Feynman's double-slit experiment

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Here's my puzzle...

Electrons through a single slit one at time - standard distribution
Electrons through a double slit one at a time - interference pattern
Set up a detector to observe which slit the electrons passed through - back to a standard distribution.

This is all well and good. In searching for the origin of this story I found it comes from Feynman's Lectures On Physics. Nice one, Richard.

The problem I have is this. The description given by Feynman appears to be a mere thought experiment. However, the result is quoted in many places as an actual result. I've tried to find the relevant papers which might have shown this result but have so far failed.

My question is then, does anybody know where this result has been shown to hold? And if nobody has actually shown this result, why is the story constantly told (especially in awful popular media - I'm looking at you Wikipedia) that this is the great lesson of the double-slit experiment?

Any ideas?

Pete
 

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  • #2
Born2bwire
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I'm terribly sorry, I've been totally unclear!

The result I'm calling into question is the breakdown of the interference pattern once the electrons are being detected as going through one slit or the other.

Feynman's thought experiment suggests a light source hidden behind the metal plate with the slits in it and between the slits, the sort of place you'd expect to be able to bounce photons off each electron as it passes through. My question is, has anybody done this? (and I suspect not!)
 
  • #4
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The result I'm calling into question is the breakdown of the interference pattern once the electrons are being detected as going through one slit or the other.[...]My question is, has anybody done this? (and I suspect not!)
What do you expect? That the pattern remains regardless (vindicating realism afterall)?

It's been done, in different ways. The ten-dollar way is to replace the electrons with photons, and mark which slit each went through by rotating its polarisation or not; cross-polarised light doesn't interfere, but you can erase the marking and recover the pattern by putting a diagonal polariser in front of the screen. See "quantum eraser" on "google scholar".
 
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  • #5
Demystifier
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Feynman's thought experiment suggests a light source hidden behind the metal plate with the slits in it and between the slits, the sort of place you'd expect to be able to bounce photons off each electron as it passes through. My question is, has anybody done this? (and I suspect not!)
It has been done many times. It's actually considered too trivial to make explicit reports in the literature.
 
  • #6
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I don't know what variations on the experiment have been carried out since Feymann's Lectures were published in 1964, but I'm quite sure that at the time he was describing a thought experiment, as the OP suggests.
 
  • #7
DrChinese
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It has been done many times. It's actually considered too trivial to make explicit reports in the literature.
As Demystifier says, you really already know the exact answer.

You knew there was an interference pattern with 2 slits. Now cover up the left one. What do you get? It's just a one slit pattern (as mentioned, no interference). Now cover up the right slit (leaving left open).

Since neither
nor
show any interference, obviously [both open] is not equal to
+
. That's 'bout it.​
 
  • #8
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But surely there are other ways of detecting which slit the electron went through then simply covering up one slit? When you cover a slit up it's no longer a double slit, so why would you even do that?

I've been wondering this myself... Is the disappearance of an interference pattern a truly quantum effect (because interference cannot occur) or is it merely because we somehow 'block' the electron (by covering up a slit, or by other means)? Or is that really the same thing?
 
  • #9
DrChinese
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But surely there are other ways of detecting which slit the electron went through then simply covering up one slit? When you cover a slit up it's no longer a double slit, so why would you even do that?

I've been wondering this myself... Is the disappearance of an interference pattern a truly quantum effect (because interference cannot occur) or is it merely because we somehow 'block' the electron (by covering up a slit, or by other means)? Or is that really the same thing?
Yes, there are other ways too. For light, you use polarizers set orthogonally (crossed). The interference pattern disappears. You can also put a detector behind one slit. But really, if you think the particle went through a specific slit, then closing off one slit entirely should be enough.

[Now, please note that there are interpretations (Bohmian) in which the particle goes through a specific slit while the hypothetical guide wave goes through both slits. These do not make any difference to the predicted outcome, however.]
 
  • #10
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Thanks very much to those that replied. That cross polarisation experiment with photons was the sort of thing I was looking for.

In response to some of the other omments, my question was much more subtle than I originally let on. I have no doubt that detection of which slit the particle went through will destroy the interference pattern. I'm concerned about how one should read Feynman's comments.

If Feynman is quoting a result from an experiment he knew of and then giving an ontological explanation, this is quite different from proposing what he thinks would happen if such an experiment were carried out. If the latter is the case, then any discussion of the interpretation of quantum mechanics would not need to account for such a result in the body of evidence which needs explaining - simply because there would be no evidence indicating that that might be the case.

I suspected the quantum eraser experiments might address the same issue but I was especially interested find out if anyone had used anything but photons to show the effect.
 
  • #11
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Actually, it is misleading to claim that path knowledge definitely disturbs the interference. At the very least, the jury is still out but here are some experiments which prove otherwise:
* R. Sillitto, and C. Wykes, Phys. Lett. A 39, 333 (1972): two slits with only one open at a time. Interference fringes clearly observed
* E. Fonseca, P. S. Ribeiro, S. Padua, and C. Monken, Phys. Rev. A 60, 1530 (1999): complete path knowledge was obtained for all photons and interference persisted
* L. Basano, and P. Ottonello, Am. J. Phys 68, 245 (2000). Two laser sources, photons from each can only pass through a single slit. Path knowledge complete yet interference obtained.
* C. Santori, et al., Nature 419, 594 (2002): Complete path knowledge, interference obtained

Oh, and the above experiments together with a hand full of others rule out self-interaction which is the current dogma. For example:
* Yu. Dontsov, and A. Baz, Sov. Phys - JETP 25, 1 (1967). Interference disappeared when the photon flux was drastically reduced by placing neutral density filters before the slits but not by placing filters after the slits.
* Y.-H. Kim, et al., Phys. Rev. A 61(R), 051803 (2000). By making sure only one photon was in the system at a given time and controlling the interval between successive photons, the appearance/disappearance of interference was heavily dependent on the time interval.
 
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  • #12
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Actually, it is misleading to claim that path knowledge definitely disturbs the interference. [...] here are some experiments which prove otherwise:
[...PRA 60 p1530 (99):] complete path knowledge was obtained for all photons and interference persisted
mn4j, I picked the reference for which your description sounded the strongest, but it appears your interpretation is false. In that experiment the interference is occurring because there is no way to know which slit of effective-aperture A1A2 the photons go through.
 
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  • #13
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One means that would not destroy phase information until after the passage of the electron is by measuring the recoil imparted to the slit. Good luck with that. As far as the cross polarizers goes, it requires that the observer not be entangled with information as to the orientation of the polarizers until after the electron has passed. I haven't been following along with this stuff. What you might be interested in might go by the name delayed choice.

Earlier than Feynman, Bohr invoked the double slit which-way thought experiment in his reply to EPR.
 
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  • #14
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mn4j, I picked the reference for which your description sounded the strongest, but it appears your interpretation is false. In that experiment the interference is occurring because there is no way to know which slit of effective-aperture A1A2 the photons go through.
Of course you fail to realize that there is no effective aperture. There are two apertures (A1 and A2) and each photon passes only through one but not the other. There are also two separate detectors, one for each aperture and it is obvious from the experiment which aperture the photon went through, yet by considering coincident counts between the apertures interference fringes can be obtained from the results, even though simply adding up the results of both does not give interference. What you call "effective aperture" is not an aspect of the experiment but a method of interpreting the results of the experiments. Unless you have a penchant for mysticism you will not suggest that the photons knew how the results would be interpreted.

This experiment clearly casts doubts to suggestions that knowing the path of the photons somehow disturb the interference. In case you are tempted to suggest that the interference is due to not knowing which side of A2 it the photon passed through, realize that D2 alone did not give an interference pattern without considering the coincidence counts at D1 (see Fig 5).
 
  • #15
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Of course you fail to realize that there is no effective aperture. There are two apertures (A1 and A2) and each photon passes only through one but not the other. There are also two separate detectors, one for each aperture and it is obvious from the experiment which aperture the photon went through[.... mysticism ...] In case you are tempted to suggest that the interference is due to not knowing which side of A2 it the photon passed through, realize that D2 alone did not give an interference pattern without considering the coincidence counts at D1 (see Fig 5).
If there is no effective aperture, why do the experimenters go to such length in reporting its characteristics? (I don't have the article in front of me today, but you'll no doubt see that it is the slit separation of the effective aperture which determines the angles of the interference maxima.)

Are you aware that the pair of photons produced in the crystal are momentum-entangled? This means they both go through complementary positions of their respective apertures. In other words, by selecting only coincidences (where neither photon has been blocked by its respective aperture) it is guaranteed that both photons have gone through the doubly-restricted space of the effective-aperture (and you could confirm this using detection rates).

Of course there is no raw pattern at D2, this is an entanglement experiment after all: If a lens is placed in front of D1 then (Wheeler's CCD at) D1 could tell exactly which part of each aperture was traversed by both photons (including the one to D2, which would contradict quantum interfering of possible paths, a la Cramer's discredited FTL communicator. Another way of viewing this is that the spontaneously emitted photon pair does not have the coherence of a laser: neither beam alone could be used directly to produces raw double-slit interference because it would not reach both sides of the aperture in constant phase). Rather, the geometry has been chosen such that D1 measures the phase difference of the possible paths (e.g., coincidence with D1 selects the photons at D2 which, in equal phase, could have traversed paths through both slits of the effective-aperture, and hence produce a sinc pattern).
 
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  • #16
Cthugha
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* C. Santori, et al., Nature 419, 594 (2002): Complete path knowledge, interference obtained
I do not know about the other papers, but I know this paper very well and it is about indistinguishability of consecutive photons from a single quantum dot. What they use to show this indistinguishability is Hong-Ou-Mandel interference, which is a consequence of the bosonic nature of photons: two photons incident on a 50-50 beamsplitter with perfect overlap will always leave the beamsplitter together at the same exit ports. This is an intrinsic two-photon interference effect, which should not be mixed up with the single photon interference pattern you get in a double slit experiment. In fact Zeilinger even showed that single photon interference and two photon interference are complementary. You cannot have both at the same time with good contrast. So in fact any demonstration of two-photon interference when the path is known shows directly that there is no single photon interference present.

After a brief look at the other references it seems to me, that they are about two photon interference, too, although I need to take some time to be sure. However, it seems your argument is void. A lot of people do not get the difference between single photon interference and two photon interference. This topic is covered very well in the bible of quantum optics ("Optical coherence and quantum optics" by Mandel and Wolf).
 
  • #17
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If there is no effective aperture, why do the experimenters go to such length in reporting its characteristics? (I don't have the article in front of me today, but you'll no doubt see that it is the slit separation of the effective aperture which determines the angles of the interference maxima.)
You keep talking about effective aperture as if there is ever a single aperture. There are two, period. When superimposed, they become equivalent to a double slit. So what you call "effective aperture" is not anything the photons care about but a result of post-processing of the data. Every photon that went through A1 went ONLY through A1, and every photon that went through A2 went only through A2. Every photon detected at D1 went ONLY through A1 and every photon detected at D2 went only through A2. Note that, when D2 is kept fixed and D1 is moved, you get interference and vice versa. Consider the former situation, note that A1 is equivalent to a single slit and that D1 only measures photons which have gone through A1. It is therefore obvious that there is complete path knowledge for every photon arriving at D1.

See the following for similar experiments without the "indistinguishability loophole":
* Z. Y. Ou, X. Y. Zou, L. J. Wang, and L. Mandel, Phys. Rev. Lett. 65, 321-324 (1990).
* P. G. Kwiat, et al., Phys. Rev. A 41, 2910-2913 (1990)


This clearly casts doubts to the idea that path knowledge has anything to do with appearance or disappearance of interference and also points to the fact that interference is a multi-photon phenomenon. You can argue that entanglement is involved, which doesn't obviate the fact that more than one photon is involved.
 
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  • #18
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This is an intrinsic two-photon interference effect, which should not be mixed up with the single photon interference pattern you get in a double slit experiment.
I challenge you to show me a single experiment where single photon interference was confirmed. In order to prove self-interference, the experiment must meet the following criteria:

1 It must ensure that photons do not overlap in transit
2 The coherence time of the source must exceed the interval between two photon emissions
3 with 1, and 2 valid, interference fringes must be obtained for arbitrary intervals between any two detections. In other words, the interval between durations should not matter.

So my challenge is for you to show me an experiment which met all three criteria above, failing which you can not claim self-interference has been experimentally verified. I've given you two examples which rule out single photon-interference or what is also called (self-interference), see the Dontsov and Baz paper I quoted above for a start. Self-interference is a myth.

A lot of people do not get the difference between single photon interference and two photon interference. This topic is covered very well in the bible of quantum optics ("Optical coherence and quantum optics" by Mandel and Wolf).
I will wait for you to show me convincing evidence of self-interference or what you call single photon interference.
 
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  • #19
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I challenge you to show me a single experiment where single photon interference was confirmed.
If there were no single photon interference, quantum mechanics would be wrong.
 
  • #20
Cthugha
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I challenge you to show me a single experiment where single photon interference was confirmed. In order to prove self-interference, the experiment must meet the following criteria:

1 It must ensure that photons do not overlap in transit
2 The coherence time of the source must exceed the interval between two photon emissions
3 with 1, and 2 valid, interference fringes must be obtained for arbitrary intervals between any two detections. In other words, the interval between durations should not matter.
I do not see, why these conditions should be necessary to prove self-interference. In fact 1) and 2) even contradict each other because coherence time is a measure of the time during which several photons are indistinguishable. While I agree that 1) is necessary, 2) must be converted to the opposite: (first order) coherence time must be shorter than the interval between two photon emissions. Otherwise you can never verify that you produced a Fock state. The further process is then very easy. You just need to do a HBT-experiment on your light source to demonstrate that antibunching is present by showing that the equal time intensity correlation function is zero. Then you direct this emission towards a double slit, where the slit seperation is still small compared to the coherence length of the emission. Additionally you have to ensure that the recoil of the photon emission does not give any information about the photon path. Although this is rather trivial maybe someone thought of it as interesting enough to publish it. I will check when I have access to the library of my university again.

I've given you two examples which rule out single photon-interference or what is also called (self-interference), see the Dontsov and Baz paper I quoted above for a start. Self-interference is a myth.
This paper is not quoted very often and two of the quotes are articles called "How to judge flawed science" and "'Pseudo-Effects' in Experimental Physics: Some Notes for Case-Studies", which makes this article look very suspicious. However, I will have a look at it when I am back in the office. Now I do not have access to that paper.

edit: If I remember correctly "Experimental Evidence for a Photon Anticorrelation Effect on
a Beam Splitter: A New Light on Single-Photon Interferences." by P. Grangier, G. Roger and A. Aspect should do the trick: Europhys. Lett., 1 (4), pp. 173-179 (1986)

They use a cascaded decay instead of a quantum dot and a Mach-Zehnder interferometer instead of a double slit, but that should not change anything.
 
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  • #21
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I do not see, why these conditions should be necessary to prove self-interference. In fact 1) and 2) even contradict each other because coherence time is a measure of the time during which several photons are indistinguishable. While I agree that 1) is necessary, 2) must be converted to the opposite: (first order) coherence time must be shorter than the interval between two photon emissions. Otherwise you can never verify that you produced a Fock state.
The reason for 2) is to ensure that the source is still coherent from one photon emission to another, so that it is not claimed later that failure to observe interference was due to absence of coherence in the source, rather that absence of self-interference. (Do you disagree with this?) This in no way contradicts the requirement that the two photons not overlap in transit.


1) Photons must not overlap in transit. (We agree on this condition)
3) Appearance/disapearance of fringes must not depend on time lag between photons going through the device. If the fringes are due to self-interference, the duration of the time lag between photons should not influence the results. (Do you disagree with this?)

Unless an experiment also fulfills (3), it has not demonstrated self-interference. However, the experiments I quoted above show that the duration of the time lag matters.

edit: If I remember correctly "Experimental Evidence for a Photon Anticorrelation Effect on
a Beam Splitter: A New Light on Single-Photon Interferences." by P. Grangier, G. Roger and A. Aspect should do the trick: Europhys. Lett., 1 (4), pp. 173-179 (1986)
This experiment meets criteria (1) but not (3) therefore it does not prove self-interference.

In case it is still not clear to you how (3) is necessary, realize that it is possible for a photon passing through a device to leave side-effects in the device that will influence the next photon arriving at the device, even if they never overlap in transit. However, such side-effects will decay with time and should be sensitive to the duration of the time lag. Such interference effects are essentially multi-photon interference. That is why (3) is necessary. Note also that the experiments I cited above showed that the appearance of fringes was dependent on the time lag between photons. This certainly rules out self-interference.
 
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  • #22
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You keep talking about effective aperture [...]
I kept giving quantitative predictions, just show them to be false and you win. You, however, seem merely to cite experiments that you do not fully understand as though that were evidence for some vague hand-wavey departure from mainstream QM. Your argument is akin to looking at a http://en.wikipedia.org/wiki/Diffraction#Single-slit_diffraction" pattern and reciting complete knowledge of broadly which aperture it went through: a strawman denial of the precision welcher weg implies.
I challenge you to show me a single experiment where single photon interference was confirmed.
http://www.teachspin.com/instruments/two_slit/index.shtml" [Broken] photon per hour passes from the collimator to the aperture, the cumulative pattern will be the same as for an unattenuated beam.
 
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  • #23
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I kept giving quantitative predictions, just show them to be false and you win. You, however, seem merely to cite experiments that you do not fully understand as though that were evidence for some vague hand-wavey departure from mainstream QM. Your argument is akin to looking at a http://en.wikipedia.org/wiki/Diffraction#Single-slit_diffraction" pattern and reciting complete knowledge of broadly which aperture it went through: a strawman denial of the precision welcher weg implies.
You are projecting here. I won't waste my time trying to explain to you the difference between a virtual double slit and an actual double slit.
http://www.teachspin.com/instruments/two_slit/index.shtml" [Broken] photon per hour passes from the collimator to the aperture, the cumulative pattern will be the same as for an unattenuated beam.
Good! Then it should be trivial for you to show me where such an experiment was actually done and the results show that the cumulative pattern was the same. If as you claim a trivial experiment can prove self-interference, your failure to produce one realization of such an experiment will be very telling. I'm waiting.

In the mean time, I have provided multiple rexamples of realization of this so-called trivial experiment, in which interference vanished when the flux was reduced and the time lag was increased.
 
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  • #24
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it should be trivial for you to show me where such an experiment was actually done [single photon at a time twin-slit] and the results show that the cumulative pattern was the same.
It's a common teaching lab experiment, see http://www.physics.brown.edu/physics/demopages/Demo/modern/demo/7a5520.htm" or Am.J.Phys 39 p420 (1971).
I have provided multiple [examples..] of realization of this so-called trivial experiment, in which interference vanished when the flux was reduced and the time lag was increased.
If you don't mind, could you specify exactly which citation(s) you think demonstrate a trivial "single photon at a time" twin-slit experiment in which the pattern alters at very low intensities? And if it isn't too much trouble, could you also explain why it hasn't revolutionised quantum physics?
 
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  • #25
Cthugha
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The reason for 2) is to ensure that the source is still coherent from one photon emission to another, so that it is not claimed later that failure to observe interference was due to absence of coherence in the source, rather that absence of self-interference. (Do you disagree with this?) This in no way contradicts the requirement that the two photons not overlap in transit.
Yes, I disagree. If the source is coherent from one photon emission to another those two photons are automatically indistinguishable and can by definition interfere. In this case it is not possible to ensure that these photons do not overlap. To have a shorter coherence time automatically rules out the possibility of first order interference coming from two different photons. I see that there might be a loophole left in an experiment, which tries to disprove single photon interference. However for an experiment trying to show single photon interference 2) is anyway by no means necessary.

3) Appearance/disapearance of fringes must not depend on time lag between photons going through the device. If the fringes are due to self-interference, the duration of the time lag between photons should not influence the results. (Do you disagree with this?)
Do you mean the time lag between several detected photons (1) or the time lag between two paths, which lead to the detection of a photon (2)? The experiment I gave you fulfills (1) (the time lag between consecutive detections is stochastic and the time lag is modified drastically by introducing the heralded/gated detection scheme), while it is impossible to fulfill (2) due to the limited coherence time of the emission.

Note also that the experiments I cited above showed that the appearance of fringes was dependent on the time lag between photons. This certainly rules out self-interference.
Which one? The Kwiat paper is about two photon interference. The Kim paper shows that the important point in creating interference is the indistinguishability between different probability amplitudes (or Feynman path amplitudes if you prefer) and shows that an interference pattern in the angular distribution of some SPDC signal vanishes if you have just one out of initially two pump beams left. This vanishing is trivial as very is no interferometer, double slit or anything left, which geven gives the possibility to have two different paths. The "paths" are given solely by the two different pump beams. The Dontsov paper is widely agreed on to be plain wrong. See for example "New Approach to Experiments on Low Intensity Interference" by D. N. PINDER & R. N. GOULD (Nature 221, 460 - 461 (01 February 1969)), which actually gives a detailed discussion.

Good! Then it should be trivial for you to show me where such an experiment was actually done and the results show that the cumulative pattern was the same. If as you claim a trivial experiment can prove self-interference, your failure to produce one realization of such an experiment will be very telling. I'm waiting.
Reference 8 in the paper I mentioned before already does that. Another good realization can be found in:
Am. J. Phys. Vol. 64, No. 2, Feb 1996, Pages 184-188
A lecture demonstration of single photon interference
Wolfgang Rueckner and Paul Titcomb

This more or less tells how to show this effect in an undergrad lab.
 

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