Welcome back everyone. I'm Charles Clark.
And in the second art of this lecture, we're going to look at how these atomic
spectra are acquired and what the sort of instrumentation used.
And then the implications of that understand the observations and for other
future experiments on quantum systems. Here's a nice simple picture, peaceful
system, something I'm sure you've seen many times before.
This I think is a very nice illustration due to Paul Doherty of the Exploratorium
in San Francisco. it shows that evidently a pond, I think
those are fish swimming about it. And you see two sort of distinctive wave,
wave structures. One of which is, let's say, around here
centered presumably at that point. Then there's another one centered around
here. So, I want to note several things about
this picture that are, that are evident to anyone who has looked at a wave
pattern of this type. First of all,you see a nice regular
motion here since it's still water and maybe some object was dropped here and
another one dropped a different time there, and the waves spread out.
And when they overlap, you, so they show these regular curve, regular wave fronts
when they're isolated. When the wave motion is mixed, you see a
more complex pattern. This is the phenom on of interference.
But significantly, when the waves have passed through each other, they continue
on as if they had not encountered any other anything other than clear water.
So, this is, the, the, the problem. The, the phenomenon of interference is
also related to the phenomenon of linearity.
In that, the presence of a second wave doesn't really disturb the, the other
wave. It's only that those two waves, for a
while, operate together and interfere. Now, it must have been an observation
like this that motivated Thomas Young to build a device that is one of the one of
the most ingenious simple experimental devices every made, in my opinion.
So, here's a schematic of the operation of Young's device.
It's, it's called today a double slit interferometer, in fact, it was a double
hole interferometer. He just took a thin piece of paper and
put two holes in it, at a a short distance of separation.
And so, the idea is at some light, light incident on the holes would produce the
following effect. And let me say, first of all, that at the
time that Young did this, there was considerable debate as to whether light
was a wave motion or a type of particle. And by constructing this device, Young
demonstrates quite conclusively that there was a wave.
And he did something even more important which was to actually be able to measure
the wavelength using this device. We will show how that works in a moment.
But basically the idea is, it's like that ripple pattern in the pond.
You create two independent sources of waves which will interfere and if you get
far out away from the, away from the the plane where the, where the holes are,
you'll see regular alternation of the, the light.
So, here's the schematic of the Young, it's just a reduced size.
You have these two holes. We'll say they're separated by a value of
d. This is the separation.
[SOUND]. That's something you can measure if
you're making it yourself. And then if you the light comes out in
all directions but it's in those directions where the, let's say, the path
difference between two rays, the ray coming from one, one hole and the ray
coming from the other. The path difference which is indicated
here, which I'll, designated by delta, well, that path difference for this angle
theta as indicated here that path difference is just d sine theta.
I think you can see that by simple geometrical construction.
And so, this is the equation for constructive interference.
This is sort of the [UNKNOWN] equation that when the path difference is an
integral number of wavelengths, you get constructive interference and so you see
a bright, you see a bright spot on the screen.
And you see those at different orders so that there's, there's here's, here, this
would be the m equals 0 order that light could go straight through.
You clearly get the same path from either slit if you're looking at the midpoint
between the slits. And then you get by convention, here's
the first-order diffraction. Down here, there'd be a minus 1th order
and so on. Now, the really striking thing about this
ex, experiment of Young's and I, I encourage you to, you read it in his own
words. Here's an excerpt from it here.
But you can find the original in our supplementary documents the one that's
entitled Young's Slit Experiment in Diffraction.
The really remarkable thing is, that he used this device to measure the
wavelength of the light. Now, this again, at a, was a time, it
wasn't even known that light was a wave motion.
But he used this analysis of the interference pattern.
And here, here's the results that he quote extreme red light must be in air
about one 36 thousandth of an inch for those of you outside the USA.
That's an inch is 2.54 centimeters, exactly.
And those are the extreme violet about one 60 thousandth.
That's a, in modern notation, 423 nanometers compared to our reference
standard 405. So not, not far away from the blue ray
pointer. And then here is the, the, the thing that
is really striking. He says, from these dimensions it
follows, calculating upon the known velocity of light.
So, in other words, he used this fundamental equation that you've just
been looking at in the previous lecture did an exercise on if I'm not mistaken,
the wavelength times the frequency is equal to the speed of light.
So there, the speed of light was known at the beginning of the 19th century, known
to some accuracy. He says, there are 500 millions of
millions of the slowest of those waves, meaning, I think, he means the lowest
frequency in the optical do, domain. So, here he has carried out an indirect
measurement of a frequency of, well, how do we say that, that's like 500
terahertz, I guess, 5 times 10 to the 14th cycles per second.
Now, that was a frequency completely impossible to measure at the time that
Young did his experiment. There were no electronics then, so the,
the fastest the fastest frequency that could be measured accurately was
presumably due to some mechanical contrivance or tuning fork perhaps.
and even, I have to say, even today, the direct measurement of an optical
frequency is by no means a routine matter.
this, this is a this is 10,000 times higher frequency than that of, of a
microwave oven, for example. It's a million times higher frequency
than FM radio. It's a frequency that can't be handled by
conventional electronics. And, you know, just as an indicator of
this in 2005, the Nobel Prize in Physics was awarded to John Hall and Ted Hansch.
as you can read for and, and especially noting this optical frequency comb
technique, which is, right now, the main way in which people are able to, to do
direct optical frequency measurement. So, it has come to pass, but Young's work
in this sense was really visionary. Now, there's been, so the interferometry,
optical interferometry has been a great tool for Science and Engineering.
And the techniques have been extended to other systems.
So, in particular, to things we would ordinarily characterize as particles,
electrons, neutrons, atoms, and molecules.
I'm just going to show you two examples. this is, this is an example of neutron
interferometry. It uses, okay, it's not a two slit
experiment per say, but it does something similar.
So, what happens is you have a beam, a neutron beam, that's incident of, this is
a, this is a solid block of silicon that's just been milled down to form
these three blades. and so the neutron beam comes in and it,
it enters this part of, part of the, sorry, part of the beam is, is
transmitted, then and part of it undergoes Bragg reflection to the second
plate. Then, part of that goes, goes through,
part of those two beams go through. But then, there's also Bragg reflection
from the internal blade. Sorry, did I make that clear?
And so then, the beams recombine and then their, the summed beams are output in two
directions here. So basically, what happens is when a
neutron go in the amazing thing about this is that at the intensities that are
used, there's never more than one neutrons in the interferometer at any
given time. In fact, there's mostly no neutrons in
the interferometer. But when you accumulate the, the pattern
of signals, you get the same interference pattern that you do for light wave.
So, this is the origin of this famous expression of Paul Dirac.
A particle only interferes with itself. I think the modern version of that is a
particle does interfere with itself. So, even on this macroscopic scale, which
you can see is just about the size of a, a 12 ounce soft drink can even on this
macroscopic scale, single neutrons actually exhibit the, the interference
pattern that you see here. And this was a very important experiment.
It was the first used to measure the effect of gravity on a quantum particle.
So, what you're seeing here is basically a, it's a rotate, this [UNKNOWN], this,
this interferometer was rotated in the gravitational field.
So, one of these paths was a little bit, was a little bit higher up in the
gravitational field than the other. And that gives this phase effect, this,
this interference effect that you see. The the de Broglie wavelength here is 10
to the minus 10 meters. just recall that for light the, the
wavelength is like 500 nanometers which would be, you know, 5 times 10 to the
minus 7 meters. So, this is, this is the, the de Broglie
wavelength here is comparable to the radius of an atom.
And you see this nice interference pattern.
Now, here's another object on which a quantum interference experiment has been
done. not exactly like the Young's double slit,
but again, with different paths, paths in space to a destination, and seeing
interference fringes. And this thing, gosh, I don't even know
if I can pronounce its name. I'll just let you read it.
TPP, it says, contains 152 fluorine atoms.
Actually, it kind of looks like the logo for the burning man festival.
Anyway, this is, this is okay, this you can't see with your eye.
It's 1 nanometer in size. But it's, it's a pretty good size for a
molecule. And it has a de Broglie wavelength of 10
to the minus 12 meters. Now, that is you know a factor of a 100
smaller than an atomic diameter. So it's really quite extraordinary that,
that people can now produce and control such large molecules to the degree that
makes quantum interference possible. But it can be done.
And I point you to this recent review article.
It's a colloquium style article. So I mean, if, if you have no physics
background whatever, you'll probably find this quite hard to understand.
But I'd say a a person with a Bachelor's degree in Physics can probably get quite
a bit out of reading this article. So, it's again, it's written at a, a
level that's intended to be accessible. In any event, the pictures are quite
remarkable and the idea that you can do quantum interference on things that are
so massive and, and so large is really, to me, quite inspiring.
So now, we're going to talk about diffraction, which is just a
generalization, you know, in the context that we're using it here, just a
generalization, the idea of interference. So this, the, the earliest really,
productive lasting work was done on this was again, by the great man Fraunhofer,
he developed a diffraction grating which you can just think of as a multiple slit
interferometer. So, you just have, you have waves coming
out from different slits or in the case that's shown in this picture, you have
rulings that are made on a mirror so that you get a, you get a reflection from a
periodic array of objects. And so, this means that instead of having
two light beams interfere, you can have a large number, literally thousands, and
the the intensity signal, of the signal goes with the square of the number of of
of scatters. Indeed Victor showed in his early
lectures, a, a picture of X-ray diffraction which is very much the same
idea. You have a periodic array.
It, it, you can, you can see that with great clarity using, in the, in that
case, X-rays in this case, light. The diffraction grating has to be one of
the most powerful passive devices that was ever thought of because you can make
it, just if you can do very accurate rule, make accurate rule, ruling marks at
regular spacing. So, this, that, that was a technology,
that was developed to quite a high degree in the 19th century.
And Fraunhofer indeed used it to make direct measurement of wavelengths.
So, the, his early work with the prism it only describes the deflection of the
light in terms of the angles of deflection because we have no way of
knowing what the wavelength was. But he repeated his studies later on
diffraction grating and that made it possible to get quantitative data on the
actual wavelengths of those dark lines in the sun.
And in about two or three slides, we'll see why that's important.
I'd like to just mention that if you're viewing this lecture right now, you are
being helped by untold thousands of the diffraction gratings, which are an
essential piece of the architecture of the the, modern fiber-optic
telecommunications infrastructure. So, a wavelength division multiplexing is
a procedure of putting a high data stream on a beam, on a beam of light.
It basically, it doesn't use white light, it uses some, it uses some band of
wavelengths that you can't see here, they're in the infrared, typically around
1,500 nanometers. but it you, if you have a broadband if
you have a optical, optical signal with a finite bandwidth, you can use a
diffraction grating to, so you have, you input the light to a diffraction grating.
It spreads it out, and then you can do encoding on the separate channels then
recombine them into another grating to put them back into the common being.
So, this wavelength division multiplexing is what makes it possibly to put such a
high transmission rate on the Internet. There are many, many other applications
of this technology as well, and again, it's governed by the simple grating
equation. So now, we're going to have a a little
online quiz that's sort, it's a non-mathematical one help you to retain
some knowledge of the, of the things that I've just mentioned in these past few
slides. Okay, I hope that was useful and let's
now take a look at the optical spectrum of the sun again.
I've taken a, I've taken and, I just, I just made an enlargement of a region of
that picture of the high resolution spectrum of the sun that we were looking
at previously. Just to show you, you know, in depth what
the, the complexity of the line structure that's there.
So, this is, this is acquired by a Fourier transform spectrometer with a
resolving power of 500,000. That means that the, it can see a
variation of the a significant variation of the optical signal over a, a
wavelength region that is one over 500,000, about two parts in 10 to the 6th
of the, the wavelength of importance. So, as you can see, there's very many
narrow lines. This is, it's a dense dark packet
communication. The sun is sending us a message, okay?
And we didn't even know that until Fraunhofer's work but it looks like it's
been sending the same message forever because these, these dark lines are very
stable in time. Their intensities may very a little bit
but they're always in the same spot. They don't wander around.
So, so, what are these things anyway? A key clue to the nature of the
Fraunhofer lines came from the study of emission of light by gasses subject to
electric discharges. Now that's a mouthful, but you're
familiar with this sort of phenomenon. Here's a, a famous neon sign in a movie
theater in California, and if you go to entertainment districts around the world,
you'll see these vibrant lights that are produced by typically rare gases.
they, they have a very striking visual appearance, which is why they're so
popular for display purposes. Now, here's a demonstration of why the,
the visual appearance of these neon signs is so striking.
And that is because they're not putting out a broad band of white light but
rather a series of, of, of quite localized features.
Here you see, this is the lower the lower curve here, lower band here.
It shows a photograph of a spectrum of neon dispersed by wavelength.
So again, here's our common 650 nanometer 650 nanometer referenced laser.
Here is the 530. You see, there's a couple green lines
there. Here's our blue ray.
And so here, is the neon spectrum is concentrated in color in one region.
That's why it's so vivid. Now, the same is true for hydrogen though
it has even a simpler spectrum. As you can see, you can see four lines
here. One at 656, very near to our our
reference laser at 650. and then another there's two more down
here. This is sort of in a cyan color.
And then, one at 410 nanometers, very close to our reference laser 405
nanometers. So this, this study of emission of light
by gasses developed independently in the 19th century.
and it was facilitated by the ability to make precise measurements.
And so, this lead to a major breakthrough.
This breakthrough was due to Robert Bunsen and Gustav Kirchhoff, who found
that emission and absorption lines of gases occur at the same wavelengths, that
is, at least in many circumstances. so, it was natural to attribute the dark
lines seen by Fraunhofer to absorption of sunlight by gases in the solar atmosphere
in cases where the gases could be could be found on earth.
And indeed, it was quickly ascertained that the in particular, this famous
hydrogen line at 656 nanometers. I'm going to use red to illustrate it,
which is called H alpha or Balmer alpha after the Swiss school teacher, Balmer.
It's quickly ascertained that that was a line associated with a hydrogen gas.
and here, here, here it is. Here's this little patch taken out of the
high-resolution solar spectrum of the sun.
So it is indeed seen in absorption. Now, why is that?
So, it's clear, there's a, there's a way of making a common identification.
One in emission, one in absorption, one is in the atmosphere of the sun, the
other is in a laboratory on earth. why are atoms always in the same state in
such different environments? And what is the mechanism that causes
them to emit light only in these very specific regions of the spectrum, rather
than in the continuum of the sun? And to me, this is actually, this is a
quantum phenomenon in the sense that we see these packets localized in in
wavelength. And that suggests there's something
highly specific that goes on. There's a sort of fundamental energy or
vibration in the atom that occurs for a reason that's rather hard to understand,
when we think of motions of particles under the usual types of forces.
So, we're going to explore that in the forthcoming lectures.