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Transcript
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