Hey. Good afternoon, everybody, and welcome to this afternoon's colloquium. Thank you for coming on such a glorious day. All right. So there are alternative attractions this afternoon, Ira. So it's it's a great pleasure to welcome Professor Miles Miles Padgett to give us this afternoon's talk. Miles started out in Cambridge work where he did did his Ph.D., but now he's out of the Calvin Chair of Natural Philosophy in the ER in the University of Glasgow.
He's very well known for his work in various aspects of optics and, and quantum optics. And over the years that work has been acknowledged by a number of number of awards of which I guess, you know, the most significant ones at least recently, are the European Physical Societies as a prize for research into the Science of Light. In 2015 and in 2017, he won the max prize of the Optical Society of America.
And so a few years earlier, he was elected as a fellow of the Royal Society of Edinburgh and subsequently of the Royal Society itself. So he's had a distinguished career in this part of science, and he's going to talk to us today about ghost imaging with quantum light. Miles, thank you. Thank you very much indeed for the introduction. Thank all of you for giving up the sunshine to come. And yeah, it's probably too hot outside. It's nice and cold in here, isn't it, to have a bit of a snooze.
So there we go. That's our main the tower of our main university building. And Glasgow University. Not as old as Oxford, of course. Quite old. 1450 something. It's in the middle of town and Queen Victoria came to stay in 1850 and told everybody it smelt terrible. At that point, the university up sticks and left and moved to a greenfield site on the outskirts of Glasgow, which is now the west end of Glasgow.
So this built in is from those mock gothic things designed by the same architect to St Pancras Station down in London. So Gilbert Scott and it is famous but is sadly famous I guess for being the home of William Thomson. William Thompson moved with his parents from Belfast to Glasgow and he was about five enrolled in the University for Natural Philosophy when he was 12. And by the time he was 21 or 22, he was the professor of natural philosophy.
And subsequently, after all his work, he became Lord Kelvin and the Calkins. The river runs underneath. Roughly speaking, if someone must have been standing above the Kelvin to take this picture, I don't know how. So there we go. So he has a his house is still there. His desk is still there. His clock is still there. His various experiments are still there. And if you ever come and visit me, it's my office. So I have an office in Kelvin's house.
I don't know what room it was, but it has windows and things, so it was a normal room. Anyway, I love all that. I'm going to talk to you today about a subject rich in physics, about what quantum optics people called ghost imaging. And of course, you say, if you should say that at a party, what you do. I think ghost imaging people would have all kinds of supernatural thoughts about lying in wait in the corridors of Kelvin's house to see whether you can find Kelvin himself.
Ghost imaging doesn't mean that in that sense it's a pun really on spooky action to distance. So that's why it's called ghost imaging. It's when it was first proposed in the 19 West, first demonstrated in the mid 1990s, people thought it was a manifestation of quantum mechanics and that's why it was called ghost imaging. I think subsequently too that it's now broadly accepted that the correlations you need in order to make a ghost imaging system are actually classical rather than quantum.
I'll talk a little bit about that later on, but it has a long history, mainly people arguing whether it's a quantum effect or not. I'm going to concentrate mainly today on what it can do or not. So first of all, I like to thank the wonderful people that I work with, in particular, Paul, who's up there who's taken the latest set of results last week, which I'll get to at the end of the presentation.
And also, I've had a long and very enjoyable collaboration with Bob Boyd at the University of Ottawa and indeed Rochester and actually Glasgow. He's an honorary professor with with us. So how does Quantum Ghost Imaging work? It's based on parametric down conversion. And parametric down conversion is something that takes place in a nonlinear crystal. What do I mean by that? I mean that the polarisation of the crystal depends on the applied electric field.
That would be a linear response, but it depends on the square of the electric field. That's a nonlinear response. And so it's a CHI two process, and you can think about it in amplifier sense as something that would have second harmonic distortion. Now that second harmonic distortion is why you can take an infrared laser beam, shine it into a second or the nonlinear crystal. And what comes out the other end is green lights, lights off twice the frequency.
But like most parametric, well, those nonlinear processes, it goes the other way, too. And so I can come in with one high energy photon and out of the crystal pop two photons of lower energy. Now, as I've drawn it here, that blue photon is actually in the ultraviolet at three, five, five nanometres. And the infrared photons that come out in the infrared 710 nanometres. And so you can see straight away that in that process, this energy is conserved.
I've got twice as many photons, but they've got half the energy. So energy is conserved. Momentum is conserved. What does that mean? It means if one of the infrared photons comes out heading slightly to the left, the other one must come out heading slightly to the right. As I've shown it there. And so the transverse momentum of the system is conserved. And so that down conversion process simultaneously conserves energy and it also conserves momentum.
Are you pleased about that? The latter is often referred to as face matching to those that work in nonlinear optics. But what they really mean is conservation of momentum. Now, if I think that that laser beam coming in is quite a big pain and I'm going to be very naughty now, I'm going to think that somewhere in there is a photon and I know the photons to localise. But let's just think. Where my two infrared photons are made somehow.
Then somehow the energy was here. The energy still needs to be here. So those two infrared photons, if I was to look very carefully at the crystal, those two infrared photons emerged from the same position. I never quite know where in the beam, so to speak, they're going to have come from, but they'll come from the same place. Those infrared photons, therefore, are energy correlated. They're momentum correlated and their position correlated.
And that's what I want to try and emphasise here so much. Now I'm looking at where those photons are created. I've got my magnifying glasses and I look at the crystal and I'm not quite sure where they are, but I find that always like like Noah's Ark created two by two and that they are strongly position correlated. So if I know the sort of star constellation here, I get exactly the same pattern here and you can see where I'm going now.
I sort of have this notion that I can put the object in one, arm it with a particular pattern of photons, knowing that the same pattern of photons will actually be will hit the camera. And so now we have the idea that somehow the image is recorded in a place where the object wasn't. And now you can sort of see why it's spooky action at a distance. Spooky imaging, ghost imaging. Let's think a little bit more carefully about how I might make such a system.
Well, just because I know the pattern, the photons that hit the camera and where they are isn't really going to help because that's all of the photons. I only want to measure the photons that actually get through the object. That's what an image means. That object, that black bit of the object, will cut some of the photons out. The white bits of the object that's meant to be transparent will let some photons through.
And so what you have behind the object is something we'll call a pocket detector. In this case, shaped like a bucket. Just to remind us, what do I mean by a bucket detector? I mean, it's just a single detector doesn't have pixels. It's not a camera. It's not a lens. And it's big. So the only thing that this bucket detector tells me is did the photon get through? Does it tell me where the photon was? It just says, did it get through?
If it did get through, then I'm actually going to measure the position of the other one because they're the ones in the same position. So it's almost like a voting system. This thing down here will measure all of the photons, but this one here tells me which the image photons where it says photon number three got through photon number seven got through photon number 13 got through. And therefore, I'll just build up the image from those down here.
Now, the original systems did that by scanning a detector at the bottom, and it's a Rasta scan pattern. And basically this thing over here was the coincidence count. So whenever both detectors went, click at the same time. This one told you that, made this what this photon got through. And obviously this bucket was in the right place, the smaller bucket was in the right place to get it.
And so you built up an image through scanning, but that's going to be very wasteful because most of the time my scanning bucket is in the wrong place to pick up the photon. And so actually, if you think about this, it's going to have a maximum efficiency of one over MN where N is the number of pixels in your image because you're only going to get a count of the buckets in the right place and you've got no control about where the photon is.
Mm hmm. So how can we make it more efficient? Replace it with a camera. Now this camera is not seeing an image. This camera is simply going to take one picture. Of one photon. A photon is going to come through here and the bucket is going to tell the camera to take a picture and I'm going to get a black image with one. And then I tell you to take another picture. And I got another photo and another picture.
Another photo and at them all together. And eventually I'll build up an image of the objects. Now, the problem here, of course, is the photon arrives at the same time here as it does here. And therefore, the bucket, by the time the bucket told the camera to take a picture, we've missed the photo. And so I put a delay line in the system. So. Goes through. Snail, snail, snail, snail, snail. Tell us the courage to take a picture. And this photon has been delayed.
So that's the delay line. It has to be a delay line that preserves the image. So it's got lenses in on the light. Whew. Those. That's the delay I know. With the lenses. I would say that it's a complicated experiment, but I've just come from a Walmsley lab, so this is incredibly simple experiments that cost almost nothing. And and even I complained about the dust collecting on the optics. So there we go. Now, just to show you that it's really doing what I said it is.
Obviously, when I go back to this thing, that's the when you tell this camera to switch on its intensifier, it takes about 30 nanoseconds. The electrical signal here takes about five nanoseconds to get out. And you've got the length of B and C cable here, which the electrical signal has to travel along in order to activate the camera.
And so I have to make sure that that begins the length of the B and C cable is correct, such that this camera switches on at the exact moment that the photon arrives. And that's what I tried to show in this next image here. What we're doing here is changing. The length of the B and C cable and changing the nanoseconds delay and set the BNC cables to short. I take a picture of nothing. It's A, B and C cables too long.
I take a picture of nothing. It's A, B and C cables. Right. I collect the photons that I wanted to, and I built up an image from those photons. So here we go. Let me let me now show you what you see. So this bear in mind, every time the camera takes a picture, that's just one more photon. What you're seeing here is the summation of all of those frames. So every time I get another photon, I'm just adding to this image. This none of these things is what the camera records.
The camera just records one speck of light at a time. But over the course of a few seconds I've got enough photon events that I can build up an image. So each of those specks of bright whiteness is a single photon being detected. Triggered by the bucket detector. And so we built up an image. None of those photons ever saw the object. All of those photons went straight to the camera. Some other photons saw the object and then triggered the camera to take an image.
So it's quite interesting. I can have an image with one photon in it and it's just one spot of light. Quite difficult to recognise anything when it's just one spot of light right through here. 7700, 7000, 70,000. So that those kind of images I've been showing you are about 70,000 photons arriving at the camera. So the question is how many photons do I really need? This is now a little digression. This next few minutes is boring. Just have a snooze. Come back in a couple of minutes time.
I'm going to talk about something which I find very interesting that I don't know very much about, and that's basically doing voicing of images and trying to guess the answer from incomplete data. Clearly, my data here is incomplete. It looks like I've taken a picture with a salt and pepper thing and I want to do it better than that. So what is it that if I'm trying to guess the image, the object, what do I know? I know a few things.
One is, I know that even if these two bits of the object to the same brightness, they're not going to have the same number of photons in the image. Because if on average, let's say I had ten photons, I'm going to say plus or minus Route ten standard deviation on that, even though the two bits of the object are exactly the same, they're never going to be exactly the same in my image. So what is it I know about images? Well, I know the images.
Aren't a collection of random pixels. If they were JPEG compression wouldn't work and wouldn't work. Skype wouldn't work. Nothing would work. So what is it about an image that makes it special? It's sparse in its spatial frequency. So if I take the form of a transform of an image, has lots of zeros in it. If I take the three a transform of noise, there's not many holes in it. And so I can recognise real images from non-real images by checking to see what the best spots or not.
And that means that I set the whole thing up as some kind of cost function optimisation where the first term is based on the likelihood I can't use chi squared because it's persona and distribution. So because it's so strongly persona and I'm using a likelihood measure of whether the answer agrees with the data the maximum. I've got to be careful here because maximum likelihood means something else. The most likely image, just given the data, is whatever it is I measured.
But it's probably not the image because now I'm going to add on some kind of regularisation term on the end, which could be the sparsity of the forest domain. And I optimised this and I won't go through any things here, but essentially I start off with something in the top left which looks like it's been made out of salt and pepper and obtained with something in the bottom. Right. Now, this clearly does not fit the data.
It isn't the data, but it's close enough to the data to be statistically allowable. And there is an answer which is much, much sparser in spatial frequencies. And so we go for that. And here's just some generic examples here. This is the data I get. This is essentially my best guess at an image. I'm not doing anything that the image processes don't really do much, much better than I do. But suffice to say, I'm taking advantage of the fact that this isn't a collection of random numbers.
I know it's an image, and therefore I can get away with essentially comparatively fewer photons than I might have expected and still recover something which we can cosmetically at least say is a image. And I have to say, I find this whole idea fascinating in that your site think under the Graduate. I must fit the data. I must fit the data, I must fit the data. But actually, it's been ten years.
Well, no, I just have to fit the data. If if a straight line went through all the data points, I get a bit suspicious. That never happens. It's more likely I'm going to have a solution of chi squared over and over to one. If I. If I. There's lots of those to choose from. Which ones will I choose from? I'll impose some bias some prior on. So my prior here is one of the spatial frequency sparsity. Here is a picture of a WASP wing with about 100,000 photons.
Now, if I take a picture with my iPhone, that would probably be somewhere in the region of 10 billion photons. Just to give you an idea. So 100,000 photons is not very much. In fact, when you're playing around with simple images, you find that you've got one photon per pixel. You'd normally think that would be a very binary image. Typically that gives you quite an acceptable image. So. Let's ask the question, is it quantum? Well, it's quantum insomuch that you're detecting single photons.
Einstein wouldn't have lost any sleep over that. Is it does it violated that inequality? Well, doesn't look like it violates about inequality. So maybe it's not quantum. Probably somewhere in the middle. How about EPR to demonstrate EPR? That would be a good question. So let's have a think to the extent that these this kind of experiments demonstrate EPR, if at all. So that's the system we know and love. I think you've set it up. I've explained how it works.
I haven't bothered to put the delay line in again. That's taken as red. I've got my incoming photon over here. It generates my two infrared photons. The plane of the crystal is imaged to the object and the plane of the crystal is imaged to the camera. Otherwise, the spatial correlation isn't measurable. So you're just looking in any old plane. My photons are spatially correlated in the plane of their birth.
Nowhere else. So it's very important that I image these systems properly after it's gone through this. I don't care. It could be any old nonsense here. I'm just collecting it. And then I take a picture. And in this instance. The imaging is the same. I'm relying on the position correlation. So an upright object here gives me an upright image because it's a 1 to 1 correlation between the position of two photons.
Now I can configure the system differently. Now remember this is that I've got position correlation. But I also said that I had momentum correlation. If one photon went to the left, the other photon went to the right. So I can do something else. I can, actually. Ross has an image showing the crystal onto the objects. I can arrange it such that the object is in the far field of the crystal. And now the position here is actually a measure of the transfer of momentum.
I went a long way to the left and therefore the photon here ended up at the top. Well, it goes a long way to the right, in which case the photon ends up in the bottom. But in the momentum plane, my correlation is an anti correlation. If one photon goes right there, the one goes left, and therefore an upright object here gives an inverted image here. This system takes advantage of position correlation. This system takes advantage of momentum correlation.
And of course, Heisenberg's uncertainty principle says you can't note both the position and the momentum at the same time. And therein lies the whole central pillar of the EPR paradox of Einstein. Podolsky Rosen. Against. Against Niels Bohr. So if we can do this, in essence, we are sort of showing the image equivalent of the EPR paradox. And so you'll be glad to know you can thank goodness for that. Quantum mechanics is true how we live. This is the position correlated image.
And so what you're doing here actually is quickly changing the lenses from that system to that system both work. But depending whether you've got those lenses in all these lenses in the image, you get to see the uprights or inverted axes. A manifestation, I won't say it's a proof because it's all kind of tiny loop holes, but it's a manifestation of an EPR correlation. Now, is it useful? Well, not really.
I wanted to do an upside down image. I'll just take it into Photoshop and make it upside down while to my camera upside down or something. So I'm not claiming that being able to take an upright image or an inverted image is, is, is, is, is uniquely sellable to anybody. But I just wanted to make the link in to Quantum and that's the extent to which ghost image is in quantum.
The fact that I can do either of these is not in itself quantum. What makes it quantum is that I can do either of them or both of them. I can choose in principle after the photons have left the source. What can it do? Something different. Can it do anything useful? Well, here's the down conversion that we know and love. And I used to have the cartoon before my down conversion was very much around my degenerate.
I had a UV photon coming in and I had to infrared photons coming out and the other photon coming in was 355. The infrared photons coming out with 710. But it needn't be that way. No one said we had to come out with equal amounts of energy. The down conversion process requires energy to be conserved, doesn't require it to be divided equally. And so my time converted photons in this case. One of them is at about 460 nanometres and the other one is at about 1.6 microns.
If I add to the energies, I still have conservation of energy, but it's not equally divided. Now you can sense where this is going to go, because now I say, Well, that's rather handy. What I'm going to do here is I'm going to have the infrared light illuminate my object, but my camera is going to image the blue light. Now, why might that be useful? That might be useful because at 1.6 microns, your single photon camera is crap.
There isn't one. At 480 nanometres, you can merrily use a good, well behaved photo cathode in an image intensifier. You can take an image of a single photon of 480 nanometres. You cannot easily do that at 1.6 microns. But I can still buy a bucket detector at 1.6 microns. Hmm. Okay, so this detector up here is in fact, this bucket detector came from the M.A. group, about to touch the lenses of the detector, his state of the art spot.
And this is an or gated, intensified camera with a sensitivity that goes from 400 nanometres to 800 nanometres. So this camera can only see visible light. This detector can detect the infrared. Everything else is the same. And so here these objects here are actually silicon wafers. Silicon wafers, as in silicon normally doesn't transmit visible light. They have metallised stuff on them, in this case, a lander. The infrared lights essentially went through the silicon, not through the metal.
And then I took a picture of the blue lights at 469 metres with the camera and it was called position correlated. And so the, the infrared light probes the object, but the object, the image is actually obtained in the visible. So that's sort of quite nice to think of ways in which you might do that with classical things or non parametric things, but sort of verging on the useful. Now how can. Ghost imaging be better understood, not in terms of understanding quantum mechanics.
Let's pretend I don't want to understand quantum mechanics. I just want to be able to predict what's going to happen. I want to predict the outcome of an experiment. So that's what we know and love. We've seen that picture before. It's the same on back again. I've got this down conversion source splitting into two photons. One goes here, one goes here. This bucket detector tells this camera when to take a picture. That's the picture I get. Look at that.
This is a realisation by Guy Klitschko, who worked with Xi in the original imaging studies. These two systems will call that the quantum system, even though it's not necessarily quantum quantum parametric down conversion. And this system is equivalence. So what you do, you replace the bucket detector with a light source, shine light back through the object onto the crystal. Replace the crystal with a mirror. And then shine light from the mirror onto the camera.
And you can see as a classical imaging system, this here would give you an inverted image over here. And the inverted image over here would give you an upright image here. Just it's fine. Now again, all the image planes of the air. And you can see that this this idea that the momentum means that when one photon goes left, the other photon goes right. It's just like a mirror. The incoming light comes in at one angle, bounces off the mirror and goes out at the same angle.
The other sides change the angle. Change the angle of angle of incidence equals angle of reflection. In a sense that mirror. And also, by the way, if the light hits over here at the left hand side, guess what? The reflection comes from the left hand side is the light over here. The reflection comes from over here. So in a sense, a mirror does for the reflected light. What a downpour virtual crystal did for the emitted light.
So this, you know, this blue parametric down conversion just becomes a mirror. And now. In a sense, I'm going to call this. This is the quantum system. That's my classical system. I can think of my classical system. It's been the classical simulator of the quantum system in terms of predicting the answer. If I wanted to optically compute the answer for that system, I could do with this.
Now, you know this differences. This one takes twice as long because the light has to go from here to the mirror and then from the mirror to here. But it's this one, both like things at the same time. So, you know, it's not it's not identical, but it's a really good insight into how systems that go to behave. And that's the four year equivalent. That's the imaging one. And then that's the far field equivalent here, the mirrors in the far field of the object both ways.
And now what I've built there is an inverted imaging system. So this idea of image inversion, I think, follows naturally from this understanding. And you can just do it for real quick. This is my quantum system over here. These are the images I get, the upright images here, the inverted image over here. And then down below here is the classical system. But it's exactly the same system.
All I've done is I've replaced one of my quantum detectors with a light bulb, and I've literally shone light back through the quantum system and use the down conversion crystal as a mirror, the facets of the down conversion, crystal as a mirror. And you see that they're essentially completely equivalent images. Well, that's imaging. Let's think about diffraction. So that's my object. Double slits. That's my light bulb. I took it as a do over here. So the image of the double slits.
And then now I've got the far field fraction f f. So I sort of thought I might see the diffraction pattern there, but I don't because I've got a little light bulb there and that's not going to work very well. If I want to say a diffraction pattern, I'm going to have to spatially filter the light bulb, a pinhole in front of the light bulb. And then when I put a pain hole in front of the light bulb, I'm going to see a diffraction pattern over here.
So there we go. Pinhole compared to the light bulb. I said diffraction pattern. Let's do the same thing with my quantum system. If I just set it up with a quantum system and I have a bucket detector behind the double slits I find here, I don't have anything that looks like a diffraction pattern, but if I make my bucket detector very small, it's like passing the light through a pinhole. Then I, lo and behold, a diffraction pattern that appears here.
So no diffraction pattern with a bucket detector. Very small pinhole in front of bucket detector. I get diffraction pattern. This is much easier to do than you might have thought because my detector is connected to my apparatus with an optical fibre. So it depends on whether my optical fibre is multimode as the multimode optical fibre. Just a big hole to shine light through. That's my single mode. Optical fibre with a narrow core.
I mean, typically a multimode optical fibre will have a 50 micron core single mode optical fibre, five micron core and a new single mode optical fibre. You can do ghost diffraction. This is a video of double slit experiment. Photon by photon. I'm not going to just. It's quite nice, obviously. You know, this is the the classic. The photons are going through both slits at the same time. At some point it's just decided haha, whereabouts on the screen photon is going to land.
But once I've accumulated over enough events, I see that what begins to emerge is the classic sinusoidal fringes corresponding to a double slit experiments. But this really, really, really is. You always see them as computer simulations. This is not a computer simulation. This is genuinely, genuinely a double slit diffraction pattern. The photon by photon accumulated over time. In this case, it's about 40,000 photons in that now.
There's an interesting question. Alice I think that's an interesting question. And it comes back to this system here where I was getting all excited about the fact that I was illuminating the object with infrared lights and not having an image in the blue. And when I used to do this, done that about 18 months ago, that work people would ask at talks like this are what sets the resolution. The regular resolution criteria, whatever land or property is it?
Is it the infrared light or is it the blue light or is it the pump? Got three different answers because this might be good, wouldn't it? I mean, if it was a if I had the resolution of the blue light, this would be an a resolution enhancement technique. So is the resolution enhanced by the fact that eliminating the infrared, I take a picture in the blue. Cut to the chase? No, but let's try to understand why. It's a shame this tape is you can find where they say yes, but they're wrong.
In my view. What sets the resolution. The correlation, the strength. I said to you that these two photons were created in the same place. Come on. It's never the same place, Miles. That must be. What is it? It turns out to be this. Now this is probably an easier one to understand which flatten it here. This is in the far fields. So here the strength of the correlation. Is dictated by the momentum conservation. I said, if one photon goes a little bit to the left, the other one goes to the right.
Does it go exactly the same or nearly the same? The way to think about it is this If my pumping was really, really, really, really big, so it had no divergence, it was perfectly consummated. There would be no momentum, uncertainty from side to side of the pump light. All the photons are going this way. And then when I down converts, if that photon goes off at 10.2 degrees, this one goes off at -10.2 degrees. But what happens when my pumping gets smaller and smaller? Delta.
X going down. Delta X going up. My pumping now has a spread of momentum values in it. And so now it's almost like my windscreen wipers, you know, if this photon goes off that way, wow, this one can do a little bit round here because basically the pump on the pump, yeah, this angle is the same, but the pumps heading in a slightly different direction. And so the correlation is not as strong. So the strength of the correlation. Depends upon things like the wavelengths and the focal lines.
But here, the size of the pumping, my pumping gets small. This is not so good. Well, let's look at that. Let's play around. Changing the size of the pumping here and see what happens to the resolution of my ghost image. Now. Just to give us something to compare it to. I'm going to make my system a bit more complicated. You see, I've sort of added an extra imaging section.
This this bit up here is what we had before. But I've now taken where I would have put the camera and I've re-engaged it to here. And this is a really good imaging system here. So there's no loss of quality going from here to here. What I'm looking at is here or here now, I can actually set up my that's my ghost imaging system that I had before. Where my object is here. The correlation appears over here and then I re image it to get my image here.
But actually I could pick up these objects and put it there and just format direct image of it onto the camera using the light emitted by the crystal. And I don't give a monkeys what I'm doing over here. I just want to illuminate it. So I'm going to call that this is the ghost imaging system and I'm going to call this the heralded imaging system. So the object here is in the same arm as the camera and all that this bucket detector is doing now is essentially telling this camera to switch on.
I mean, it's actually still useful. Because the camera spends most of his time switched off. It's a camera spends most of its time switched off. It doesn't measure any noise. If I tried to take the only way I can take actually single photon images is by just switching the camera on when I need to. Otherwise, the thermal noise in the photo cathode swaps it out. So every time I switch the camera on, I switch the camera on for two nanoseconds.
That's why I have to get the LEDs, the B and C cable. Right. And I'm going to be doing that about 50,000 times a second. So you can work that out, roughly speaking. The camera is actually spending the vast majority, 99% of its time, switched off. And so that noise is 100 times slower than you might have thought it was going to be.
But what I want to do is compare the resolution of these two systems, because that is just the resolution of a classical imaging system, whereas that is the resolution of a ghost imaging system. And when I do that. I'm going to start changing the size of the pumping. That's what I want to do. I want to do that here. Does it matter whether the beam is big or small? The quality of my image doesn't change because it's just it's just lights.
I'm illuminating it, and it depends upon the resolution of the camera, the quality of this optics here, which is really good. And so that's absolutely fine. Then we go small being big, being small, being big, being small, being big being the ghost image and the heralded image look. So now. Look at this one. Small being. That's that's a large pumping. In the ghost imaging, the large pumping in the heralded imaging, the small pumping in the heralded imaging, the small pumping in the ghost imaging.
And you find out that this image here becomes blurred. It becomes blurred because you by making this beam small, you mean that the correlations in these two photons is not as strong as it was. Now, I've said all of that. That's a computer animated graphic. Let's look at the real thing. So I haven't got the skull here anymore. I've got a. A test will target will. So these are new results on Friday. The contrast isn't very good on this screen, but I'm hoping I can convince you.
So this is the Herald Imaging and this is me going with the heralded imaging as I go from a large pumping to a small pumping. And as I reduce the size of the pumping, well, okay. It gets darker as I get fewer photons through. But actually the resolution is maintained. Here. On the other hand, with ghost imaging, I make the pumping smaller. The resolution gets worse. I hope I can convince you that from those images.
And so now the bad news is there's nothing I can do to make the resolution better than the conventional system. But I can make it worse than this otherwise than making the resolution worse. I know, but they're not as much fun as this. Now, just to finish off with, if I may. I now realise it's all been a bit technological so far. And so now I'm going to do a really bad job at describing poppers. Objection to the Copenhagen interpretation of quantum mechanics.
And I'm, dare I say, going to say why he may have been a little mistaken. But it's a bloody good question. This. Let's consider this is my down conversion source and rather than my two photons going off left and right, I've drawn it as we often toyed with them going off in opposite directions. This is the classic EPR sketch. So these are my two photons and I've put mirrors in or whatever. So actually they're heading in opposite directions and I would find that they don't.
Even though my pump beam is beautifully pollinated, the town converted like this and it spreads out. And actually the amount by which it spreads out depends on the strength of the underlying correlations, but we won't show that just at the moment. And so this light beam spreads out some time. So you get single photons detected all over here and you get single photons detected all over there and the patterns match. Well, find whatever. And now I'm going to put in a narrow slip here.
And you know what happens when you put a narrow split into a beam? It's. Cause is diffraction. And if I switch narrow enough, the light here will now refract more than it was going to do before. Sounds sensible. What about this light? This is the proper question. I put a slit in here, causing these photons to different. What happens to these photons that they're entangled, that correlated? That's spooky. They're connected. What happens to these photons?
To these photons. Bear in mind, look, I think here the ghost image of the slit would be here. Just the ghost image of the slit caused these photons to be fracked. Yes. So, no, I'm afraid that's an interactive. We've entered the interactive phase of my lecture by telling those of you you're not going to get off lightly here. Hands up, if you think these photons different. Because I've put a slit in here. Hands up if you just think they carry on doing whatever they were going to do.
And the fact that it's an entangled source is irrelevant. Why? This quantum is the Copenhagen. I thought these photons were meant to be correlated. And the photons don't exist until I measure them. So I measure something over here, and it's got this very sort of strong downward momentum. I don't know. There's a slit there. Surely that must mean that the correlated photon over here has got a very strong upward trajectory. Isn't that what quantum mechanics is about? No.
So. I don't want to put words in his mouth. And I don't really understand what you wrote, but I think this is correct. So his question was, do the two particles show equal scatter in the momenta? If they do not, which is what you all, which is what you all thought. Popovic So is that the Copenhagen interpretation is wrong? If they do, we've got an even bigger problem because I can use this for faster than light signalling. I tropism a drop a slit in here. All of a sudden, these photons, in fact.
Not great pasta night certainly. So that's the that's the question that that popped raised. Let's think about that. Now what I'm going to show you is this. So, first of all, I'm going to do it with the restricted pump size. That's my. Schlitz. That's my small bucket. And I get something here. I get some diffraction pattern based on these slits. Oops. But I don't get as many as I get here. So this is the real diffraction pattern. I've got a lightning coming out here.
I've got a small pocket over here, and it's the diffraction pattern. I moved to the coast diffraction pattern. And actually the ghost diffraction patterns are not as good. Now, why is the ghost diffraction pattern not as good? It's not as good because actually there's a limited resolution in ghost imaging. And so there is these slits here, the ghost image of these slits. The slits were not as narrow as I thought they would be.
Because it is a finite correlation of strength and the down conversion source. And therefore, because the slits are wider, the envelope functional, my diffraction pattern doesn't come out as far. I hope I've managed to convey that. And so this is what I want to show here. This is the real experimental data as you change the pumping size in the Herald.
That's when you've got the diffraction pattern here. So you just do a normal diffraction trick it by this detector, change the size of the pump beam. No one cares. It doesn't matter. I still get five or six diffraction orders. Large, medium, small, going to the ghost configuration with a big pumping. I get a good ghostly factual pattern as I make the pump being smaller. I get fewer and fewer diffraction orders because the correlation is not there to create the small switch.
And so actually now this is not proof of the Copenhagen interpretation, by the way. It just says the Copenhagen interpretation isn't challenged by the proper experiments. And so that's what I really want to say. What Popper perhaps didn't realise. Is that? Yes. I put a small slit in here and that will indeed different. These photons. But the pretend slit the ghost image of the slit was not as narrow as you thought it was, and therefore it does not deflect the photons on the other side.
And that's a very hand-waving argument that I've just given. And therefore, Copenhagen is safe. Not proven necessarily, but at least not challenged by this thought experiment. Oh, that's enough of that. So if you want to read more about that, there's some papers you can you can download to. I can just give them to you. So that pretty much is that. I'll just finish off with this thing here that. I guess my take home message is that ghost imaging is not the same as conventional imaging.
However, unfortunately, it doesn't do better. It can match conventional imaging and it can match it with some interesting properties of the wavelength transformation, for example. But I don't believe. It's a route to enhanced resolution. It's only as good as the resolution of your classical imaging system. You can actually work out just from the properties, simple lengths of the crystal wavelengths, focal length of the lenses, precisely the pumping.
You get these two equations here which tell you what the resolution is in the far field, and this one here tells you what the resolution is. You get in the image plane. And so it's absolutely possible to work out from the geometric geometry of the system what resolution you expect, and then we to grade it. The resolution in our case by playing with this parameter here, the diameter of the pump. And so that is that. So I didn't mean to show your pictures of me skiing.
Not that it's particularly impressive thing. So thank you very much indeed.