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A delayed choice quantum eraser, first performed by Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, and
Marlan O. Scully,
[1] and reported in early 1999, is an elaboration on a
quantum eraser experiment involving the concepts considered in
Wheeler's delayed choice experiment. It was designed to investigate peculiar consequences of the well-known
double slit experiment in quantum mechanics, as well as the consequences of
quantum entanglement.
Introduction
In the basic
double slit experiment, a very narrow beam of
coherent light
from a source that is far enough away to have almost perfectly parallel
wave fronts is directed perpendicularly towards a wall pierced by two
parallel slit apertures. The widths of the slits and their separation
are approximately the same size as the wavelength of the incident light.
If a detection screen (anything from a sheet of white paper to a
digital camera) is put on the other side of the double slit wall, a
pattern of light and dark fringes, called an
interference pattern, will be observed.
Early in the history of this experiment, scientists discovered
that, by decreasing the brightness of the light source sufficiently,
individual particles of light that form the interference pattern are
detectable. They next tried to discover by which slit a given unit of
light (
photon) had traveled.
Unexpectedly, the results discovered were that if anything is
done to permit determination of which path the photon takes, the
interference pattern disappears: there is
no interference
pattern. Each photon simply hits the detector by going through one of
the two slits. Each slit yields a simple single pile of hits; there is
no interference pattern.
It is counterintuitive that a different outcome results based on
whether or not the photon is constrained to follow one or another path
well
after it goes through the slit but before it hits the detector.
Two inconsistent accounts of the nature of light have long
contended. The discovery of light's interfering with itself seemed to
prove that light could not be a particle. It seemed that it had to be a
wave to explain the interference seen in the double-slit experiment
(first devised by
Thomas Young in his classic
interference experiment of the eighteenth century).
In the early twentieth century, experiments with the
photoelectric effect
(the phenomenon that makes the light meters in cameras possible) gave
equally strong evidence to support the idea that light is a particle
phenomenon. Nothing is observable regarding it between the time a photon
is emitted (which experimenters can at least locate in time by
determining the time at which energy was supplied to the electron
emitter) and the time it appears as the delivery of energy to some
detector screen (such as a
CCD or the emulsion of a film camera).
Nevertheless experimenters have tried to gain indirect
information about which path a photon "really" takes when passing
through the double-slit apparatus.
In the process they learned that constraining the path taken by one of a pair of
entangled
photons inevitably controls the path taken by the partner photon.
Further, if the partner photon is sent through a double-slit device and
thus interferes with itself, then very surprisingly the first photon
will also behave in a way consistent with its having interfered with
itself, even though there is no double-slit device in its way.
In a
quantum eraser experiment,
one arranges to detect which one of the slits the photon passes
through, but also to construct the experiment in such a way that this
information can be "erased" after the fact.
In practice, this "erasure" of path information frequently means
removing the constraints that kept photons following two different paths
separated from each other.
In one experiment, rather than splitting one photon or its probability wave between two slits, the photon is subjected to a
beam splitter.
If one thinks in terms of a stream of photons being randomly directed
by such a beam splitter to go down two paths that are kept from
interaction, it is clear that no photon can then interfere with any
other or with itself.
Experiment that shows delayed determination of photon path
If the rate of photon production is reduced so that only one photon
is entering the apparatus at any one time, however, it becomes
impossible to understand the photon as only moving through one path
because when their outputs are redirected so that they coincide on a
common detector then interference phenomena appear.
In the two diagrams to the right, photons are emitted one at a
time from the yellow star. They each pass through a 50% beam splitter
(green block) that reflects 1/2 of the photons, which travel along two
possible paths, depicted by the red or blue lines.
In the top diagram, one can see that the trajectories of photons
are clearly known — in the sense that if a photon emerges at the top of
the apparatus it appears that it had to have come by the path that leads
to that point (blue line), and if it emerges at the side of the
apparatus it appears that it had to have come by way of the other path
(red line).
Next, as shown in the bottom diagram, a second beam splitter is
introduced at the top right. It can direct either beam towards either
path; thus note that whatever emerges from each exit port may have come
by way of either path.
It is in this sense that the path information has been "erased".
Note that total phase differences are introduced along the two
paths because of the different effects of passing through a glass plate,
being reflected off its first surface, or passing through the back
surface of a semi-silvered beam splitter and being reflected by the back
(inner side) of the reflective surface.
The result is that waves pass out of both the top upwards exit,
and also the top-right exit. Specifically, waves passing out the top
exit interfere destructively, whereas waves passing out the upper right
side exit interfere constructively.
A more detailed explanation of the phase changes involved here can be found in the
Mach-Zehnder interferometer article. Also, the experiment depicted above is reported in full in a reference.
[2]
If the second beam splitter in the lower diagram could be
inserted or removed one might assert that a photon must have traveled by
way of one path or the other if a photon were detected at the end of
one path or the other. The appearance would be that the photon "chose"
one path or the other at the only (bottom left) beam splitter, and
therefore could only arrive at the respective path end.
The subjective assurance that the photon followed a single path
is brought into question, however, if (after the photon has presumably
"decided" which path to take) a second beam splitter then makes it
impossible to say by which path the photon has traveled.
What once appeared to be a "black and white" issue now appears to
be a "gray" issue. It is the mixture of two originally separated paths
that constitutes what is colloquially referred to as "erasure." It is
actually more like "a return to indeterminability."
The experiment
The experimental setup, described in detail in the original paper
[1],
is as follows. First, a photon is generated and passes through a double
slit apparatus (vertical black line in the upper left hand corner of
the diagram).
The photon goes through one (or both) of the two slits, whose
paths are shown as red or light blue lines, indicating which slit the
photon came through (red indicates slit A, light blue indicates slit B).
So far, the experiment is like a conventional two-slit experiment. However, after the slits a
beta barium borate crystal (labeled as BBO) causes
spontaneous parametric down conversion (SPDC), converting the photon (from either slit) into two identical
entangled photons with 1/2 the frequency of the original photon. These photons are caused to diverge and follow two paths by the
Glan-Thompson Prism.
One of these photons, referred to as the "signal" photon (look at the red and light-blue lines going
upwards from the Glan-Thompson prism), continues to the target detector called D
0. The positions where these "signal" photons detected by D
0 occur can later be examined to discover if collectively those positions form an interference pattern.
The other entangled photon, referred to as the "idler" photon (look at the red and light-blue lines going
downwards
from the Glan-Thompson prism), is deflected by a prism that sends it
along divergent paths depending on whether it came from slit A or slit
B.
Somewhat beyond the path split,
beam splitters
(green blocks) are encountered that each have a 50% chance of allowing
the idler to pass through and a 50% chance of causing it to be
reflected. The gray blocks in the diagram are mirrors.
Because of the way the beam splitters are arranged, the idler can be detected by detectors labeled D
1, D
2, D
3 and D
4. Note that:
If it is recorded at detector D
3, then it can only have come from slit B.
If it is recorded at detector D
4 it can only have come from slit A.
If the idler is detected at detector D
1 or D
2, it might have come from
either slit (A or B).
Thus, which detector receives the idler photon either reveals
information, or specifically does not reveal information, about the path
of the signal photon with which it is entangled.
If the idler is detected at either D
1 or D
2, the which-path information has been "erased", so there is
no way of knowing whether it (and its entangled signal photon) came from slit A or slit B.
Whereas, if the idler is detected at D
3 or D
4, it
is known that it (and its entangled signal photon) came from slit B or slit A, respectively.
By using a
coincidence counter,
the experimenters were able to isolate the entangled signal from the
overwhelming photo-noise of the laboratory - recording only events where
both signal and idler photons were detected.
When the experimenters
looked only at the signal photons whose entangled idlers were detected at D
1 or D
2, they found an interference pattern.
However, when they looked at the signal photons whose entangled idlers were detected at D
3 or similarly at D
4,
they found no interference.
This result is similar to that of the double-slit experiment,
since interference is observed when it is not known which slit the
photon went through, while no interference is observed when the path is
known.
However, what makes this experiment possibly astonishing is that,
unlike in the classic double-slit experiment, the choice of whether to
preserve or erase the which-path information of the idler need not be
made until
after the position of the signal photon has already been measured by D
0.
There is never any which-path information determined directly for the photons that are detected at D
0, yet detection of which-path information by D
3 or D
4 means that no interference pattern is observed in the corresponding subset of signal photons at D
0.
The results from Kim, et al.
[1] have shown that whether the idler photon is detected at a detector that preserves its which-path information (D
3 or D
4) or a detector that erases its which-path information (D
1 or D
2) determines whether interference is seen at D
0, even though the idler photon
is not observed until after the signal photon arrives at D
0 due to the shorter optical path for the latter.
Some have interpreted this result to mean that the delayed choice
to observe or not observe the path of the idler photon will change the
outcome of an event in the past. However, an interference pattern may
only be observed
after the idlers have been detected (i.e., at D
1 or D
2).
Note that the total pattern of all signal photons at D
0,
whose entangled idlers went to multiple different detectors, will never
show interference regardless of what happens to the idler photons.
[3]
One can get an idea of how this works by looking carefully at both the
graph of the subset of signal photons whose idlers went to detector D
1 (fig. 3 in the paper
[1]), and the graph of the subset of signal photons whose idlers went to detector D
2
(fig. 4), and observing that the peaks of the first interference
pattern line up with the troughs of the second and vice versa (noted in
the paper as "a π phase shift between the two interference fringes"), so
that the sum of the two will not show interference.
Time relations among data
Raw results for D
0 are all delivered to the same detector regardless of what happens at the other detectors.
Raw results for D
0 can be sorted according to correspondences with the other detectors,1 through 4
By noting which photons reaching Detector 0 correspond with photons
reaching Detectors 1, 2, 3, and 4, it is possible to sort photon records
collected by Detector 0 into four groups. Only then will it become
possible to see interference patterns in two groups and only diffraction
patterns in the other two groups. If there were no coincidence counter,
then there would be no way to distinguish any photon that arrives at
Detector 0 from any other photon that reaches it.
Photons will not reach detectors one through four in regular
rotation, so the only way to sort out the photons that are entangled
twins with the ones that reached each of those detectors is to group
them according to which of those four detectors was activated when a
photon reached Detector 0. Note that in the schematic diagrams the
fringes or interference patterns imaged by Detector 1 and Detector 2
will add together to form a solid band. The addition of the diffraction
patterns paired with the diffraction patterns seen by Detector 3 and
Detector 4 will make the center area somewhat brighter than it would
otherwise be, but would have no other influence on the confused picture
produced by the raw data gathered at Detector 0.
It is impossible to know which group a photon appearing at Detector 0 at time T
1 may belong to until
after its entangled partner is found at one of the other detectors and their coincidence is measured at some slightly later time T
2.
Discussion
Problems with using retrocausality
This delayed choice quantum eraser experiment raises questions about
time, time sequences, and thereby brings our usual ideas of time and
causal sequence into question. If a determining factor in the
complicated (lower) part of the apparatus determines an outcome in the
simple part of the apparatus that consists of only a lens and a
detection screen, then effect seems to precede cause. So if the light
paths involved in the complicated part of the apparatus were greatly
extended in order that, e.g., a year might go by before a photon showed
up at D
1, D
2, D
3, or D
4,
then when a photon showed up in one of these detectors it would cause
the photon in the upper, simple part of the apparatus to have shown up
in a certain mode a year earlier. Perhaps by re-routing light paths to
the four detectors during that one year so that the number of possible
outcomes is reduced to two or even perhaps to one, then the experimenter
could send a signal back through time.
Changing between the first
possible arrangement and second possible arrangement of parts in the
complicated part of the experiment would then function like the opening
and closing of a telegraph key. An objection that seems fatal is soon
raised: The photons that show up in D
1 through D
4 do not follow some regular rotation. Therefore the photons that show up in D
0
pile onto the same detection screen in random order. There is no way to
tell, by simply looking at the time and place of each photon detected
using D
0, which of the other four detectors it corresponds
to. So the result will be like trying to watch a motion picture screen
on which four projectors are focused. The whole screen will be awash
with light. In order to segregate the photons arriving at D
0
into the ones that will form one or the other of two overlapping fringe
patterns and also the two diffraction patterns, it will be necessary to
know how to collect them into four sets. But to do that it is necessary
to get messages from the second part of the experiment about which
detector was involved with the detection of the entangled partner of
each photon received at D
0. To oversimplify a bit, the data collected at D
0
would be like an encrypted message. However, it could only be decrypted
when the key to the code was delivered by a message that could travel
at no faster than the speed of light. This daunting obstacle to sending
messages back in time has not, however, stopped all researchers from
trying to find some way of getting around the stumbling block.
Details pertaining to retrocausality in the Kim experiment
In their paper, Kim, et al.
[1] explain that the concept of
complementarity is one of the most basic principles of quantum mechanics. According to the
Heisenberg Uncertainty Principle,
it is not possible to precisely measure both the position and the
momentum of a quantum particle at the same time. In other words,
position and momentum are
complementary. In 1927,
Niels Bohr
maintained that quantum particles have both "wave-like" behavior and
"particle-like" behavior, but can exhibit only one kind of behavior
under conditions that prevent exhibiting the complementary
characteristics. This complementarity has come to be known as the
wave-particle duality of quantum mechanics.
Richard Feynman
believed that the presence of these two aspects under conditions that
prevent their simultaneous manifestation is the basic mystery of quantum
mechanics.
According to Kim, et al., "The actual mechanisms that enforce complementarity vary from one experimental situation to another."
[1]
In the double-slit experiment, the common wisdom is that
complementarity makes it seemingly impossible to determine which slit
the photon passes through without at the same time disturbing it enough
to destroy the interference pattern. A 1982 paper by Scully and Drühl
circumvented the issue of disturbance due to direct measurement of the
photon,
[4]
according to Kim, et al. Scully and Drühl "found a way around the
position-momentum uncertainty obstacle and proposed a quantum eraser to
obtain which-path or particle-like information without introducing large
uncontrolled phase factors to disturb the interference."
[1]
Scully and Drühl found that there is no interference pattern when
which-path information is obtained, even if this information was
obtained without directly observing the original photon, but that if you
somehow "erase" the which-path information, an interference pattern is
again observed.
In the delayed choice quantum eraser discussed here, the pattern
exists even if the which-path information is erased shortly later in
time than the signal photons hit the primary detector. However, the
interference pattern can only be seen retroactively once the idler
photons have already been detected and the experimenter has obtained
information about them, with the interference pattern being seen when
the experimenter looks at particular
subsets of signal photons that were matched with idlers that went to particular detectors.
The main stumbling block for using retrocausality to communicate information
The total pattern of signal photons at the primary detector never
shows interference, so it is not possible to deduce what will happen to
the idler photons by observing the signal photons alone, which would
open up the possibility of gaining information
faster-than-light
(since one might deduce this information before there had been time for
a message moving at the speed of light to travel from the idler
detector to the signal photon detector) or even gaining information
about the future (since as noted above, the signal photons may be
detected at an earlier time than the idlers), both of which would
qualify as violations of
causality
in physics. The apparatus under discussion here could not communicate
information in a retro-causal manner because it takes another signal,
one which must arrive via a process that can go no faster than the speed
of light, to sort the superimposed data in the signal photons into four
streams that reflect the states of the idler photons at their four
distinct detection screens.
In fact, a theorem proved by Phillippe Eberhard shows that if the accepted equations of
relativistic quantum field theory are correct, it should never be possible to experimentally violate causality using quantum effects
[5] (see reference
[6] for a treatment emphasizing the role of conditional probabilities).
Yet there are those who persevere in attempting to communicate retroactively
Some physicists have speculated about the possibility that these
experiments might be changed in a way that would be consistent with
previous experiments, yet which could allow for experimental causality
violations.
[7][8]
See also
References
- ^ a b c d e f g Kim, Yoon-Ho; R. Yu, S.P. Kulik, Y.H. Shih, and Marlan Scully (2000). "A Delayed Choice Quantum Eraser". Physical Review Letters 84: 1–5. arXiv:quant-ph/9903047. Bibcode 2000PhRvL..84....1K. DOI:10.1103/PhysRevLett.84.1.
- ^ Jacques,
Vincent; Wu, E; Grosshans, Frédéric; Treussart, François; Grangier,
Philippe; Aspect, Alain; Rochl, Jean-François (2007). "Experimental Realization of Wheeler's Delayed-Choice Gedanken Experiment". Science 315 (5814): pp. 966–968. arXiv:quant-ph/0610241. Bibcode 2007Sci...315..966J. DOI:10.1126/science.1136303. PMID 17303748.
- ^ Greene, Brian (2004). The Fabric of the Cosmos. Alfred A. Knopf. p. 198. ISBN 0-375-41288-3.
- ^ Scully, Marlan O.;
Kai Drühl (1982). "Quantum eraser: A proposed photon correlation
experiment concerning observation and "delayed choice" in quantum
mechanics". Physical Review A 25 (4): 2208–2213. Bibcode 1982PhRvA..25.2208S. DOI:10.1103/PhysRevA.25.2208.
- ^ Eberhard, Phillippe H.; Ronald R. Ross (1989). "Quantum field theory cannot provide faster-than-light communication". Foundations of Physics Letters 2 (2): p. 127–149. Bibcode 1989FoPhL...2..127E. DOI:10.1007/BF00696109.
- ^ Bram Gaasbeek. Demystifying the Delayed Choice Experiments. arXiv preprint, 22 July 2010.
- ^ John G. Cramer. NASA Goes FTL - Part 2: Cracks in Nature's FTL Armor. "Alternate View" column, Analog Science Fiction and Fact, February 1995.
- ^ Paul J. Werbos, Ludmila Dolmatova. The Backwards-Time Interpretation of Quantum Mechanics - Revisited With Experiment. arXiv preprint, 7 August 2000.
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