Hi Everyone! Have you ever wondered about how big a photon
of visible light is? It must be smaller than the pupil in your eye, right? In fact, it should
be small enough to fit through a 1 micron slit. Yet, it should also be big enough to completely
cover two slits, that are spaced more than a thousand microns apart. So, I guess, answering
this question is not going to be a trivial thing. In the past, I always used to think
of a photon as something really tiny, like a little electromagnetic wave
traveling through space at incredible speed. But in the last few years, my views have changed.
And in this video, I will discuss why that is So, if you Google for information about
the size of a photon you will not find one definitive answer. It seems everybody has their
own opinion about this subject, or even about how size should be defined. Some say that, because
a photon is massless, it does by definition not have size because it does not occupy space like
a physical object. But you can also define size as the “distance” or “volume” over which
something interacts with its surroundings or even with itself. And if that’s your
definition, then photons definitely have size. Now, in school I was taught that a photon is the
smallest amount of energy that can be present in light of a particular wavelength. So, photons
do have wavelength and for visible photons that wavelength is generally in the order of half a
micron. But wavelength is not the same as size. For humans, size is important, I guess. If you
buy a new car, you better make sure it’s the right size for your family and your garage. And
so, if you see that a lens can focus light to a spot smaller than a micron, it is tempting to
think that a single photon should be smaller than the spot, right; because light is made of
photons. Well, things may not be that simple. For one: is that spot size really 1
um, or is it actually much bigger? One of the most fascinating properties
of light is indeed its wavelength. If you look carefully, light constantly reminds
us that it must have one. As soon as we create a disturbance in the path of the light, we can
observe this phenomenon called interference. A very famous example where we can observe
interference is of course the double slit experiment, where the “disturbance” in the path
of the light is a mask with two narrow slits. So here the light can only to go along two well
defined paths. And the result is that we observe these areas of higher and lower intensities
behind the slits. And these areas are where the light waves are either in phase or out of
phase. Now, this is just one example: we can also create interference by for example recombining
the light of a source and its mirror reflection. Or we can even manipulate the interference very
cleverly by using a Fresnel zone plate pattern. Interference is caused by the fact that
light is an electromagnetic wave or field. And this is the way that you generally see
alternating electromagnetic fields visualized: as a wave travelling along a narrow line.
Now, looking at this kind of depiction, you should ask yourself a few questions. The
picture suggests that the perpendicular magnetic and electric fields indicate the field
strength at the direction of propagation. But it also suggests that the field
travels along a very narrow line. But this is obviously not correct. If only,
because magnetic field lines are always closed loops and extend into space quite a bit, actually
quite a bit more than is shown in this picture. And since the electric- and magnetic fields
are always directly related, we know that the same is true for the electric field. So even an
electromagnetic field with the lowest possible energy, which we refer might refer to as a
single photon, can never be this localized entity travelling along a very narrow line. Instead, it
must be something widely distributed in space. On the other hand, if we try to detect light, we
find that the detection events themselves are very localized as well as quantized in energy.
We can only detect the field of the light by removing discrete amounts of energy from the
field, and when we do this, the process occurs very locally. For example, it can happen when
a photon is absorbed in one particular pixel of a CCD sensor. Or should I say in one
particular atom in a pixel of a CCD-sensor. So, this is where things get a bit weird: on the
one hand, we know that the field representing a photon is distributed in space. But when we try
to detect it, we can only do so very locally. And we might ask ourselves: what do mean exactly
with the term photon: does it refer to the field or part of the field itself, or do we refer
mostly to the processes of transferring energy to and from the field? And now that we
are asking ourselves all these questions, how long is the electromagnetic wave
of a photon? Is it like 1 wavelength, or approximately 2.5 like is shown here,
or maybe a few thousand wavelengths? As I said earlier, my views on what photons are,
have changed quite a bit in the last few years. In fact, there was this one experiment I did
in October 2020 that really got me thinking. I showed this experiment earlier, as a side note at
the end of a previous video. So, what I build was a modified version of the double slit experiment.
And the modification I made was that I had split the path leading to the slits into two spatially
separated paths. Each of these paths leads to only 1 particular slit and both paths have a
different length. In fact, I made the longest path about 40 mm longer than the shortest path.
And even though 40mm may not sound like much, this distance is equivalent to more than
75000 wavelengths of the laser light I used. Now, when I brought down the beam power
to “single photon” level, I did not really know what to expect. But it turned out, the
experiment still showed very clear interference, even with this additional path difference present.
So, the experiment suggested that, not only can a single photon simultaneously take paths that are
spatially separated over a substantial distance, but it also allows these paths to have
a very significant difference in length. If you were used to visualize a photon as
being this little local electromagnetic wave, like I used to do, this experiment burns a
hole in your brain. Because it shows that the interference properties of single photons
extend over amazingly long distances in space. And at that point I realized that my ideas
about the photon were completely inadequate. And there were several people, that told me the
outcome of my experiment had to be wrong. Of course, without offering any particular insights
on why. Personally, I am convinced that the result of the experiment is correct, but I now also
think that the explanation I gave for the behavior is flat-out wrong. So, we are going to do
this experiment again but now stretch that difference in path length a bit further and see
what happens. Will there be interference, no matter how long we make that second path, or will
at some point maybe the interference just go away? Let me just walk you through the schematic:
a HeNe-laser produces a beam of coherent monochromatic light. The intensity of
this beam is then attenuated to single photon intensity levels with a series
of gray filters. Later in this video, I will discuss how that was done. Next, there is
a beam splitter that creates 2 different paths for the light. The short path leads directly to
a detector, while passing a second beam splitter. The other path takes the beam on a little
sightseeing tour and eventually brings the light back to recombine with the light
from the of the first path. As you can see, the long path is about 5 times as long as
the short path. After the light of the two paths is recombined, it is detected here in a
camera where we can look at the interference. Let me show you around the actual setup. Here is
the HeNe-laser, a golden oldie which was produced in December 1979. At its last calibration, it was
generating < 1mW. But wait, does it say in 1985? Now even though this laser has matured as
gracefully as I have in the last 35 years, it has lost quite a lot of its mojo.
Because now, it only produces about 0.3mW. But all the better actually, because we
don't need a lot of light for this experiment. Next in the setup there is a mirror under
45 degrees that is used to control the beam direction, followed by a set of neutral density
filters to bring the power of the laser to single photon level. The light then passes through
a beam splitter, creating the two paths. The first path continues in a straight line to the detector,
while passing a second beam splitter. The detector by the way is a pretty standard IP camera, with
a Peltier element to reduce thermal noise a bit. The longer path in the setup is routed via
a Porro prism to the second beam splitter, where it is recombined with the first beam.
As you can see there is also a lens here, which is used to compact the interference
pattern a bit to make the detection more sensitive. The additional mirror for the
second path was necessary to achieve a detour of more than a meter long on the base plate.
By placing the two recombined beams under a very small angle, the interference pattern displays
only a few minima and maxima, which is convenient, because a pattern like this allows for
very sensitive recognition of interference, even at extremely low intensities. The
interference is recorded using a camera. And because the light levels in the room are
way too high for doing single photon detection, I also shielded the setup from ambient light.
For this, I used a few pieces of cardboard, just to give the setup a nice high-tech look and feel.
The most important question in this experiment is: how can you be sure that the beam power of
the laser is in the single photon range? Well, imagine that we have a continuous light
beam coming out of a laser and we start adding gray filters that each transmit a certain fraction
of the light, say 10%. At some point we will reach an output power in the beam that is equivalent
to on average only a single photon at any time. So how do we do the calculation? Well, we assume
that the light is quantized in discrete amounts of energy. We start out by calculating
the maximum life time of such a quantum in the setup, given the speed of
light and the maximum path length. For 1300mm, this value is 4.3 nanoseconds. This
means that, for an average of 1 photon in the beam at any time, the photon flux can be as
high as two 230 million photons per second. And using the photon energy of the laser
light, this flux is equivalent to 74 picoWatts. With the current power output
of the laser, which is 0.3 mW, we can calculate that we need to attenuate
the beam by at least a factor of 4 million to get to this 74 pW. This means we need a filter
with an optical density of 6.6 in the beam. Now, in practice I was able to detect interference
with filters having an optical density of 9. And if we use these last filter settings,
we can calculate that, the beam intensity is 250 times lower than that of a beam
containing, on average, 1 photon at any moment. Now that we know that we can indeed go
into the single photon intensity regime, I can finally show you the
result of the experiment. Do we still observe interference with
a difference in path of over a meter? Let’s not keep you in the dark any longer. This
is what we observe in the single photon regime if either one of the paths is closed off and
this is what we observe if both paths are open. Now, there is no doubt about it: even in this
case we observe an interference pattern. Hence, at single photon intensity level, the photons
do exhibit interference. Even if the 2 paths differ in length by a factor of 5 and in absolute
length by more than 1.6 million wavelengths. Now I can assure you, the more you think about
this result, the whackier it gets. And I guess whacky results ask for whacky explanations. So,
in the previous video on the subject, I proposed a pretty whacky explanation. In an attempt to
explain, I suggested that we could assume that the phenomenon of interference is somehow be detached
from our temporal and spatial observations. So basically, my suggestion was that, because
light travels with the speed of light, it does not experience time and distance, so all
paths are covered instantaneously when viewed from the perspective of the photon. But in retrospect
that explanation is rather silly and raises more questions than it answers. Also, there is a much
simpler explanation that actually makes sense. And this explanation was suggested to me by David
Nadlinger, a researcher at Oxford university. He very kindly explained where the experiment
went wrong. The physics behind it is pretty hefty and not YouTube video material, so
I’ll try to explain this in my own words. The essence is that the electromagnetic field of
the beam, after leaving the attenuation filters, is a more or less a continuous wave or
field, like drawn here schematically. And you’re probably are thinking: where is the
quantization? I thought light was made up of individual photons? Well, yeah but no but. [Vicky
Pollard] yeah, but no ,but yeah. Thing is that, even though the energy transfer processes to-
and from the field have a quantized nature, the electromagnetic field itself is actually is
not quantized. It can basically take on any value. So let me explain this in a little more
detail. Contrary to spontaneous emission, which is sort of a random statistical process
of energy emission in discrete packages, a continuous laser like a HeNe laser emits a beam
of coherent light. And the field exiting the laser is a continuous electromagnetic wave
which has a high field strength. And that is because, almost all the quanta
of energy are added to the beam in phase, due to the stimulated emission process. If
such a beam passes the gray filters, it will decrease in intensity because of absorption
of a part of the energy in the beam. And yes, this absorption process has a quantized nature,
and happens in discrete steps. But it happens in sort of a random manner in time and also spread
out in space within the volume of the filter. So, each absorption event takes sort
of a random little bite out of the remaining field, decreasing the intensity a bit.
Now, because the electromagnetic field strength itself is not quantized, this process eventually
results in a sort of continuous field strength that is much lower than what is found in
a true single photon event produced by spontaneous emission. The field strength can
at times even be almost zero or actually zero. But even though the field is very low, it is
still coherent and more or less continuous. So, this could very easily explain why we
observe interference in this configuration: it is because in essence we have 2 continuous
coherent beams interfering. So yes, the power of the beam is far below single photon
intensity level, but none the less it is continuous. And this is very counter-intuitive
if you are taught that light is quantized. So basically, I had poor choice of light
source. Had I chosen a fluorescent lamp instead of a laser, my single photon
calculation had actually made sense. And of course, I would also never have observed
single photon interference in the current setup. The experiment by the way also shows a
few other interesting aspects of light. You see that the interference pattern consists
of these individual sensor pixels that light up. And it is good to realize that these are in
fact not single photon detection events. What we see is CMOS-pixels that collected a specific
minimum number of photons. And the reason that it is displayed like this, is because I cranked
up the gain of the camera to a very high level. Anyway, even though we are not observing
single photons, we can observe this interesting phenomenon, called “shot noise”. Basically, we
see that the spatial distribution of photons is not the same for each individual measurement.
And this is caused by statistical variations in the photon detection for each measurement.
It’s also a subtle reminder of the fact that when we can never observe interference from just a
single photon. Because demonstrating interference always involves collecting many photon-detection
events. In other words, what we do when we look at interference, is gathering statistical
information about the spatial probability of detecting a photon somewhere. And this probability
itself, like the field, is also not quantized. I guess my main problem with understanding the
behavior of light was that everybody always told me that the energy in light is quantized. But they
forgot to tell me that the electromagnetic wave, so the carrier of the photon energy, is not
quantized. An electromagnetic field can be attenuated, diluted by traveling through space
and can be split in arbitrary fractions when passing a beam splitter. The field has no problem
whatsoever with this because it is not quantized. But of course, the probability of detection, being
proportional to the square of the field strength will also be diluted or split. And
that is basically what we observe when we look at interference: these dark and
bright bands we observe are just the result of local variations in field strength, due to
phase differences between different paths. If you consider the field as the leading
property for the probability of detection, the things we observe in diffraction experiments,
like for example the double slit experiment, become almost kind of trivial. Because, if
quantization is not a property of the field, but just of the energy transfer
processes between field and matter, the outcome of the experiment is
basically what you would expect. But what is definitely not trivial to imagine,
is how the energy contained in a wave, spread out in space can be converted back to another form
of energy in a very local and quantized event. So, to get back to our original question: “how
big is a photon of visible light”? Well, if you consider the photon to be the same thing as the
electromagnetic field, photons can be absolutely huge. Or at least their volume of interaction
can be huge. In fact, within this definition is no fundamental limit to its size. But if you
define the photon as the quantized interaction between field and matter, then a photon is in fact
an extremely localized phenomenon. You choose. [DELETED SCENE] Here is the HeNe-laser, a golden
oldie which was produced in December 1979. At its last calibration, it was generating
< 1mW. But wait, does it say in 1985? Hah, I remember that year. [music]
