One Electron at a Time?

Nicky
In the electron double-slit experiment performed by Tonomura et al. (http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000057000002000117000001&idtype=cvips&gifs=yes [Broken]) it is claimed that only one electron can be in the apparatus at a time, because the electron wavepacket is much smaller than the effective distance between electrons.
The distance from the source to the screen is 1.5m, while the average interval of successive electrons is 150 km. In addition, the length of the electron wave packet is as short as ~1 um. Therefore, there is very little chance for two electrons to be present simultaneously between the source and the detector, and much less chance for two wave packets to overlap.
I am wondering whether this assumption is valid. How can they be sure that each electron is so localized when they do not measure its position prior to its striking the photodetector screen? In other words, how do they know that the beam is a sequence of discrete bursts and not a continuous flux, other than the final result of a hit on the photodetector?

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Staff Emeritus
Nicky said:
In the electron double-slit experiment performed by Tonomura et al. (http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000057000002000117000001&idtype=cvips&gifs=yes [Broken]) it is claimed that only one electron can be in the apparatus at a time, because the electron wavepacket is much smaller than the effective distance between electrons.

I am wondering whether this assumption is valid. How can they be sure that each electron is so localized when they do not measure its position prior to its striking the photodetector screen? In other words, how do they know that the beam is a sequence of discrete bursts and not a continuous flux, other than the final result of a hit on the photodetector?

The devil is in the DETAILS of the experimental setup, including how they create and then "process" the electrons. What you get is the number of electrons being produced per unit time and the KE of those electrons. You get get a statistics on the average distance between these electrons. Luckily, you don't just rely on calculations, but rather you have to first test this out before doing the experiment. Your counter has to be calibrated to be sensitive to at least the detection of 1 electron. Based on this, one can tell if one is detecting a series of 1 electrons within the calculated time interval.

Only after this can one perform the experiment and be certain that one is getting only 1 electron at a time in the apparatus.

Zz.

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Nicky
ZapperZ said:
[...]Your counter has to be calibrated to be sensitive to at least the detection of 1 electron. Based on this, one can tell if one is detecting a series of 1 electrons within the calculated time interval.[...]

Presumably this calibration step would involve some kind of position measurement parallel to the beam direction. Such measurement would be necessary to establish the "distance between electrons" to which Tonomura et al. refer. But then the Born rule implies that the calibration doesn't just observe the beam's localization in the measured variable -- it creates that localization. The beam coming into the calibration device could still have a continuous, many-particle character, even though it emerges from the calibration device as localized, single-particle pulses.

Here is another way of looking at the experiment: let's say the electron source is a sharp, conducting needle at high voltage. That needle forms a potential well in which many thousands (millions?) of electrons are trapped. Also assume the surface of the detection screen is held at a voltage of opposite polarity to the needle. This forms a second potential well in the vacuum gap between the needle and the screen.

Both potential wells (needle and vacuum gap) have their own bound states. The needle's bound states are almost all full, whereas the vacuum gap's bound states are almost all empty. Nevertheless, wouldn't the needle states and gap states be hybridized, such that all the thousands of electrons are in a superposition of needle+gap states? If that is the case, then we could view the detection events not as the measurement of a single electron that's already in flight, but as creation of an electron-hole pair -- the electron is the one measured and absorbed in the detector, and the hole cancels one of the hybridized needle+gap states.

If this view is wrong, what am I missing?

Staff Emeritus
Nicky said:
Presumably this calibration step would involve some kind of position measurement parallel to the beam direction. Such measurement would be necessary to establish the "distance between electrons" to which Tonomura et al. refer.

No, not really. Naively, all it involves is the measurement of how many "clicks" per second. Knowing how much KE each electron had (since it went through the same potential gradient), I can easily tell you how far apart on average each electron is.

Zz.

Nicky
ZapperZ said:
No, not really. Naively, all it involves is the measurement of how many "clicks" per second. Knowing how much KE each electron had (since it went through the same potential gradient), I can easily tell you how far apart on average each electron is.

What's clicking? Is it the same screen that displays the interference pattern?

Staff Emeritus
Nicky said:
What's clicking? Is it the same screen that displays the interference pattern?

I used "clicks" as metaphor for detection. After all, that's what they're doing, aren't they, detecting one electron at a time?

Zz.

Nicky
ZapperZ said:
I used "clicks" as metaphor for detection. After all, that's what they're doing, aren't they, detecting one electron at a time?

That's exactly my question. Is it "detecting one electron at a time" or "one electron-detection event at a time". I'm thinking one electron isn't plucked out of the many-particle system made up of source+vacuum gap until the moment of detection.

Staff Emeritus
Nicky said:
That's exactly my question. Is it "detecting one electron at a time" or "one electron-detection event at a time". I'm thinking one electron isn't plucked out of the many-particle system made up of source+vacuum gap until the moment of detection.

No, we CAN detect one electron at a time. Unlike photon detection in which the quantum efficiency of detector doesn't approach 100% (we'd be lucky if it's 50% without applied potential), electron detection can be quite close to 100%.

It is why I've always argued that until more Bell-type experiments can be done using electrons and other charged particles (there have been a few already), we'll never silence those skeptics who are clutching at the last straw they can via the detection loophole.

Zz.

Nicky
ZapperZ said:
No, we CAN detect one electron at a time. Unlike photon detection in which the quantum efficiency of detector doesn't approach 100% (we'd be lucky if it's 50% without applied potential), electron detection can be quite close to 100%.

Even if the detector clicks account for 100% of the electron current, there is still a question as to what's happening between clicks. The phrase "only one electron in the apparatus at a time" makes it sound like the beam emitted from the source is composed of very brief, discrete pulses, but how do we know this is so? The discreteness of the clicks could be an artifact of the detector and not the source.

Staff Emeritus
Nicky said:
Even if the detector clicks account for 100% of the electron current, there is still a question as to what's happening between clicks. The phrase "only one electron in the apparatus at a time" makes it sound like the beam emitted from the source is composed of very brief, discrete pulses, but how do we know this is so? The discreteness of the clicks could be an artifact of the detector and not the source.

If you haven't done enough calibration with the detector to have any confidence in it, then this experiment should not have been done.

If it is an artifact of the detector, the accumulated signal should be nonsense and would not have produced such coherent and well-defined interference pattern. This is not the signal of random dark counts. It would be VERY difficult to convince me that the detector is producing a result that JUST HAPPEN to look like an interference pattern, and not only that, reproducible over several different experiments.

Zz.

Nicky
ZapperZ said:
If it is an artifact of the detector, the accumulated signal should be nonsense and would not have produced such coherent and well-defined interference pattern. This is not the signal of random dark counts. It would be VERY difficult to convince me that the detector is producing a result that JUST HAPPEN to look like an interference pattern, and not only that, reproducible over several different experiments.

No, no, that's not what I meant. By "artifact of the detector" I don't mean a spurious effect, so maybe "artifact" is the wrong word. I mean it's the presence of the detector that causes the discretization of the beam.

The double-slit experiment is always portrayed as if the clicks represent a collision between a single, distinct particle and the detector. The big mystery is then, how does this one particle pass through both slits at the same time in order to interfere with itself?

But maybe this picture is too classical. Not only is each emitted electron in a superposition of trajectories through the slits, but there is a huge ensemble of electrons that are each in a superposition of emitted and not-emitted states. If we project all those occupied states on the spatial region between source and detector, the total density may be less than one electron over the entire region. But that's different than saying there is exactly 1 or 0 electrons in the apparatus at any given time.

To really know that exactly one electron is in flight, there would have to be not one click but two clicks, one as the electron leaves the source (but before the double slits) and another one when it hits the detector. However, since the first click represents a time measurement, wouldn't that cause an uncertainty in energy that destroys the interference pattern?

Staff Emeritus
Nicky said:
No, no, that's not what I meant. By "artifact of the detector" I don't mean a spurious effect, so maybe "artifact" is the wrong word. I mean it's the presence of the detector that causes the discretization of the beam.

The double-slit experiment is always portrayed as if the clicks represent a collision between a single, distinct particle and the detector. The big mystery is then, how does this one particle pass through both slits at the same time in order to interfere with itself?

But maybe this picture is too classical. Not only is each emitted electron in a superposition of trajectories through the slits, but there is a huge ensemble of electrons that are each in a superposition of emitted and not-emitted states. If we project all those occupied states on the spatial region between source and detector, the total density may be less than one electron over the entire region. But that's different than saying there is exactly 1 or 0 electrons in the apparatus at any given time.

To really know that exactly one electron is in flight, there would have to be not one click but two clicks, one as the electron leaves the source (but before the double slits) and another one when it hits the detector. However, since the first click represents a time measurement, wouldn't that cause an uncertainty in energy that destroys the interference pattern?

You do this FIRST without the slit. See if the set up is actually producing what you think it is producing. All the detector can do is detect. If it does not conform to a "standard" source, then all bets are off.

All electron analyzers have to be calibrated this way. This range from those used in photoemission experiments, all the way to large scintillators. Compare to detecting photons, detecting an electron is a walk in the park, honest!

Zz.