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.