was measuring a circular polarization but not when Alice was measuring a
linear one? This can only be orchestrated by a global dynamic of the system as
a whole, it cannot be locally carried by each photon on its own. This
experiment demonstrates the phenomenon of microscopic non-locality.
Selected
and edited from Wikipedia
** **
Kim and Paul just went up to bed. They are
heading to the airport about four in the morning. You worry a bit when they
travel but they are excited and should have a good time. It is a wedding after
all.
2238 hours. The article above is interesting to read. It reminds me of
my senior year in high school when I read a book about the concepts of
Einstein. I got the gist, some of it, and that was enough to pique my interest.
I have liked physics and quantum physics ever since.
Post. - Amorella
No comments:
Post a Comment