Download Quantum Trinity Lecture, Wroclaw, October 2016 All phrases are to

Quantum Trinity Lecture, Wroclaw, October 2016
All phrases are to be translated to Polish
The Quantum Trinity
wave, particle, spin
Joseph Indekeu (KU Leuven, Belgium)
University of Wroclaw, Poland, October 2016
Our purpose
•
Explore quantum physics with simple experiments
Experience the limits of our understanding
using
LIGHT
and
ELECTRONS
LIGHT
• Light rays
We are used to consider light as a bundle of rays. White light is a mixture of rays
that can be separated into rays of different colors by a glass prism.
Color spectrum
Intensity
Wavelength
During the 19th century it became clear that light belongs to the family of
electromagnetic waves and that the color of light corresponds to the wavelength.
At the beginning of the 20th century, in 1900, Max Planck created quantum
physics by introducing a new fundamental constant, “h”, named after him. He
introduced a new “quantum”, or “fixed amount”, of energy, proportional to h.
With this new quantum he could explain the spectrum of electromagnetic waves
with short wavelength, including x rays. Before 1900 only electromagnetic waves
with long wavelength, including infrared and radio waves, were understood.
LIGHT
• Light as a wave
How do waves behave?
Look at waves on water…
Waves display typical phenomena that we can easily observe using water waves.
Waves display reflection, refraction and diffraction. Waves can go around
1
corners and can pass through different openings simultaneously. The most
pronounced wave behavior is interference. In physical and mathematical terms,
interference is the local amplification or reduction of the intensity due to fixed
phase differences of waves.
Waves display…
INTERFERENCE!
We can demonstrate that light can behave as a wave by sending light through a
diffraction grating, which is a series of very narrow parallel open lines or “slits”.
The width of an opening is fixed and smaller than the wavelength of the light.
The distance between the openings can be chosen freely as long as it is larger
than the wavelength of the light. If we use visible light the wavelength is roughly
half a millionth of a meter, or half a thousandth of a millimeter, also called half a
micrometer. So we can put at most 1000 lines per running millimeter. We can of
course put less lines, say 50 lines per running millimeter, but the sharpness or
“resolution” of the image will be poorer. The experiment even works with only 2
lines!
Diffraction gratings
There are many ways of making a diffraction grating. An ultrathin metal foil can
be used, or, as on this image, lines can be carved on a glass surface.
When we shine the light of a green laser with wavelength 0.500 micrometer
through this diffraction grating with 600 lines per running millimeter, we see
this interference pattern. When we use a longer wavelength, from a red laser
with wavelength 0.650 micrometer, the interference maxima are farther apart.
We now wonder what will be the diffraction pattern of a bundle of white light, in
which all colors are present. We see that each color is diffracted in a direction
that is specific for that color. We observe that a diffraction grating allows us to
separate colors like we have done before using a glass prism.
Now comes a surprise. When we use a diffraction grating with less openings, say
50 lines per running millimeter instead of 600, we observe that not less but more
places are illuminated on the screen. This characteristic behavior is the signature
of interference of waves.
Next we shine a red laser on a piece of paper on which we have colored different
regions with fluorescent markers. We observe the reflected light. We always see
the same color. It is not surprising because a red laser emits only one color, only
one wavelength. Now we do the same with a green laser. We observe the
reflected light. Surprisingly, on some painted patches the light changes color. If
light were just a wave this would be impossible because a reflected wave always
has the same wavelength as the incident one. We conclude that some colored
pathches can absorb light and emit new light of different color. This indicates
that light can behave as a bundle of particles, and that different light particles are
associated with different colors. This insight was conveyed to us by Einstein and
2
the light quanta would later be called photons. In summary, we conclude that
light can behave as a wave but also as a particle.
LIGHT
• Light as particles
ELECTRONS
Now we leave light behind us for some time and turn our attention to particles
called electrons. Around 1923 the situation was as follows. Light has no mass
and no charge. Light often behaves as a wave but sometimes not. Light does not
often behave as a particle but sometimes does. The quantum of light will be
called photon. In contrast the electron was identified as an elementary particle
just before 1900, with mass and negative charge. It was not recognized as a wave
but only as a particle of matter.
Around 1923…
LIGHT
Mass: no Charge: no Wave: yes/no Particle: no/yes, “photon”
ELECTRON
Mass: yes
Charge: yes
Wave: no
Particle: yes
Then, with the doctoral thesis of de Broglie (in Paris) everything changed. All
particles with mass were attributed also a wavelength: a revolutionary idea.
PhD thesis 1924
A particle such as an electron has mass m, charge q, position x,
velocity v and …
WAVELENGTH lambda = h/mv,
with h Planck’s constant.
Just as we have done with light, a diffraction experiment was used to try to
decide once and for all, whether an object of nature is really a wave or really a
particle. The experiment was also done with electrons, and with a grating with
just two openings or slits, which is enough. The result was astonishing. Although
the electrons pass one by one, in the end an interference pattern results!
“Double slit experiment”
Are you particle or are you wave ???
Confess !!!
3
… when both slits are open, some areas receive LESS impacts than when
one slit
is closed …
This is the signature
of interference
SO: an electron is NOT JUST a particle, it is ALSO A WAVE
Wave-particle duality
Uncertainty relations of Werner Heisenberg
By measuring the position of the electrons,
one ignores their wavelength.
By measuring their wavelength,
one ignores their position.
We have now arrived at the heart of quantum mechanics, the duality of particles
and waves. By 1925 it became clear that the question whether something is a
particle or a wave is in fact meaningless. Massive particles as well as light can
behave in either way depending on the experiment they are subjected to!
We can illustrate quantum behavior in a simple way that you can try at home,
using a small water balloon, which represents the model of an atom proposed by
Niels Bohr combined with the idea of de Broglie that an electron has a
wavelength. The balloon can absorb and emit light like electrons in an atom. The
balloon can also vibrate illustrating how electrons that orbit around the nucleus
like planets around the sun, are in fact stationary waves. In fact, de Broglie
predicted the wavelength of the electron by demanding that the circumference of
the orbit in Bohr’s model be a multiple of the wavelength. The patterns of these
electron waves can be calculated since 1926 using the new wave equation of
Erwin Schrödinger.
Wave functions of Erwin Schrödinger
Yet, there is something missing. Even if light can behave both as a wave and as a
particle, the following experiment can never be explained. We shine light
through a polaroid sheet. Only a part of the light goes through corresponding to
one direction of polarization. We add another polaroid oriented perpendicular to
the first. No light passes anymore. Now we make it even more difficult for light to
pass by adding a third obstacle, another polaroid. Of course no light passes.
However, if we insert the third between the first two, some light succeeds in
passing all three! This was impossible if light were just a wave. This was
impossible if light were just a beam of particles. But light possesses a third
character called spin, which allows it to be manipulated in a new way.
Photon spin: polarisation
4
Not only light but also elementary particles such as an electron possess spin. The
electron spin is very special. It is called spin ½. It signifies that an electron must
make not one but two full turns about itself before it is the same again! We can
not illustrate this in any normal way, but Dirac found an analogy in our daily
world. It is called Dirac’s belt and we will now illustrate it.
Do like me. Take of your belt and seek a partner to assist you. That person holds
one end firm. You hold the buckle. You make a full twist with the buckle. This
cannot be undone by a simple shift. Do like me and try. Now follow me and make
another full twist with the buckle. Let us try to undo this double twist by a simple
shift. Now it works! You may try this at home. This is how you can illustrate spin
½ to your friends.
Electron spin: spin-1/2
Also the proton, which is the nucleus of the hydrogen atom, has spin ½. The
proton spin exposed to magnetic fields can absorb and emit a quantum of energy.
This property is used to make high resolution images of parts of our body that
contain large amounts of hydrogen atoms. It is a very precise and harmless way
to distinguish healthy tissue from ill tissue and is used by medical doctors all
around the world. The technique is called Magnetic Resonance Imaging (MRI)
and the following images illustrate it.
Nuclear spin and Magnetic Resonance Imaging
MRI images
with thanks to prof. dr. Raf Sciot, UZ Leuven
The three properties we investigated, or “characters” that we observed, thus
form what I would like to call the wave-particle-spin trinity in quantum physics.
It is my personal view developed for this presentation. The traditional view is to
speak of wave-particle duality and I recommend that you remember it as such.
Micro-Electronics
1948
2x Physics Nobel Prize
1956 and 1972
We close this presentation by examining some properties of the transistor, a
quantum tool by excellence. The transistor is perhaps the most important
invention of all times so far. It is the building block of all Information and
Communication Technology. Without transistor, no computer. Without
transistor, no mobile, no GPS, no etc.
5
We will use a hydraulic analogy to illustrate first a diode, then a transistor.
Before that, we must say a few words about semiconductors, which are the
materials diodes and transistors are made of. Semiconductors posses a quantum
energy gap, which means they carry no current when only a very small voltage is
applied. However, when the voltage is not small, two kinds of currents flow: a
current carried by the negatively charged electrons and a current carried by the
positively charged “holes”. We can simulate both currents using a colored liquid
in a tube, provided we hold the tube in the correct orientation in the
gravitational field of the Earth. The liquid drops represent the electrons, the air
bubbles represent the holes. If we change the “polarity” by turning the tube
upside down, no currents flow. This illustrates how a diode can be used to give a
unique direction to a current.
Around 1948 John Bardeen, who holds two Nobel Prizes in physics (!), and his
colleagues, added an important feature to a diode. They found how the currents,
even when they are very large, can be manipulated to switch on or off, using a
very small force. This is illustrated using this second tube. This invention also
made miniaturization of electronic devices possible. The following images show
some applications in the micro-electronics of the 21st century.
•
Diode and transistor:
hydraulic analogy;
applications in the 21st century
6
Materials and devices
Exploration of the 3rd dimension
3D demonstration
DRAM on processor
with thanks to prof. dr. Staf Borghs, imec and KU Leuven
I hope you all enjoyed this introduction to quantum physics.
Thank you !
Want more? …
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
7