Understanding Single Photon Detection in the Double-Slit Experiment

[jeremyfiennes]

TL;DR Summary

How do they no.

When double-slit experimenters say an interference pattern is obtained even when only one photon at a time is fired at the slits, how do they know it was only one? The same when a photon detector is said to respond to single photons.

 

[jeremyfiennes]

Something went wrong. On the email notification I see "No, that isn't the case." But when I open here, I don't find any reply.

 

[PeterDonis]

Something went wrong. On the email notification I see "No, that isn't the case." But when I open here, I don't find any reply.

The person who posted that deleted the post.

 

[Frodo]

I think an interesting thing about the double slit experiment is to do it this way.

Experiment A: Get 100 different people located all over the world. Each person does their double slit experiment with just one photon or electron. All the experiments are done at different times so there is nothing in common with them.

Experiment B: Get one person to send 100 photons through his experiment.

When you collect the results from the 100 separate experiments in A, and the 100 results from the single result in B, they will be identical. This is, of course, subject to the fact that the result is a probabilistic one so they are unlikely to be absolutely identical any more that two people tossing a coin 100 times will get the same number of heads.

The probabilistic nature of the result is built into nature not into the apparatus.

It is possible to generate a single photon. I went to this public lecture a few years ago: "All you ever wanted to know about photons (but were afraid to ask)" by Dr Peter Mosley of the University of Bath, UK.

Abstract: Single photons – individual particles of light – have enabled ground-breaking experiments that test the foundations of quantum physics. Furthermore, single photons are likely to play an important role in the future of communication, sensing and computation. However, making a reliable source of single photons is not as easy as just dimming a light bulb.

This talk will discuss generation mechanisms for single and entangled pairs of photons, as well as the fundamental experiments and technological advances for which they can be used.

I sent the following synopses (written from memory) to a colleague who could not attend. I make no claim for its being correct or even an accurate representation of the lecture but it's what I think I heard

I got to ask "How long is a photon" and was a tad gob smacked by the answer. There was me thinking "point source" and I get the answer "As long as a piece of string ...".

Basically, to be a photon, you must have at least one complete wave, so a Long Wave radio photon is at least 1,500m long! Gamma ray photons are typically very short. But photons have a bell shaped envelope for something he called c?, to do with time, so there is a probability of finding it anywhere. The more waves a photon has, the better you know its frequency, and the less probability you have of finding it away from the concentration of the waves. In private discussion afterwards he made some comment about [a well known public scientific figure's] understanding of photons!

I came across this https://www.physicsforums.com/threads/size-of-photon-particle.32102/page-2#post-292379

He described how he creates single photons but I did not really follow it. It's all based on probabilities because it is quantum.

You cannot just shine a laser through "sunglasses" and attenuate the number of photons until you get them coming out as singles because the laser is sending 10^15 photons/second (his laser pointer does), they travel in bunches where the average rate is 1 per 10^-15 sec, but the actual number of photons in a small interval has a Poisson distribution. (I think that was correct, but it may be that the attenuation is probabilistic? or both are probabilistic? Whatever, your photons after the sunglasses are probabilistically distributed in time.) So, if you attenuate to an average of 3 per time interval, you actually get, say, from 0 to 10 per interval on a Poisson curve which goes off to an infinite number at a tiny probability.

Make the glasses darker so you get an average 1 per time interval but now most intervals have 0, very few have 1, very very fewer have 2 etc. It's Sod's Law - the darker the glasses, the fewer "single photons per interval" you get.

The key is getting rid of the intervals with 0 photons because the largest set left is intervals with 1 photon.

To do this he shines a very powerful laser pulse which is very short (10^-15 sec), so limiting the number of photons (still 10^lots!) into a glass (in his case fibre) which produces a highly non-linear electric field response. As a consequence (a bit like a diode detector for an AM radio signal) you generate pairs of photons, one with higher and one with lower frequency. (His tiddly $5 green laser pointer is actually an IR laser which is frequency doubled to get green.)

There is a lot of statistics and basically you produce photon pairs for about 1 in 10^2 incoming photons, and 2 x photon pairs for 1 in 10^4 and 3x photon pairs for 1 in 10^6. You now detect one of the pair, which absorbs it, but this means you know you have also generated a "nice, untouched, virgin photon" as its pair (and 2 virgins in 1 in 10^4 cases and 3 in 1 in 10^6 cases).

Critically, you can discard all those instances when you do not create a photon pair because you don't detect any photons, so you have got rid of the "0 photons bunch". The parameters are set to have a very low probability (1%) of producing a single pair, because that simultaneously means you produce few double and few few triple pairs. But until you have a detector which discriminates between single and multiple photons - he doesn't - you just have to live with the odd double or triple or quadruple photon - which screws up your experiments.

How long do you need to wait for getting a some photons out? It's a log scale - one comes out in 10^-10 seconds, 3 takes about 1 second ... but 12 takes 10^20 secs, or longer than the age of the universe. He runs 4 x guns in parallel and combines the outputs to get 12 photons per second.

When a single photon hits the Mona Lisa it is absorbed. The excited electron drops back and emits a new photon in any random direction. So, you only see the Mona Lisa because so many photons hit it, that enough are randomly generated in your eye direction for you to see it.

 

[PeterDonis]

It is possible to generate a single photon.

Yes, but as the quote you give notes, doing so is not as simple as just dimming a light bulb. Or even dimming a laser. But most of the talk about doing a double slit experiment where "only one photon at a time" is inside the experiment are talking about using a very dim light bulb or laser as the light source. They are not talking about using the kind of specialized sources described in the lecture you refer to, which produce (something close to) Fock states, whereas light bulbs and lasers produce coherent states. The two are very different.

 

[Frodo]

Yes, but as the quote you give notes, doing so is not as simple as just dimming a light bulb. Or even dimming a laser.

Thank you for pointing that out although I credit the readers here with the ability to spot that without needing you to recap it for them. btw, it isn't a quote - it is my recap of a lecture I attended.

But most of the talk about doing a double slit experiment where "only one photon at a time" is inside the experiment are talking about using a very dim light bulb or laser as the light source.

Each to his own but I read those accounts differently to you.

In order to explain the experiment the describer says if you dim the light until only one photon is emitted then that single photon seems to go through both slits. Note the important if. By considering a single photon, even though there are many, the reader is forced to confront that "one photon seems to go through two slits at the same time but does not hit the screen where classical physics says it should".

Do you nitpick explanations of what happens if you go to the event horizon of a black hole just because no one has been to an event horizon?

Finally, you seem to have needed to get things off your chest so rapidly that you don't appear to have read what I posted before coming in with your objections. Did you completely miss the first line of the Abstract? If so, let me repeat it for you here so you don't have to bother to scroll back - I have underlined the important bits for you.

Abstract: Single photons – individual particles of light – have enabled ground-breaking experiments that test the foundations of quantum physics

In other words, experiments testing quantum physics are today being done with single photons.

 

[PeterDonis]

I read those accounts differently to you

You're not giving the relevant part of the accounts. The relevant part of the accounts is: what is the actual light source? Any experimental paper will tell you that explicitly. And then you don't have to guess at what kind of quantum state the source emits; the paper has told you.

n order to explain the experiment the describer says if you dim the light until only one photon is emitted then that single photon seems to go through both slits. Note the important if.

No, the "if" is not the important part. The important part is what you left out: what is the "light"? The term "light" can refer to many different kinds of light sources, from light bulbs to lasers to the kind of specialized sources referred to in the abstract you quoted. And without knowing which light source is present in the particular experiment being described, we do not know what "only one photon is emitted" means.

Do you nitpick explanations of what happens if you go to the event horizon of a black hole just because no one has been to an event horizon?

Of course not. But I do quite often have to point out to people that they have not actually specified a precise scenario, and until they do, the questions they are asking are unanswerable. Which is exactly what is happening in this thread: the OP has just said "double slit experiment when only one photon at a time is fired at the slits" without telling us what kind of light source is being used.

you seem to have needed to get things off your chest so rapidly that you don't appear to have read what I posted before coming in with your objections. Did you completely miss the first line of the Abstract?

No. But you appear to have completely missed the fact that the kind of experiment described in that abstract is most likely not the kind of experiment the OP of this thread is talking about. The kind of specialized light sources described in that abstract, in every paper I've seen that talks about them, are used for quantum optics experiments, not double slit experiments. But the OP of this thread asked about a double slit experiment. So unless you can show me a paper where the kind of light source described in the abstract you quoted is used in a double slit experiment, everything you are saying about "single photon"sources, while it is technically correct, is irrelevant to the discussion in this thread.

let me repeat it for you here so you don't have to bother to scroll back - I have even underlined the important bits for you.

This kind of snark is going to get you a warning and a thread ban if you keep it up. You will be much better off assuming that, if I'm raising an issue, it's a genuine issue, than assuming that I have not read what you posted.

experiments testing quantum physics are today being done with single photons.

Sure, but "quantum physics" is a lot more than "double slit experiments". Do you have any references to papers where the single photon sources the abstract you reference describes are being used in double slit experiments? If so, please post the references. If not, you are hijacking this thread with irrelevancies.

 

[PeterDonis]

When double-slit experimenters say an interference pattern is obtained even when only one photon at a time is fired at the slits, how do they know it was only one?

Usually it's because they have dimmed the light source to the point where the calculated probability for detecting more than one photon inside the apparatus, if there were a photon detector placed there, is negligible. (In more technical language, the expectation value of the photon number operator is less than or equal to $1$ everywhere inside the apparatus).

The same when a photon detector is said to respond to single photons.

This is actually a different case, because a photon detector is designed to detect discrete photons--in other words, regardless of what kind of light source you use, a photon detector will show individual, discrete "photon detection" events (dots on a screen, audible clicks, or whatever the detector is designed to show). So the reason we know the photon detector responds to single photons is that we designed it to do that. (In more technical language, we design the detector to physically realize the photon number operator.)

 

[StevieTNZ]

Something went wrong. On the email notification I see "No, that isn't the case." But when I open here, I don't find any reply.

Apologies! I mis-read your original post and thus deleted my response.

 

[Frodo]

Do you have any references to papers where the single photon sources the abstract you reference describes are being used in double slit experiments? If so, please post the references.

Today students do experiments with single photons. For example I refer you to the Advanced Laboratory Physics Association's Single Photon Quantum Mechanics which says

Thirty years ago, such experiments represented a tour de force of technology and equipment; today they can be done in a few afternoons in a junior-level optics lab, thanks to current photon-counting technology and the use of nonlinear crystals to produce entangled photon pairs. Yet these experiments are still closely related to active research in quantum information and the fundamentals of quantum mechanics ...

We will then observe that photons incident one at a time on an interferometer nevertheless exhibit interference fringes, highlighting the wave/particle duality.

If you can accept that an interferometer is equivalent to a double slit I think your objection is answered.

You may also care to visit the University of Minnesota's https://sites.google.com/a/umn.edu/mxp/advanced-experiments/SPQI or read A hands-on introduction to single photons and quantum mechanics for undergraduates, B J Pearson and DP Jackson, Am. J. Phys. 78, 471 (2010).

 

[PeterDonis]

If you can accept that an interferometer is equivalent to a double slit

Interference is present in both, true. I'll leave it up to the OP whether it addresses the questions he was asking.

 

[vanhees71]

Yes, but as the quote you give notes, doing so is not as simple as just dimming a light bulb. Or even dimming a laser. But most of the talk about doing a double slit experiment where "only one photon at a time" is inside the experiment are talking about using a very dim light bulb or laser as the light source. They are not talking about using the kind of specialized sources described in the lecture you refer to, which produce (something close to) Fock states, whereas light bulbs and lasers produce coherent states. The two are very different.

Indeed, it is not easy to prepare a true single-photon state. Dimming down a laser just gives you (with some good approximation) a coherent state of very small intensity, i.e., you prepare a superposition of all photon-number eigenstates (Fock state) with a huge portion being the vacuum (the photon-number statistics is Poissonian, and the average photon number can be made as small as you want).

One modern way to prepare a true single-photon state is to create an entangled photon pair by parametric down conversion shooting with a laser on a BBO crystal. Then you can detect one of the photon ("idler photon") and then know with certainty that there's another photon you can use to experiment witt ("signal photon"). If you even measure the idler photon's polarization you get a specific polarization state also of the signal photon.

I don't know, whether one has ever made the simple double-slit experiment with true single-photon states, but one has done more sophisticated versions like quantum eraser demonstration experiments and the like. What comes out is indeed that you build up a diffraction pattern by shooting many single photons at the double slit, i.e., on average you find interference effects as in classical electromagnetic wave optics. Each single photon, however is registered on the screen at a single spot. You cannot predict at which place this single photon is detected but the position-probability distribution for these detection events is given by the classical intensity of wave optics (i.e., the energy density of the em. field normalized to 1).

 

[jeremyfiennes]

All. Thanks. For some reason I didn't get notifications. And only now checked back to complain that you had forgotten me. I see you hadn't!
The double-slit reference was only to a situation where the term "single photon" is used. My real question is not their production, which seems clear to me. But their detection. A manufacturer asserts "Our device detects single photons". And I say "Prove it". What is his answer? How does he demonstrate that it was indeed a single photon that was detected, and not a bunch of two or three?

 

[Drakkith]

A manufacturer asserts "Our device detects single photons". And I say "Prove it". What is his answer? How does he demonstrate that it was indeed a single photon that was detected, and not a bunch of two or three?

You can't usually look at a single detection event and say with 100% certainty that you've detected ONLY one photon, and not more than one. However, you can do statistical analysis on many different detection events and come to the reasonable conclusion that the detecting device is indeed detecting single photons regularly.

For example, let's say I set up my CCD camera for my telescope and start recording an image every tenth of a second. Then I use a light source that put outs approximately 10 photons per second and I run the experiment for 10 seconds. So that's 100 images, each of which should, on average, contain a 1 photon signal.

I then sum the different images together and, after compensating for drops in efficiency and other effects, come up with a final image whose pixels should contain 100 'counts'. So, either the detector is indeed detecting single photons on nearly every image, or the light source is emitting bunches of photons that are detected all together. The latter effect would show up as bright spots on some of the images and no bright spots on most of the others.

This does not happen. I image extremely dim light sources in the sky all time and my images would not look the same if my CCD didn't detect single photons. These sources are so dim that you're often lucky if you get 50+ photons in a 5 minutes exposure. So either my detector is working correctly, or the light isn't behaving at all like we think it is. And if it isn't acting like we think it is, it would be obvious in our images of both natural objects and lab experiments.

 

[Frodo]

I don't know, whether one has ever made the simple double-slit experiment with true single-photon states ...

Students do the double-slit experiment with single photons these days - see the links above.

 

[jeremyfiennes]

Ok. That makes sense, and I've now got the general picture. Thanks all.

 

[Frodo]

A duckduckgo search with single photon detector found much of interest including Invited Review Article: Single-photon sources and detectors. Have a look at C. Photon-number-resolving detectors which discusses several techniques.

Before describing specific PNR detectors we should clarify what is meant by “photon-number-resolution.” It is important to lay out the degrees of photon-number-resolution that a detector can have. First we note that as mentioned earlier, photon-number-resolving does not mean that one determines the number of photons incident on the the detector. Without 100% detection efficiency, the measured number is at best just a lower estimate, and with dark counts it is not even that. This is particularly an issue for detectors with very low efficiency. In addition we attempt to categorize the degree of PNR capability into three groups defined as

(a) “no PNR capability” for devices that are typically operated as a photon or no-photon device,​

(b) “some PNR capability” for devices made of multiple detectors that individually have no PNR capability and thus are limited in the maximum photon number that can be resolved to the number of individual detectors, and​

(c) “full PNR capability” for devices whose output is inherently proportional to the number of photons, even if their detection efficiency is low and their proportional response ultimately saturates at high input photons levels.​

(We are assuming relatively narrow band light incident on these detectors so that a detector with an output proportional to the incident energy is used to provide information on photon number, rather than the energy of those photons.) While this categorization is somewhat arbitrary, it is of some use in understanding the types of mechanisms used to produce PNR capability.

 

[jeremyfiennes]

Interesting article. Many thanks.