Books Quantum Physics Basic Physics Knowledge
1 Mr Administrator,
Dear colleagues,
Ladies and gentlemen,
2 " I think I can safely say that nobody understands quantum mechanics ". This statement, made by physicist Richard Feynman, expresses a paradoxical truth about the scientific theory that revolutionised our understanding of Nature and made an extraordinary contribution to our means of acting on and gaining information about the world. In this lecture, I will discuss quantum physics with you by attempting to resolve this paradox. And if I don't succeed, Feynman's joke will at least comfort us in the knowledge that many of us are in the same boat.
3 From the infinitely small to the infinitely big, covering over 60 spatial orders of magnitude, quantum theory is used as much to describe the still largely mysterious vibrations of the microscopic strings that could be the basic constituents of the Universe, as to explain the fluctuations of the microwave radiation reaching us from the depths of outer space. Between these two extremes are all the objects of the world around us (Fig. 1). Add 20 zeros to the dimensions of the hypothetical strings I have just mentioned and there you have the size of an atomic nucleus, the heart of radioactivity and nuclear energy. Another five zeros and there's the atom, the nucleus held to its cortege of electrons by electromagnetic force, as well as simple molecules, small clusters of atoms that form and break up according to the laws of chemistry. Go up another two or three orders of magnitude and we reach biomolecules, where life manifests itself at the most basic level. Still another six to nine orders of magnitude and here we find the range of dimensions going from one centimetre to ten metres, that of the human scale, with its diversity of macroscopic objects, solid, liquid or gaseous, consisting of billions of billions of billions of atoms. From our scale to that of astronomical objects – planets and stars governed by gravitational force – add another eight or nine zeros. Finally, we need another 16 orders of magnitude to complete our journey, through the exploration of galaxies, to the far end of the Universe.
Figure 1
From hypothetical microscopic strings (top left) to fluctuations of cosmic radiation (the map of these fluctuations revealed by the COBE satellite is shown bottom right), quantum physics must explain phenomena across more than 60 spatial orders of magnitude.
4 Along the vertiginous journey we have just taken, physics must describe and explain an infinite variety of phenomena. Some have been empirically known for a long time, others were discovered during the last century owing to the development of powerful means of investigation. At the far ends of the infinitely small or the infinitely big, others still raise questions that remain unresolved. But few have not had at least some aspects brought to light by quantum theory, which accomplished brilliant achievements over the course of the last century. Theorists will no doubt point to the extremely precise description it provides of the interactions between electrons and photons in quantum electrodynamics. They will first note the remarkable quantitative agreement between experiments and theory. They will also talk about the unification of three of the four fundamental forces – electromagnetism and weak and strong nuclear forces – into a unique formalism that reveals Nature's profound symmetries. They will mention the promising attempts to include gravitation into this unification, by developing a quantum string theory, and will insist on the universality of physics, a remarkable consequence of the properties of quantum theory. This theory explains the spectrum of the radiation emitted by the hydrogen in the discharge lamps in our laboratories, as well as in interstellar space. Quantum chemistry applies to the reactions in a chemist's test tube, as well as to those that take place in specks of intergalactic dust in which molecules are formed and separated, their radiation picked up by our telescopes after millions of years travelling through space. Finally, cosmology and parallels between the infinitely small and the infinitely big, stimulated by quantum theory, highlights the profound similarities between the phenomena that occurred at the origin of the Universe in an environment whose density and heat are difficult to imagine, and those that occur during the violent collisions between particles in our giant accelerators.
*
5 Quantum physics does not simply offer a precise description of the structure of matter. By providing us with in-depth knowledge about the phenomena that take place within matter, it offers us means of action, computation and diagnosis of a power and precision that were previously unimaginable. Take the small laptop I am using to present this lecture: if you examined its insides, you would find a small case under the keyboard, containing a silicon chip a few centimetres long, on which a labyrinth of electric circuits is printed. These circuits link stacks of semiconductor material, tiny transistors constituting as many small logic gates. The properties of these materials are governed by quantum laws ("tunnel effect", "Pauli's exclusion principle", etc.). Articulating these laws makes it possible to perform highly complex programmable computations. The principles of a computer have been known for a long time; the capacity to store information and compute goes back at least as far as Pascal's machine (Fig. 2). The principle of computing programming is attributable to Babbage, who in the 19th century imagined a complex machine made up of an assemblage of cogs and mechanical elements. The development of the electric industry in the first half of the last century led to the replacement of mechanical circuits with vacuum tubes and thus the first computers of the modern era. The machines that Léon Brillouin, a professor at the Collège de France, helped develop in the United States just after the war (Fig. 2), were nevertheless enormous and largely unreliable, and required constant maintenance by an army of technicians. And their performance was far inferior to that of the small modern computer I mentioned just now (Fig. 2). The discovery of transistors and the possibility of integrating huge numbers of them into a semiconductor material is what allowed for the proliferation of computer applications. The logical principles of modern computers could have been understood by a person of the 19th century, but their practical realization necessitated technology that would have been inconceivable to a pre-quantum mind.
Figure 2
Three generations of computers. Quantum technology has allowed for the miniaturization of the computer and all its applications in daily life.
6 The laser is another example of an invention based on a quantum effect, now omnipresent in our daily lives. I remember how the young student I once was marvelled at the first lasers emitting their directional beams of intense and monochromatic light. Nowadays this is no longer a remarkable sight, but until the 1960s we had never seen anything like it. Since time immemorial, light had been a rebellious wave, awkward to direct and to concentrate; its oscillation at a well-defined frequency had been difficult to achieve. The laser changed this and allowed us to domesticate radiation by exploiting the properties of atoms' stimulated emissions, established by Einstein in the early days of quantum theory. Lasers now have an infinite number of uses, from the most trivial to the most sophisticated, from the reproduction of sounds recorded on compact discs, to the barcode readers of supermarket checkouts, through microsurgery or fibre optic telecommunication.
7 Another important application of quantum physics relates to the precise measurement of time. The atoms in each element emit and absorb light at characteristic, unchanging and well-defined frequencies. As a result of this fundamental quantum property, the measurement of time is now no longer based on the oscillations of pendulums, springs or quartz crystals, subject to perturbation, or even on the movement of celestial bodies which also fluctuate despite their apparent regularity. Instead, it is founded on the oscillations of physical variables associated with atomic electrons. Thus were born the first clocks that now define time with a precision of the order of a second over geological eras. These are the atomic clocks which, synchronised together and sent on board satellites, send signals to the receiving devices of the Global Positioning System (GPS). By measuring the instants of arrival of the signals, the position of the receptors can be determined by triangulation with ultimate precision of a few centimetres. These devices have become standard navigation tools, and no one is surprised anymore to be directed in this way, from the sky, with extraordinary precision.
8 Medical magnetic resonance imaging (MRI) provides me with my last example of technology based on the understanding of quantum processes. MRI images are actually produced by the convergence of three quantum technologies, developed to a remarkable level of sophistication. A powerful magnetic field produced by superconducting coils (first quantum technology) and sequences of radiofrequency fields suitably arranged create resonance between the magnetic moments of our atoms' nuclei (another effect that only quantum physics can explain). The signals emitted by these nuclei are finally processed and transformed into images by powerful computers, constituted of materials within which quantum effects, as I have said, also play a powerful role. We can thus for example reconstitute the inside of our brain in three dimensions, and even follow the evolution of the cerebral activity that modifies the signals emitted by our protons. Thought, or at least its material manifestation, thereby becomes visible.
*
9 What do all these inventions founded on the understanding of microscopic phenomena share? Originally, the study of these phenomena was not driven by the applications it would come to serve at the end of an oft fortuitous journey. What stimulates research is first and foremost curiosity for its own sake, the need to understand the intimate nature of things. Applications only come later, and often there where we did not expect them. When the first laser appeared in 1960, no one knew what purpose it would serve. Back then we called it – only as a half-joke – "a solution looking for a problem". Neither the laser nor the laptop nor the MRI could have resulted from a utilitarian programme. These inventions share another common trait: all have produced tools which we now use with the phased indifference of habit, without being conscious of the fact that their functioning depends on subtle microscopic phenomena. As things stand at the start of this century, the study of these phenomena is still not necessarily part of an educated person's general knowledge. At the end of their high school years or even of their scientific classes préparatoires, students will be familiar with pendulums, springs, pulleys and other mechanical machines. They will know Ohm's law and Ampère's rule. In short, they will be enlightened about what made the success of the first industrial revolution of the 19th century – the steam engine and the electric motor – as well as the physics of Galileo, Newton and Maxwell. They will have quite a precise idea of what happens under the bonnet of their car but not in the entrails of their computer. Therein lies a paradox that we will revert to, of general education in France, as in most other countries, that fossilised at the end of the 19th century.
10 The fact that the devices I have just described would be incomprehensible to a classic mind becomes apparent if we consider the debates that took place, in a fin de siècle atmosphere similar to that which we recently experienced, between scientists who in the 1890s pondered over the future of science. Imagining the future world, they had foreseen air transport, the development of cars or cinema, and even space travel, all natural continuations of classical physics. Nobody had thought of the microcomputer, medical imaging, the GPS or the laser, which a physicist from 1900 returning among us would probably think of as magical. In 1894 Marcelin Berthelot, a great chemist at the Collège de France, was asked to give a talk at the end of a banquet about the future of his discipline. For the year 2000, he described a world in which food would be entirely produced through chemical synthesis, freeing our civilization from arduous labour in the fields. Even though he was unfortunately not too far from predicting certain aspects of our modern diet, we do have to recognise that his vision was a little short sighted. He had not foreseen any of the extraordinary developments of chemistry, for example the manipulation and synthesis of new molecules for therapeutic purposes, or the steering of chemical reactions with laser light. It is true that he did not really believe in the existence of atoms.
11 Around the same time, Lord Kelvin made a statement that has remained famous; I here quote the spirit of his statement more than his exact words: "Apart from two small clouds that continue to darken our horizon, we understand pretty much everything about luminous and thermal phenomena". This sentence reflects the prevailing frame of mind in physics at the time, influenced by Ernst Mach. Mach considered that if, in a physical system, one could simply establish quantitative relationships between the measurable macroscopic observables (electric current, electric tension, temperature, pressure, etc.), one had understood everything about it. Some, such as Boltzmann with his statistical thermodynamics, did foresee or were convinced that an atomic reality existed beneath the surface of things. But that this was an objective reality and not simply a convenience of thought remained a fiercely debated question. The other interesting aspect of Lord Kelvin's assertion is the allusion to the two small clouds. The one refers to ether, a hypothetical medium supposedly surrounding the Earth, which Michelson's recent experiment had just shown to have contradictory properties. The other relates to certain anomalies in the distribution of energy in heated bodies and the light they emit, revealed by increasingly precise calorimetric measurements. The fact that Lord Kelvin had sensed the existence, in two seemingly marginal experiments, of a problem for the science of his time, is remarkable. He had clearly seen where the great change was to come from. One of these clouds would lead to Einstein's relativity revolution and the other to that of quanta, of particular interest to us in this lecture. The anomaly in the radiation of heated bodies would soon lead Planck to formulate the principle of the quantification of energy exchanges between matter and radiation, setting the quantum revolution in motion, with all the consequences I have recalled.
*
12 I have mentioned the successes of quantum theory, its predictive power and its radical departure from the physics that preceded it, but I have not yet said what it actually is. Discussing quantum concepts in qualitative terms is a challenge that takes us back to Feynman's comment mentioned at the start of this lecture. Quantum physics, after a century of brilliant achievements, still remains profoundly unsettling, as it is grounded on concepts that run deeply counter to classical intuition. Its fundamental principle is that of the "superposition of states". It tells us that when a system can exist in several different states, it can also find itself in all of those states at the same time, as though suspended between several realities. For example, the single electron of the simplest atom, hydrogen, is caught in a superposition of an infinite number of possible positions around its nucleus, the proton. All of these positions are spread across a volume with a dimension of about an angstrom. However that is not to say that the electron is a diluted object, like a sort of ectoplasm. If we were to measure its position by lighting it up with a very short wave radiation, acting as a precise local probe, we would find it in one point or another, perfectly localised. This would nevertheless be a random point, a priori unpredictable, different from one measure to the next on identical atoms.
13 The cloud of points which corresponds to the initial superposition is mathematically described with a table of complex numbers, each corresponding to a point. This table summarises all the information that exists on the electron. The square of the amplitude of each of these numbers gives us the probability of finding the electron at the corresponding point. This table is called the "wave function", and its evolution in space and time is governed by the famous Schrödinger equation, akin to the one satisfied by a classical, acoustic or electromagnetic wave. However this is not a matter or light wave, but an abstract probability wave. This simple example brings together all the paradoxical aspects of quantum theory: dualism between the wave and corpuscular descriptions of matter; the irreversible nature of all measurements that fundamentally affect the measured object; and finally the statistical nature of the theory, which can only predict the probabilities of the results of measurements of a physical system, making a cross on the absolute determinism of classical physics. In the quantum world, "God plays dice", as Einstein used to regretfully point out.
14 The principle of superposition leads directly to the phenomenon of matter-wave interference, which Feynman claimed to be quintessentially characteristic of quantum strangeness. A simple experiment, that of Young's interferometer, illustrates this phenomenon (fig. 3).
Figure 3
Young's interferences created with material particles express the quintessence of quantum strangeness.
15 Particles are sent one by one through a screen pierced by two slits and their position is then detected in a plane parallel to that of the screen, through the impacts they produce on it. A network of bright fringes can thus be observed where the points converge, separated by dark lines where no particles have reached. You will literally see this interference figure build itself before your eyes, through the accumulation of the successive impacts. This is the recording of an experiment with atoms recently performed at the University of Tokyo. The phenomenon seems simple if one is studying a wave; the two slits separate it into two partial waves whose amplitudes, if they are of the same sign, add themselves to the bright fringes or, if they are of opposite signs, cancel themselves out on the dark lines. That is in fact how this experiment has been interpreted for a long time when performed with light waves.
16 However, since the beginning of the last century we have known that all light can also be described as a flow of corpuscles, photons (here again we find the wave-corpuscle dualism, applied not to a material system but to radiation). How are we to understand this experiment? How are we to interpret it, especially when as you can see here it is performed using particles of matter, atoms crossing the device one by one? Each atom is thus telling us, seemingly contradictorily: "I am a particle, see my discrete point of impact on the screen", and at the same time, "I am a wave, look at these beautiful interferences"! One has to admit then that each atom crosses the device through the two holes at the same time, without choosing one or the other, in the strange superposition of states described by quantum physics. This experiment is enough to highlight the surprising logic of the microscopic world. To determine the probability of an event, one must combine amplitudes that can be subtracted as well as added up. As a result an event, the arrival of an atom on a dark line, is less probable when the system has two independent paths to get there than when there is only one!
17 The wave and corpuscular aspects actually correspond to two descriptions of the world that are not contradictory but complementary, according to Niels Bohr's expression. The wave aspect, along with its associated interferences, is in fact observed only if nothing in the experimental device allows for the path followed by the particle to be determined. If we wished to determine this path, we would need to modify the equipment, to introduce an element capable of detecting the slit through which the particle passed. By interacting with the particle, the detector would then disturb it enough to make the fringes disappear. Hence the corpuscular aspect prevails. The wave or corpuscle property is therefore not intrinsic. It is a property of the particle in relation to the specific equipment used in each experiment.
18 The superposition principle becomes all the more disconcerting in systems comprised of different parts that interact with one another and then separate. Consider two atoms of the same mass and of opposite speeds that collide, then move away from each other (Fig. 4). Detectors are placed all around the point of collision to observe the outcome. In accordance with the superposition principle each atom will, before any measurement is taken, find itself suspended between states associated with different speeds and directions, and eventually one of the detectors will randomly record a click, thus "choosing" the final speed of the atom. Remarkably, the clicks associated with the two atoms will always be emitted by two opposite detectors. Classical physicists will recognise this as a consequence of the conservation of the system's global momentum. There is nevertheless something surprising about the perfect correlation between two fundamentally random events that take place in two different regions of space. In mathematical terms, the system's wave function is represented as the sum of terms corresponding to each of the possible results of this correlation experiment. In each term, the contributions from each of the atoms form a product. The global wave function can however not be separated into the product of two wave functions of independent atoms. In other words, before being detected, each atom does not have a wave function of its own. There is then only one inseparable wave function for the whole system. This is what is called quantum entanglement. As a result, what happens in one corner of the universe on one of the atoms is inextricably entangled with what happens to the other atom in another corner of the universe, regardless of the distance between them or the type of measurement performed. Einstein found this property very bewildering when he and his colleagues Podolsky and Rosen analysed it for the first time in 1935. The remote immaterial link between two particles described by this type of non-separable function expresses what has since been called the EPR paradox.
Figure 4
The quantum entanglement of particles separated by large distances leads to the EPR paradox.
19 In fact, the notion of entanglement ties in with that of complementarity, mentioned earlier. As we have seen, to determine the trajectory of an atom in an interferometer it must be coupled with a detector that records information, evolving in two different states depending on which path the atom chooses. For example, the two slits will be lit with a laser light beam and the photons will be transmitted by each atom in two different directions depending on whether it goes through one slit or the other. This coupling of the atom and the photon leads to an entanglement of their respective states. The atom then no longer has a wave function of its own: there is no longer any wave that could interfere. The entanglement of the particle with the detector, produced by the measurement of its trajectory, is what explains the fringes disappearing.
20 Let us consider another crucial consequence of the superposition principle, with regard to systems formed of identical particles. The notion of identity takes on a much deeper meaning in the quantum world than in that of classical physics. To illustrate this point, suppose that a particle is enclosed in a box, in a well-defined state. Through some system, the details of which are of little importance, let us imagine putting another identical particle in the box, and then detecting each of them in turn. The classical equivalent of the experiment could consist of a person saving up money who, already having one Franc (or Euro) in a safe, puts another one in, before spending them one after the other. Can that person know if these Euros are being spent in the same order as they were saved up or the other way round? Although the question does not seem to present much interest – whether practical or economic –, in principle nothing would prevent our classical money saver from observing the sequence of operations with a camera placed in the safe, or painting the two Euros different colours and thus determining the order in which the coins are taken out. This is however not an option for those counting microscopic particles, and for them the very notion of the order of events has no meaning. The final detection of the two particles thus results from a process of superposition of two totally indiscernible paths. Its probability is obtained, similarly to Young's experiment, by adding up the amplitudes associated with the two possibilities, and then squaring this sum.
21 For a certain type of particle, fermions (one example of these being electrons), the two partial amplitudes are of opposite signs and are thus subtracted, as in the case of the black fringes in Young's experiment, cancelling out the final probability. It is therefore simply impossible to put the two particles in the box. This is Pauli's famous exclusion principle, which states that two electrons cannot be in the same state: bad news for those saving up electrons, but a very fortunate principle for the diversity of our world. This property plays a fundamental role in explaining the structure of atoms and molecules, all the laws of chemistry, and therefore also the principles of biochemistry on which life has been built. In short, all the electrons of a physical system must be spread out over an equal number of different quantum states, giving the system a wealth of structures and combinations that would not exist if they were classical particles able to accumulate in a small number of states. The world would be far less varied if electrons were not fermions and physics would most likely be less favourable to our existence. For example, we would probably all go through the floor of this room. It is because the electrons of the soles of my shoes refuse to be in the same point as those of the ground on which I am standing that this very ground applies the healthy reactive force that keeps me in front of you. The discernibility of solid objects, the fact that clear distinct boundaries exist between them, is thus – paradoxically – a consequence of the fundamental indiscernibility of the fermions that constitute them. Other – not so trivial – consequences of the exclusion principle condition the properties of materials, metals and semiconductors, which as we have seen have such rich practical applications.
22 For other particles, bosons, the amplitudes associated with the classical "histories" followed by the particles in and out of our box are added up rather than subtracted. Not only is it then possible to accumulate them in a same state, the probability of achieving this is also greater than in the classical case. Bosons have a gregarious behaviour and their collective properties are different from those of fermions or of classical particles. Light would not be what it is if photons were not gregarious bosons. A number of remarkable phenomena linked to the properties of bosons were discovered in the 20th century. The superfluidity of liquid helium is a consequence of the bosonic character of this atom. The supraconductivity of certain metals at a low temperature – the fact that they conduct electricity without heating up and thus make it possible to produce powerful electromagnets whose use we saw namely for MRIs – is due to the fact that in these metals electrons couple into pairs behaving like bosons, and no longer like fermions. The phenomenon of condensation in a same quantum state of a boson gas, predicted in 1924 already by Bose and Einstein, was observed in 1995 in a spectacular experiment performed on Rubidium atoms cooled down to a temperature of a fraction of a millionth of a degree above absolute zero. This experiment paved the way for research that no doubt promises a wealth of future applications. This work was rewarded with the 2001 Nobel Prize in physics.
*
23 Quantum physics is essential for describing phenomena on an atomic or subatomic scale. As the previous examples have shown us, it is also needed to understand collective macroscopic problems. On this scale, however, quantum effects generally only manifest themselves indirectly, covertly so to say. No one has ever seen a pool ball go through two holes at the same time (Fig. 5). It is difficult to even imagine what such a phenomenon might mean. One could also argue that it is because our intuition has accustomed itself to the observation of macroscopic phenomena where quantum superpositions do not appear, that these are difficult for us to envisage. Our brains, programmed by our personal experience as well as Darwinian evolution, "understand" the collisions of pool balls, not those of electrons or atoms.
24 Therein lies a paradox that takes us back to Feynman's statement. Why do macroscopic objects, particularly measuring devices, behave in a classical manner? These objects are still constituted by atoms which, separately, have distinctly quantum behaviours. How do these behaviours disappear on a macroscopic scale? How does the classical appearance of the world emerge from the underlying quantum laws? Here – at the blurry threshold between the microscopic and the macroscopic – is where the trickiest problem in the interpretation of theory arose and still persists today.
Figure 5
Understanding the classical appearance of the macroscopic world and the non-existence of superpositions of macroscopic states is the major problem of interpretation of quantum physics.
25 Schrödinger illustrated this problem by describing the famous experiment with the cat named after him (Fig. 5). He imagined a situation in which an atom enclosed in a box with a cat would be used to put it in a superposition of two dramatically different states, one state where the animal would be alive and another state where it would be dead. If we accept the idea that the cat can be described by a well-defined wave function (and this, as we shall see, touches on a crucial aspect of the problem), it should be possible for such a situation to directly result from the application of quantum laws to the "atom + cat" system. However no one has ever observed this ludicrous situation nor seen interferences associated with the superposition of a living and a dead cat. Why do these interferences disappear at macroscopic level? The answer to this question draws on the fundamental notion of decoherence. The situation we schematised to the extreme overlooked a crucial element. Our cat cannot be isolated from the rest of the world. The cat – as in general all macroscopic systems – is coupled to a complex environment which, in the particular case we are considering here, is constituted by a very high number of molecules and photons. And our cat entangles itself with that environment very fast, and cannot therefore be described as being in a proper quantum state. The molecules and photons surrounding it evolve very quickly in different quantum states, depending on whether the cat is alive or dead. A piece of information on the state of the cat is therefore lost in the environment, destroying the quantum interferences that would be associated to the superposition of these two states, in the same way that the trajectory detector in Young's experiment causes the fringes to disappear. The decoherence that maintains the classical appearance of the world is thus a consequence of the notion of complementarity and of the inevitable entanglement of complex systems with their environment.
*
26 Describing quantum physics with words and images developed through the classical experience of the macroscopic world presents limits and risks. The first of these risks, inherent to the exercise required by an inaugural lecture, is that of appearing trivial to specialists, and incomprehensible to everyone else. But there is another deep pitfall awaiting the lay audience. It consists in thinking of quantum physics as something vague. Associating waves and particles in an apparently hybrid being could conjure up images of those half-human half-beast monsters found in the sculptures of Romanesque churches, and suggest that quantum physics is ill-defined, which is also reinforced by the inappropriate use of expressions like quantum "indeterminacy" and "uncertainty". Nothing could be further from this physics that describes the world with incredible precision, with universal reach and with a stability of forms and structures that classical physics could never offer.
27 But to access this description, one has to let go of inappropriate images and plunge into the mathematical structure of the theory, which is of great elegance and simplicity. The notion of superposition of states, so vague in classical terms, is simply associated with the mathematical linearity of the theory, with the fact that the states of any quantum system are described by vectors of an abstract space that can be added up or combined according to rules of simple linear algebra. Once these rules are defined, the theory describes all the phenomena free of ambiguity. The vague notions, for a layperson, of superpositions, interferences, complementarity or entanglement are obvious consequences of this outcome. A new logic, different from that of the classical world, though perfectly coherent, is revealed. However to access this simplicity, a significant effort in abstraction is needed. Moreover, the relationship between concrete observation and theory is more indirect than in classical physics. The combination of these two aspects – the need for abstract formalism and the apparent distancing between direct observation and theory – is most probably what makes quantum physics difficult to teach at a basic level.
*
28 In the microscopic world, the tangible can only be accessed through an arduous journey that the founders of the theory had to take. They had to carry out formidable investigation work, following a few brilliant intuitions suggested by indirect observations of the microscopic world (for instance de Broglie's intuition about matter waves in 1923, and in 1925 de Pauli's about the exclusion principle). The mathematical formalism of the theory was then elaborated, in 1925-1926, in Heisenberg, Schrödinger and Dirac's work. To discuss the new theory, its founders often relied on "thought experiments", in which they imagined the manipulation of electrons, atoms or photons in simple situations, stripped of all unessential complications, by trying to directly illustrate quantum notions and put them to the test of logic. Figure 6 shows a drawing by Bohr, representing his famous "photon box".
Figure 6
Diagram by Bohr illustrating his "thought experiment" with the photon box (Niels Bohr Archive, Copenhagen).
29 Such experiments seem completely impossible to implement. Schrödinger, perhaps still influenced by Mach's thinking, asserted until about 1950 that the behaviour of isolated atoms would forever remain unobservable. How amazed he would be by the very real experiments manipulating isolated quantum objects that technological progress – allowed by quantum concepts – now enables us to perform!
30 Thanks to the tunnelling microscope, atoms and molecules can now be "seen", moved around on the surface of a crystal and used to build structures on a scale of a billionth of a metre, like the three letters formed of atoms you can see in Figure 7.
Figure 7
The tunnelling microscope makes it possible to write on an atomic scale (Photograph: IBM Almaden Research Center).
31 Written on this scale, all the books of the French National Library would fit on the surface of a stamp! Atoms can also be trapped one by one by leaving them suspended in a vacuum, supported by a subtle interplay of electromagnetic forces. Using light beams these atoms can be manipulated and prepared in well-defined quantum states, and their quantum jumps observed. Here are a few images of such atoms, observed through the detection of the laser light they scatter (Fig. 8).
Figure 8
Seeing and manipulating atoms one by one: the fluorescence of one, two... seven trapped atoms (Photograph: University of Innsbruck).
32 We also know how to produce photons one by one, entangle them together or individually trap them in a box during a fraction of a second and observe them without destroying them. The set-up we use at the École normale supérieure to perform these experiments with actual "photon boxes" is shown in Figure 9. Manipulating these particles in this way provides concrete illustration of the foundations of quantum theory. Quantum interferences, complementarity, entanglement and decoherence are directly revealed, so to speak, in these thought experiments that have turned into tangible ones. But these experiments also pave the way for a new science called quantum information processing. I will conclude the scientific part of this lecture by addressing this subject, which my lectures will focus on over the next few years.
Figure 9
The ENS "photon box" makes it possible to put into action thought experiments and to demonstrate simple quantum information processing operations (Photograph: Steve Murez).
*
33 All the signals our computers exchange are coded in the form of discrete elements, bits, which are to information what atoms are to matter. Each bit can have two values, 0 or 1. A sequence of bits describes a letter of the alphabet, a text, a piece of music, an image. The interaction between bits means they can be added up or multiplied, and through combinations the most complex computations can be performed. In our computers or in our telecommunication optic fibres, bits are carried by currents or light beams associated with macroscopic flows of electrons or photons. These are classical bits. The manipulation of microscopic systems now allows us to envisage machines wherein bits would be carried by a single atom or photon, possessing two quantum states that we can still call 0 and 1. This would pave the way, in principle, for extremely dense storage of information. But there is more. Unlike classical bits, quantum bits can exist in superposition of 0 and 1 values. The controlled manipulation of atoms and photons thus provides information theory with the new dimension of quantum logic, of a world where, contrary to the saying taken up again by Musset's, a door can be both open and shut, a cat both alive and dead, and a bit can simultaneously take on both values 0 and 1.
34 Quantum logic promises to be very useful, for instance, in cryptography, the science of secret information exchanges that is as old as the history of diplomacy or war. To secretly send each other a message, two partners which computer scientists have come to call Alice and Bob, must simply each hold a copy of a random sequence of 0's and 1's, which constitutes a secret key that is as long as the message they wish to exchange. By adding one bit of the key to each of the bits of the message, term by term, Alice produces a coded text that she sends to Bob through a public medium of communication. Bob can then subtract the bits of his key from the message to decode it. No spy, no matter how, can decipher it if they do not have a copy of the key. The confidential sharing of the key is therefore the crucial point of the operation.
35 This sharing is where quantum physics comes into play. Suppose that Alice produces pairs of entangled particles in an EPR-type state. She keeps one element of each pair to herself and sends the other to Bob. The two accomplices thereby share a set of non-separable quantum systems. If they take a measurement of their particles, each obtains a random sequence of 0's and 1's and their two sequences are perfectly correlated, due to the remote quantum link between the EPR pairs. If a spy were to try to measure the key, by intercepting the particles sent by Alice to Bob, they would necessarily disturb the correlations between their measurements, in a way acting as an environment that "decoheres" the EPR pairs. Alice and Bob will then only have to check a small sample of the key to see that no decorrelation has occurred, in order to be sure that their communication line is secret. This ingenious protocol has already been demonstrated by several research groups, and its feasibility proven over distances of tens of kilometres. In this case the entangled particles are photons spreading across optic fibres.
36 A quantum bit is a more subtle object than its classical counterpart. Curiously, its state is generally unknown, and even fundamentally unknowable. Of course, if it can only take the values 0 or 1, it is no more mysterious that a classical bit. But what happens if it is in a superposition of 0 and 1 values? Can the amplitudes associated with these values be known to someone who has not prepared the bit? The theory's answer is clearly no. If one tries to measure it, one will obtain the value 0 or 1 with a probability determined by its amplitudes. The bit will however be modified by the measurement and its previous state will not be known. Is that to say that this kind of bit is of no use? Once again, the answer is no. It may seem strange that inaccessible information could be useful, yet that is the case. The quantum bit in a superposition of 0 and 1 can become entangled with other bits and give rise to interference effects that allow for measurements which will themselves produce usable information. It can therefore be interesting, even without knowing its state, to send a quantum bit between two points in order to remotely perform operations on it. The classical computing equivalent of this operation is the well-known fax. Alice gets a machine to read a sequence of 0's and 1's, which it sends through a telephone line to Bob. The quantum equivalent is more subtle to perform. What can Alice do if the bit she wants to transmit is in a superposition of 0 and 1 that she cannot read? Here again, entanglement provides the solution. Once more, Alice and Bob must first share an EPR pair of particles. Alice makes her EPR particle interact with the bit she wants to send to Bob and performs a measurement on the system thus formed. Remote EPR correlations cause Bob's EPR particle to be immediately affected by Alice's measurement. She just needs to share the result of her measurements with him using a classical channel for Bob to be able to reconstitute the initial state of Alice's bit by manipulating his particle. Paradoxically, neither Alice nor Bob know the states of this bit. Note also that this quantum version of the fax, unlike the classical procedure, destroys the original. Finally, I wish to point out that the method does not violate the principle of causality. The transfer of information requires classical communication between Alice and Bob which cannot happen faster than the speed of light. This quantum fax process, imagined about ten years ago by computer science theorists, was called teleportation. I do not know what is more brilliant here, the principle or the name chosen, but the term, with its science fiction connotation, has been immensely successful in the media. The experiment, in slightly different forms from the one I have just described, has been performed in several laboratories.
37 I cannot complete this overview without talking about the quantum computer, its remarkable theoretical possibilities and the formidable difficulties surrounding its practical realization. As we have seen, all current computers run with technology founded on the quantum properties of the materials they are made of. The operations they perform nevertheless obey a classical logic. The gates of their circuits are open or shut, never in a superposition of these two states. In a quantum computer, things would be different. It would juggle quantum with bits in superpositions of states, and these bits would be woven into entanglements. A machine manipulating such bits would evolve in a gigantic superposition of states and would thus, in a sense, be equivalent to the sum of a large number of machines computing in parallel. Certain computations, extremely long to complete on a classical computer, would be much faster on this kind of machine. The most interesting example as yet is the factorization of large numbers, for which a quantum algorithm was discovered a few years ago, setting off the current surge of research on quantum computation. The theory behind these computers raises subtle problems. The information is situated not in the bits themselves, but in the correlations that are established between them. The information is eventually revealed in an interference signal in which the computations performed in parallel find themselves mutually reinforced, in a sense.
38 Basic operations with quantum gates and the programmed entanglement of two, three or four quantum bits were recently performed using trapped atoms and photons. Simple algorithms, involving up to seven bits, were demonstrated by manipulating the magnetic moments of simple molecules using magnetic resonance methods. Nevertheless, assembling these elements together in large numbers to produce a practical computer presents enormous difficulties relating to decoherence, and the theorist's dream can become the experimenter's nightmare. What we are trying to create is in fact a gigantic Schrödinger's cat computer. The coupling with the environment becomes more and more difficult to control as the size of the machine increases. Very fast, the information loses itself in the environment and the subtle correlations between the quantum bits begin to deteriorate. Admittedly, theorists have been able to develop very ingenious processes, allowing for certain types of error to be detected and for the entanglement destroyed to be re-established. In principle, these methods should suffice to solve the decoherence problem, provided each element of the machine becomes sufficiently reliable. In practice, however, no one knows whether physical systems exist in which to secure these conditions. The atoms, photons or molecules in current experiments will certainly not do. Other systems, artificially created in solids or superconducting circuits, are hoped to offer better prospects. However the decoherence in these systems is yet to be evaluated and controlled.
39 To draw an analogy with the story of classical computers, I will say that current systems are the equivalent of the mechanical gears or antique machines of Pascal or Babbage. Their low reliability made it impossible to assemble these elements in sufficient numbers to construct an efficient computer. As we have seen, the solution came from the semiconductor transistor. Does an equivalent of this transistor for the quantum computer exist in Nature, waiting to be discovered? I cannot answer this question, which has much to do with science fiction. I will simply say that if this wonderful transistor were discovered, it would bring on a revolution affecting far more than the factorization of large numbers. It would make it possible to build macroscopic objects with an openly quantum behaviour. Schrödinger's cat would be among us and the blurry boundary between the classical and quantum worlds would cease to exist. Can we envisage this revolution for the end of this century, as some are doing? Examples of predictions made in the past call for caution. Even if the quantum computer is not waiting at the end of the road, the combination of information theory and quantum physics is a fascinating area of study. Computer science concepts are going to help us quantitatively define quantum complexity. The precise experimental manipulation of microscopic systems is going to make it possible to further knowledge about this complexity. There will be applications for this research, most likely not the ones we expect.
*
40 Reaching the end of this journey through quantum physics, I would not like to leave you with too reductionist an impression. I have tried to show that quantum laws are essential for understanding Nature, and that most physical effects we depend on in our daily lives – from biological mechanisms to those used by modern technology – depend on some level on quantum processes. However that is not to say that our understanding of the world is limited to these concepts, or that macroscopic physics is only the sum of microscopic effects. Principles of organization of matter exist on a macroscopic scale which it would be pointless to try and explain through a computation following the evolution of each atom of the system step by step. Other approaches are needed through which a small number of essential parameters describing the complexity of the system studied are defined, and with which the underlying microscopic dimension is only accounted for from a global perspective. These approaches often reveal new effects. Understanding Nature therefore requires the use of a combination of tools. Quantum theory is necessary, but it is not enough. This is especially the case when looking at chemistry, biology or the neurosciences, which call for other conceptual approaches. I for example doubt whether quantum laws can, as some have claimed, be of any use whatsoever in explaining the cerebral phenomena in which conscience originates.
41 In this lecture I have stressed the remarkable achievements of physics throughout the last century. Paradoxically, these successes are sometimes used against it to announce its doom. It is often said for example that biology has replaced physics at the frontier of knowledge. The idea that having achieved its programme, physics is now an accomplished science which serves only to produce useful tools for other sciences, is as inaccurate now as it was a hundred years ago. Let us recall Lord Kelvin's two small clouds. No one can say whether quantum theory in its current form is here to stay forever, or whether it will be replaced by another construct, incorporating its concepts into a more general and more powerful formalism. What is certain is that it is always arrogant to underestimate Nature's capacity to surprise us. The current incompatibility of quantum theory with gravitation is perhaps one of the clouds that will force us to call the construct into question. Or perhaps the surprise will come from cosmology, with the missing mass of the Universe. There are still surely many unsuspected phenomena in organization of complex systems waiting to be discovered, even at the human scale. And no one knows what applications will see the light of day, which would seem as incredible to us as a laptop would have seemed to Marcelin Berthelot.
*
42 Describing the evolution of a discipline, asking fruitful questions that move the reflection forward, and explaining the enthusiasm as well as the doubts and questions surrounding research: those are the objectives you all set yourselves, my dear colleagues, in your teachings at the Collège de France. This is a difficult task, for whether in quantum physics or Egyptology, there is neither a recipe, nor a captive audience whose assiduity might be encouraged by the pursuit of a degree. There are only free listeners, who share the same interest and expectation. Each professor tackles this task with their own personality, shaped by their encounters and singular experiences. It is customary to conclude an inaugural lecture by alluding to this personal journey.
43 I will begin by remembering my parents who very early on encouraged me to think, closely following my studies, even when these took a scientific turn, moving away from their familiar frame of reference. I would also like to talk about the woman who has shared my life for longer than physics... But I will not linger on these personal aspects of my story which relate to the private sphere. These are domains on which physics, even quantum physics, could not shed light, and that – based on a division of labour between us – my wife Claudine has precisely been studying for a long time.
44 I familiarised myself with atoms at the École normale in the 1960s. Coming so to speak from the 19th century – I mean the classical education of the classes préparatoires – I was immediately thrown into the quantum world by the postgraduate classes of exceptional teachers. Alfred Kastler gave us a lyrical description of the dance of atomic kinetic moments, and gave atoms and photons a near poetic existence. Jean Brossel brought us back to Earth by describing the great experiments thanks to which quantum concepts were established, instilling in us the austere passion for precision. And Claude Cohen-Tannoudji revealed the theory's formalism to us with extraordinary depth and clarity. I still remember three books I read avidly at the time. Quantum Mechanics by Albert Messiah, where I truly understood the depth and beauty of the theory; Principles of Nuclear Magnetism by Anatole Abragam, who introduced me to the subtle world of atomic magnetic moments; and Feynman's Lectures on Physics, which was a revelation. That was the time when the various optical methods for the manipulation of atoms were being invented. The lessons were immediately illustrated by everyday reality at the ENS laboratory where I wrote my thesis under the enthusiastic supervision of Claude Cohen-Tannoudji.
45 I then had the opportunity to be exposed to the research atmosphere of the English-speaking world at Stanford, in the laboratory of Arthur Schawlow, one of the inventors of the laser, where I completed a postdoctoral visit. This was far from the theoretical rigour of the courses I had just studied in Paris. We had a lot of fun with the marvellous toys that were the tuneable lasers sent exclusively to Californian laboratories at the time, by the commercial companies of what was to become Silicon Valley. Art Schawlow's enthusiasm was contagious. Every day, a new idea would spring up, sometimes whacky, sometimes brilliant. There came the first "edible" laser the day he had the idea of turning those ghastly food jellies of garish colours that he loved to eat into lasers, but also many demonstrations of clever spectroscopic methods, every time pushing the limits of the precision and sensitivity of measurements further. Art had a deep sense of humour, which I believe is essential to maintain a healthy atmosphere in a laboratory. "To succeed in research," he often said, "one doesn't need to know everything about everything, it's enough to just know a few things that others don't". This sentence, pronounced with his contagious kindness and laughter, went a long way in relieving us of the intimidating weight of universal knowledge, which so often inhibits one, whether it is discouraging, or leads to an overly sceptical attitude about the world and the discoveries still to make.
46 I was fortunate in my career to have exceptional students, two of whom have become close colleagues. My presence here is in large part owed to recognition of the collective work of the team that Jean-Michel Raimond, Michel Brune and myself lead at the ENS. I would like to publicly tell them what a pleasure it has been working with them throughout all these years in an atmosphere full of trust, critical thinking, imagination and humour. I would also like to mention what I owe to the stimulating atmosphere at the ENS, and to dialogue with colleagues who share the same passion for research and teaching. Not to forget the students who, through their ever novel vision of the world, cause us to constantly call into question our knowledge and the way we share it.
47 My work – that is one of its great advantages – has afforded me the opportunity to meet many foreign colleagues and share with them the same passion and diversity of our experiences. Some, having become very close friends, have given me the joy of being here today. I hope my teaching in the next few years will give me the opportunity to further deepen these ties. In these uncertain times, where the globalization of exchanges comes with inevitably entangled hopes and fears, reflection and research is a domain, if there ever was one, where globalization is undeniably positive.
Books Quantum Physics Basic Physics Knowledge
Source: https://books.openedition.org/cdf/3296?lang=en