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Atoms and Radiation

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Jean Dalibard

Atoms and Radiation

Inaugural Lecture delivered on Thursday 18 April 2013

Jean Dalibard
Traduction de Liz Libbrecht

Texte intégral

1Mr Administrator,
Dear Colleagues,
Ladies and Gentlemen,

  • 1 Johannes Kepler, De cometis libelli tres. I. Astronomicus… II. Physicus… III. Astrologicus…, August (...)

2At the beginning of the seventeenth century, German astronomer Johannes Kepler sought to understand a mysterious phenomenon: comet tails, celestial objects alleged to have supernatural properties, always point away from the Sun. When a comet goes towards the Sun, it matches the image of hair floating in the wind. But when the comet moves away from the Sun, the tail comes before the nucleus, which seems counter-intuitive. Kepler sought to explain this phenomenon with the following proposition1: “A comet’s tail is formed by matter that the Sun’s rays chase through their impulses outside the comet’s body”.

  • 2 Nicolas Hartsoeker, Principes de physique, published in Paris by Jean Anisson, Head of the Imprimer (...)

3At the end of the same century, Dutch physicist Nicolas Hartsoeker, associated with our Académie des sciences, wrote in his Principes de physique2: “Commuters are adamant that the Danube is far slower in the morning when the Sun’s rays counter its course than in the afternoon when they aid it”.

4Of these two scientists, Kepler was at least partially right; Hartsoeker was only describing an optical illusion. But the two scholars had the intuition of a phenomenon that plays a crucial role in today’s physics: light, and electromagnetic radiation more generally, can act on the atoms and molecules that make up matter.

5The two words that make up the title of this Chair, atoms and radiation, represent the core of the physical world, as we know it. Light is both a channel for information on our environment and a means of controlling it. It serves as an information channel for astronomers for instance, who are able to deduce a star’s age from observing its colour. As a means for action, light can locally provide a determined quantity of energy, as the cutting of materials with lasers illustrates.

6Matter and radiation are closely linked in the progression of knowledge. Advances in our modelling of the motion of particles and in that of light have gone hand in hand; each research path has provided keys to overcome deadlocks in the other’s progress. Thus, in the seventeenth century, Fermat explained the laws of light reflection and refraction – previously set out by Descartes and Snell – based on the principle that “nature always acts through the shortest and simplest paths”. A hundred years later, Maupertuis, Lagrange and Euler extended Fermat’s idea to mechanics. This gave rise to the principle of least action, which is still highly significant today. At the turn of the twentieth century, the study of the light emitted by an oven allowed Max Planck to lay the foundations of what was to become quantum physics, and was to provide an explanation of the stability of matter. Fifty years later, Willis Lamb's high precision measurements of the structure of atoms led to the development of quantum electrodynamics, the now universally accepted model for describing radiation.

7Quantum electrodynamics is an extraordinarily precise theory: despite increasingly stringent tests, it has never been called into question. Its success even raises a crucial question: on a fundamental level, are there still any open problems in the science of atoms and light? In other words, have optics and atomic physics not become technologies at the service of other disciplines?

8I would like here to provide a few answers that prove the full vitality of this research field. We owe this vitality to a device, the laser, which actually refers to a wide variety of tools. It can represent a beam sent to reflect on the moon to measure the latter's distance from the Earth, a light source injected into an optical fibre as a medium for information, or a train of short and intense pulses to probe chemical reaction dynamics or to initiate fusion of atomic nuclei.

9It would be too ambitious to try to describe all these research fields in one lecture. This presentation will therefore focus on one of the most spectacular and paradoxical applications of laser, namely: the cooling of atomic gases. While laser is traditionally associated with the idea of heat, it can also be used to reduce the random motion of a gas’ particles considerably, and to arrive at a virtually perfect order, less than a millionth of a degree above absolute zero. This is how quantum matter is produced, with radically different properties from those of the fluids or solids we encounter in daily life. Interest in this quantum matter extends far beyond the scope of atomic physics specialists. Physicists of condensed matter, chemists, mathematicians and astrophysicists all use it as a source of illustrations and research questions regarding phenomena related to their discipline.

10Before presenting this vast research field in more detail, I would like to emphasize the strong tradition of the Collège de France in which it is embedded. Many professors at this institution have made their mark on the physics of light and atoms at the highest level. I will mention only a few prestigious names of scientists who forged this discipline. In the nineteenth century, André-Marie Ampère, Jean-Baptiste Biot and Félix Savart laid the foundations, here in this institution, of electric conduction and magnetism, which were then unified in Maxwell’s electromagnetic theory. In the early twentieth century, Paul Langevin took advantage of his Chair at the Collège de France to spread Einstein’s ideas on relativity theory and to propose a model of the electron, the elementary particle of charged matter to which I will revert. A little later, Léon Brillouin developed and taught solid state physics, a new discipline which adapted the concepts of quantum mechanics to material systems with a large number of particles; I will also come back to this point in the lecture. Finally, I would like to salute two great physicists and professors whom I was fortunate to know. Through his study of nuclear magnetism, Anatole Abragam laid the foundations of a theory that extends to many physical phenomena, particularly to my own research field, quantum optics. Claude Cohen-Tannoudji was my PhD supervisor; he guided my first steps in research with extreme benevolence, and has done me honour and kindness of being here tonight. For over thirty years, Claude’s teachings have played a considerable role in the entire French atomic and molecular physics community, and have supported if not triggered the profound changes that have taken place during this period.

11After citing these great names, it is difficult not to feel humbled and somewhat intimidated by the task at hand. I am certainly fully aware of what an honour it is to hold a Chair devoted to this subject at the Collège de France. I would like to thank you, dear Serge Haroche, for having one day offered me this challenge and for supporting my candidacy before the Faculty, and all of you, dear colleagues, for putting your trust in me.

Bohr’s atom is a hundred years old

  • 3 For details on Niels Bohr’s approach, see Max Jammer’s book The Conceptual Development of Quantum M (...)

12I propose that we begin this journey to the land of cold atoms with a celebration. This month of April 2013 is a special anniversary in the history of the evolution of ideas on the description of matter. Just a hundred years ago, the young Danish physicist Niels Bohr proposed a model to save classical physics from the dead-end it had reached in trying to account for atoms’ stability.3

13At the beginning of 1913, Niels Bohr returned to Denmark after two visits to Thomson’s laboratory in Cambridge, and Rutherford’s one in Manchester. He was aware of their latest experimental discoveries: matter is composed of positively charged particles, atomic nuclei, in which the bulk of mass is concentrated, and far lighter negatively charged particles, electrons. All these particles occupy but an infinitely small fraction of space. If an atom were dilated to the size of this room, the atom’s nucleus would have the dimension of a pinhead and the electrons would be even smaller, perhaps punctual. Between the nucleus and the electrons, there is just emptiness, nothing but emptiness. The question that Bohr, like many other physicists, was grappling with was the surprising stability of the atomic structure. What is it that prevents each electron from falling to the nucleus?

14Bohr often stated that everything became clear to him when he was introduced to Balmer’s formula. This formula concerned hydrogen’s spectral lines, that is, the wavelengths of light emitted by this gas when it is hot. Here are some of their values: 656.2 nm (red), 486.1 nm (blue-green), 434.0 nm and 410.0 nm (violet), to which we can also add 121.5 nm and 102.5 nm, situated in the ultraviolet spectrum. In 1885, Balmer noticed that these wavelengths could be written in a simple mathematical form, with a formula that was later completed by Rydberg and Ritz:

1/λ =1/λ0 (1/p2 – 1/n2)

where p and n are two integers (1, 2, 3, …) and where λ0 = 91.1 nm.

15Was this link between the light emitted by hydrogen and integer numbers a mere coincidence or did it hide a profound truth? Bohr, convinced of the latter, based his reasoning on a planetary model of the atom, popularized by Jean Perrin some ten years earlier. In this model, the nucleus is immobile at the centre, in the Sun’s role, with the much lighter electrons turning around it like the planets. But Bohr added the crucial hypothesis that these electronic planets are only allowed certain orbits, with the integers p or n of Balmer’s formula serving to identify them.

16With Bohr’s additional hypothesis, a fundament idea emerged, which was subsequently validated by the development of quantum theory, and which extended to all atomic species. This idea was that if one measures an atom’s internal energy, in other words the energy of the electrons moving around the nucleus, the only possible results are discrete values E1, E2, E3, etc. Any given atomic species – hydrogen, helium, lithium, etc. – is characterized by this scale of energy levels, which can be thought of as its ID card.

17Bearing in mind a few subtleties that are of no importance here, it is enough to assert that an atom has internal energy E1 to determine the state of its cloud of electrons. The atom – or more precisely its electronic cloud – can change state, that is, shift from State 1 towards a higher energy state, State 3 for example, by absorbing a photon, in other words a particle of light (Figure 1). This process is possible if the photon has energy E3E1, which ensures that the “atom and light” system’s total energy is conserved. Once in State 3, the atom can return to State 1 by emitting another photon, with the conservation of energy here again requiring that the photon have energy E3E1. These two basic processes, photon absorption and emission, are the cornerstones of the interaction between matter and radiation.

Figure 1

Figure 1

Process of absorption by an atom. To the left, a photon with energy E3E1 arrives on an atom prepared in its fundamental state, with energy E1. To the right, the atom has absorbed the photon and has shifted to the energy state E3.

18Knowledge of a given atomic species’ internal energy scale therefore allows one to determine the energy of the photons, in other words the colours of the light that an atom of that species is able to absorb and emit. This is particularly the case of the spectral lines of hydrogen, which served as Niels Bohr’s vital lead.

Cooling matter with light

19Now that we have celebrated this foundational act, let us get to the core of this lecture: how can matter be cooled with light?

20Thermodynamics teaches us that temperature and disorder are intimately linked. In a gas, the movement of atoms or molecules is erratic and their thermal velocity increases with temperature. Thus the nitrogen and oxygen molecules that make up the ambient air have typical speeds of a few hundred metres per second and the temperature is about 300 K. I here use the notion of absolute temperature, obtained by taking the usual temperature, measured in degrees Celsius, and adding 273.15 degrees. Using absolute temperature is interesting, since it immediately shows the difference from complete rest, obtained at temperature zero.

  • 4 A. Kastler, “Quelques suggestions concernant la production optique et la détection optique d’une in (...)

21Cooling an assembly of particles therefore means reducing its disorder. With the invention and development of optical pumping, Alfred Kastler and Jean Brossel made a first step in that direction4. In order to grasp their idea, consider an atomic species with an energy scale that has two low-energy states, called 1 and 2 in Figure 2. These states are assumed to be stable, in the sense that an isolated atom, which has been prepared in State 1 or State 2, will definitively remain there. We then choose an initial configuration of our assembly such that the atoms are randomly distributed across one or the other of States 1 and 2. The disorder here consists of the fact that the state occupied by a given atom is unknown, and the aim is to make this element of randomness disappear.

22Let us try for example to put all the atoms in State 1. To do so, we irradiate the atoms with a light whose photons have an energy E3E2. This light will efficiently make the atoms of State 2 move to State 3, which has a higher energy. An atom occupying State 1 is however insensitive to this radiation: it will therefore remain there indefinitely.

Figure 2

Figure 2

Optical pumping principle. At the top, an assembly of six atoms is randomly distributed across the energy states E1 and E2. At the bottom, after light has been focused on the atoms with photons with energy E3E2, all the atoms have been accumulated in the energy state E1. The initial disorder has been removed.

23An atom that has risen from State 2 to State 3 does not remain in this high energy state for very long. This state is chosen to be unstable, and the atom ends up dropping back down into State 1 or State 2 by emitting another photon. If it drops into State 1 it stops there: this is the accumulation sought. If it drops into State 2, it will again absorb a photon, rise back up to State 3 and try again. After quite a while, the steering towards State 1 has occurred for all atoms: the initial disorder of the atomic assembly has been significantly reduced by means of light.

24Optical pumping is merely a first stage towards low temperatures. In order to cool a gas, it is not enough to order the distribution of atoms across their internal energy state. The velocity of each atom’s mass centre, in other words their “nucleus and electrons” set, must also be reduced. Starting with atoms going in all directions of space at different speeds, the aim is to bring them to a virtual standstill. Several methods have been implemented to do so and I will present one highly efficient such method, called Sisyphus cooling.

  • 5 C. Cohen-Tannoudji, “Observation d’un déplacement de raie de résonance magnétique causé par l’excit (...)

25Let me start with a preliminary comment about our possible means of action. I have already stated that the energy scale E1, E2, … was characteristic of a given atomic species. Nevertheless, this scale is not completely fixed: when atoms are subjected to an electric or magnetic field, the position of the energy levels changes. This is also the case when light is shed on the atoms with a light beam, as Claude Cohen-Tannoudji showed in 1961: light can shift atomic energy levels upwards or downwards.5

26As with the description of Kastler and Brossel’s optical pumping, consider an atomic species with two internally stable levels of energy, called 1 and 2. Suppose that these levels can be shifted by a light beam in opposite directions: the light shifts Level 1 slightly downwards and Level 2 slightly upwards. In the absence of light, the levels are closer together, and move away from each other when there is light.

27To simplify our analysis, let us limit the movement of our atoms to a single direction in space. We focus light on them with a light beam propagating along this axis. Using a mirror, we send the beam back on itself. An interference phenomenon then produces a stationary wave. At certain points, the “antinodes” of the stationary wave, the amplitude of the “outbound” wave and that of the “inbound” wave add up to give a significant total intensity. In other points, the “nodes” of the stationary wave, the amplitudes cancel one another out and the total light intensity is virtually zero.

28The modulation of the light’s intensity is impressed on the atom’s energy levels. At the stationary wave’s nodes, there is no light shift: Levels 1 and 2 are close to each other; at the stationary wave’s antinodes, these shifts are significant and Levels 1 and 2 are far apart. When the energy of Levels 1 and 2 are outlined according to the atom’s position in the stationary wave (Figure 3), a periodical variation is obtained, like the potential energy of a marble rolling on corrugated iron.

  • 6 J. Dalibard and C. Cohen-Tannoudji, “Dressed-Atom Approach to Atomic Motion in Laser Light: the Dip (...)

29We now have the necessary ingredients to understand Sisyphus cooling.6 Consider an atom moving in this hilly landscape, as represented in Figure 3. The atom starts off for instance by ascending a hill of potential associated with Level 2. After reaching the top of the hill, the atom is in principle going to go down the other slope. But we can disrupt its course by resorting to optical pumping. More precisely, we can make sure that when the atom reaches the top of the hill, it is transferred to Level 1, where it finds itself at the bottom of a valley. The atom then ascends a second time, after which it arrives on top of a hill for Level 1. At this point, if well controlled, the optical pumping can bring the atom back towards Level 2, forcing it to climb a third hill in a row, and so on. The atom therefore goes through a series of ascents, until its energy is too weak to reach the following top and it remains trapped at the bottom of a valley.

30Our atoms are therefore in a situation that is reminiscent of the mythological hero Sisyphus who, because he dared to challenge the gods, was condemned to endlessly pushing a rock to the top of a mountain. The end of the particles’ story, however, differs from that of Sisyphus: unlike the hero who seemed to have an infinite reserve of energy, they end their course virtually still, at the bottom of the wells drawn by the stationary light wave. Their initial kinetic energy has been taken away by the photons emitted during the optical pumping processes. We use the term optical molasses to describe this viscous environment created by the laser beam, in which the motion of atoms is slowed down like that of a spoon in a honey pot.

Figure 3

Figure 3

Sisyphus cooling principle. In a stationary light wave, the energy levels are modulated in space. Configurations exist such that the atom constantly ascends hills of potential, with optical pumping placing it at the bottom of a valley as soon as it reaches a hilltop. When its energy becomes too weak, the atom is trapped at the bottom of a well of potential.

31The temperatures measured when observing the atoms’ residual thermal agitation after the Sisyphus cooling are extraordinarily low: they sit in the area of the microkelvin. To give an idea of a temperature of that order, let me place a few points of reference on a logarithmic scale, such that each notch of the scale corresponds to an increase by a factor of 10 (Figure 4). The temperatures measured on Earth, whether at a pole or by the equator, are very close to each other on that scale, between 200 and 350 kelvins. On the surface of the Sun, the temperature is 20 times higher than on Earth, at about 6,000 kelvins, and the centre of the Sun is at about 20 million kelvins. Air becomes liquid around 80 kelvins, a temperature four times lower than the ambient temperature.

32For their part, the cold atoms I am talking about are right at the bottom of this scale, 100 million times colder than our immediate environment. On our logarithmic scale, the heart of the Sun, five notches above our immediate environment, is ultimately closer to us than optical molasses, eight notches below!

Figure 4

Figure 4

(Logarithmic) scale of temperatures. Cold atomic gases correspond to the lowest kinetic temperatures ever measured.

33Since the atoms irradiated by the cooling laser beams scatter light, they can be observed by the naked eye at the centre of a vacuum chamber. The photograph in Figure 5 shows an assembly of a few million sodium atoms, placed at the intersection of three stationary waves. The combination of the Sisyphus effects due to these waves allows for the movement of the atoms to be frozen in the three directions of space. When the atoms penetrate this area, they are literally caught by the light and accumulate in large numbers, making it possible to visualize them.

Figure 5

Figure 5

Image of a sodium optical molasses containing a few million sodium atoms at the intersection of three pairs of laser beams.

Photography: W. D. Phillips, NIST, 1987.

  • 7 See for example the Nobel lectures: S. Chu, “The Manipulation of Neutral Particles”, Reviews of Mod (...)

34The temperatures reached in cold atom experiments are the lowest ever measured.7 By comparison, with liquid helium-based cryogenics, outstanding technological feats can be accomplished, in which the millikelvin range is reached. To be fair, I should add that cold atom experiments are far more modest in terms of the number of particles handled; the sample shown in Figure 5 contains a few million atoms, whereas the assemblies found in a liquid helium cryostat count quintillions of particles.

Cold atoms and the measurement of time

35Now that I have presented the cooling of atoms, I shall discuss one of its earliest applications: improving atomic clocks. These clocks are our guardians of time and are therefore of great importance, both for industry and services, and for fundamental research.

36Let me begin by outlining their working principle. The reference for time has long been astronomical, founded of the sidereal day. But as the precision of terrestrial clocks improved, particularly with the invention of quartz devices, the irregularities of the Earth’s rotation movements made this definition problematic. In 1967, during the thirteenth General Conference on Weights and Measures, it was decided to switch to an atomic reference, which, at the time, was considered infallible. For practical reasons, the caesium atom was chosen, with its two lowest energy states, 1 and 2, represented in Figure 6. Let us once more draw on the fact that, if its colour is well chosen, radiation can induce a transition between the atomic states. We define the second by positing that the electromagnetic wave capable of inducing optimally the transition between State 1 and State 2 performs 9,192,631,770 oscillations per second.

37To put this definition into practice, we build a caesium atom jet in State 1, we send these atoms into a cavity where the electromagnetic wave propagates, and we detect how many atoms have transited to State 2. A feedback loop locks in the frequency of the electromagnetic wave to maximize this number. Once the electromagnetic wave is at the right frequency, to know that a second has just passed, we “simply” need to use an electronic device to count the right number of oscillations of this wave, in other words the 9 billion and a bit mentioned earlier. Let me attempt a comparison with a living room clock that is comprised of two crucial elements: a pendulum, and a counting system which detects the pendulum’s oscillations and transcribes them into the movement of the hands. As an illustration, we can say that the atoms here play the role of the pendulum, and the electromagnetic wave the role of the counting system.

Figure 6

Figure 6

Block diagram of an atomic clock.

38Using cold atoms in a clock offers many advantages. I will mention just one, linked to the Doppler effect, which indicates that the wave emitted by a moving source does not have the same frequency as a wave emitted by a stationary one. In an atomic clock, the Doppler effect is therefore detrimental; if the atoms are animated by random motions, it modifies these atomic pendulums’ frequencies in an undesirable way, and increasingly so, the faster the atoms go. On the other hand, if the atoms are very slow, the Doppler effect is much weaker and its detrimental role becomes negligible.

  • 8 A. Clairon, C. Salomon, S. Guellati et W. D. Phillips, “Ramsey resonance in a Zacharias fountain”, (...)

39In order to make the most of the very low temperatures of optical molasses, André Clairon and Christophe Salomon from the Observatoire de Paris developed an atomic fountain that is about a meter high, many duplicates of which were then produced all over the world.8 This fountain clock has now reached a formidable precision, of 10–16 in relative value. If it had functioned since the Big Bang, it would be only a few seconds slow or fast.

40Far from being a simple stylistic exercise, this performance has proved useful both in daily life and for fundamental science. Its many applications include navigation, satellite navigation, geodesy and, in the near future, very high-speed telecommunication. The spin-offs for physics include the testing of Einstein’s relativity, which can be carried out with unprecedented precision. Moreover, astronomers use these clocks to implement very-long-baseline interferometry, in order to improve their telescopes’ resolution power.

41With this relative precision of 10–16, have atomic clocks reached their final limit? Certainly not: several paths are currently being explored to render the measurement of time considerably more precise, that is, by a factor of 10 or even 100.

  • 9 C. Salomon, N. Dimarcq, M. Abgrall, A. Clairon, P. Laurent et al., “Cold Atoms in Space and Atomic (...)

42The first path consists in placing the atoms in a weightless environment, to take advantage of their slow speeds for an even longer period of time. The ACES mission, funded by the Centre national d’études spatiales and the European Space Agency, is trying to put a cold atom clock into orbit, thereby providing any Earthbound observer with a universal time reference.9

43Moreover, there is talk of changing the definition of the second, using a reference electromagnetic wave in the visible rather than the microwave domain, as is the case for the caesium atom. This apparently technical change is based on a very simple consideration: all other things being equal, the faster a clock's pendulum oscillates, the greater its precision will be.

44Finally, researchers are studying the possibility of using the transitions within atoms’ nuclei, instead of the transitions between levels of the electron cloud. This coherent control of the nuclear levels with a light beam, which would be a breakthrough, would allow for clocks to be built in complete isolation from their environment, thereby ensuring their exceptional reliability.

45I will finish this brief presentation of atomic clocks with a question that may seem strange: do these clocks all indicate the same time? If a clock using caesium atoms measures that a second has just gone by, will a clock using rubidium atoms provide the same result? In principle, the oscillations of the pendulums corresponding to two different species, caesium and rubidium for example, are compared using a simple rule of three. This rule of three involves the quotient between the two energy differences E2E1 for caesium, and E’2E’1 for rubidium. This quotient is itself a function of fundamental constants that are dimensionless numbers. An example of a fundamental constant is the ratio between the proton’s and the electron’s masses, which any physics textbook will tell us is about 1,836. If these fundamental constants are immovable, caesium clocks and rubidium clocks must always indicate the same time lapse provided the right rule of three is applied.

  • 10 J. C. Berengut and V. V. Flambaum, “Astronomical and Laboratory Searches for Space-Time Variation o (...)

46But are fundamental constants truly constant? Has the proton always been and will it always be 1,836 times heavier than the electron? By comparing two atomic clocks at several years’ interval, using caesium for the one and rubidium for the other, it is possible to find out whether these dimensionless numbers have remained the same, considering the precision of the measurements, or whether they have drifted slightly.10

47Variation of the fundamental constants would have considerable repercussions on the models that are currently being developed to describe our physical world. It would also somewhat dash the hopes of the 1967 General Conference on Weights and Measures. If clocks using different atomic species did not measure the same length of time, the choice of one pendulum over another would bring arbitrariness back to where it had apparently been permanently eliminated.

Atomic interferences and space sensors

  • 11 For a recent review of matter-wave interferometers, see the article by A. D. Cronin, J. Schmiedmaye (...)

48We have just seen that cold atoms are at the core of our most precise time standards. They are also becoming very high performance space sensors, in other words sensors of acceleration or rotation fields. This uses the matter wave associated with each atom. The existence of this wave was foreseen by Louis de Broglie in 1923, and almost immediately became the cornerstone of quantum mechanics. The wavelength characterizing it, in other words the distance between two successive crests of the wave, is inversely proportional to the particle’s velocity. For the atoms of a gas at ambient temperature, the thermal velocity is high, the wavelength is short, far smaller than the atomic size, and the wave effects are difficult to observe. For cold and therefore slow atoms, the wavelength is much greater and the matter’s wave effects are easier to exploit.11

49For this, an interferometer with matter waves is produced, schematically represented in Figure 7. The atoms are emitted from Point A and are detected in Point C. To go from A to C, there are two possible paths, respectively going through Points B1 and B2. In wave physics, the probability of an atom arriving at Point C therefore results from the interference between the wave that took the top path and the one that took the bottom path.

Figure 7

Figure 7

Diagram of a two-path matter-wave interferometer (Young’s holes).

50Suppose that a slight difference between the two paths appeared, for example because an external mass came to modify the gravitational field locally. The presence of this mass is directly observed in the number of atoms detected at Point C. The difference between the paths translates into a lag between the crests of the two waves, and changes their interference figure.

51I will not discuss these sensors’ functioning in any further detail; let me simply point out that that they now match the best devices for measuring the gravity field. There is hope that we will soon reach a level of precision greater than the billionth of terrestrial gravity, which will open up very interesting perspectives in many domains – geophysics and mining detection for example.

Atomic physics and fundamental laws

52The great precision of the measurements that can be carried out by combining atoms and lasers makes it possible to address seemingly unexpected questions in my field of research. I will illustrate this point here by looking at the detection of a potential dissymmetry between matter and antimatter, a question linked to an enigma of cosmology.

53In order to situate the problem, let us return to our atoms. Until now, I have described them as being comprised of a nucleus and electrons. But the nucleus is actually a composite object, an assemblage of protons and neutrons. These protons and neutrons are themselves comprised of quarks. When protons, electrons and nuclei collide inside accelerators, other particles appear. To explain this multitude of objects, high-energy physicists have a theory, the standard model, which classifies these particles in families and explains their mass. The Standard Model has a spectacular predictive power, as the recent discovery of the Higgs boson, the model’s cornerstone, demonstrated.

54The Standard Model is based on the fact that each particle has an associated antiparticle. This antiparticle has the same mass as the initial particle and an opposite charge. When a particle and its antiparticle meet, they annihilate each other by transforming their mass energy into radiation. The annihilation of antimatter is routinely observed, for example during natural radioactivity processes. However, no significant energy releases that would signal the encounter of large masses of matter and antimatter are detected in the universe; the visible universe seems to be comprised almost exclusively of matter.

55This observation, however, hardly seems compatible with the standard model, which gives matter and antimatter a virtually symmetrical role. Within the framework of the Big Bang theory, matter and antimatter should therefore have been created in similar quantities.

56Several richer theories than the Standard Model have been proposed to break the symmetry between matter and antimatter. They offer an explanation for the quasi-total extinction of antimatter in the first few moments of the Universe, and result in two categories of effects that can be tested experimentally. The first concerns the existence of particles that have not yet been observed; they are being actively searched for with large accelerators. The second category of effects relates to well-known particles, the electron for example. These particles’ charge distribution should not be as simple as what has been attributed to them until now. As an illustration, the electron may not be completely round.

  • 12 For the description of the most precise measurement of the electron’s rotundity to date, see the ar (...)

57Detecting this effect, technically called an electric dipole moment, is in principle within the reach of atomic physics experiments. It should be observable by measuring very precisely the shift of the energy levels of atoms or molecules when they are placed in an electric field.12

58Within this framework, atomic physics experiments complement those carried out in high-energy physics: a crucial physical phenomenon, the possible dissymmetry between matter and antimatter, can thus signal its presence subtly but indisputably.

Cold atoms and collective phenomena

59Until now, I have focused on the behaviour of an isolated atom irradiated by a light beam. Another aspect of research on cold atoms relates to the study of the collective behaviour of these particle assemblies. This behaviour underpins the “quantum matter” mentioned in the introduction, which I will now briefly present.

  • 13 See for example the Nobel lectures of E. A. Cornell and C. E. Wieman, “Bose-Einstein Condensation i (...)

60The shift to the gas’ collective quantum behaviour was made possible by the development of a second cooling mechanism, which complements optical molasses. This is evaporative cooling, in which the particles with the most energy are eliminated so as to keep only the slowest ones. In 1995, with the combination of these two cooling methods, a new state of matter was reached, the gaseous Bose-Einstein condensate.13 Although, Einstein had in the 1920s predicted this state, it remained hypothetical for lack of sufficiently cold gas to observe it.

61The threshold determined by Einstein for the appearance of a condensate is the result of the comparison of two length scales (Figure 8). The first is the average distance between particles, directly linked to the gas’ density. The second scale is specifically quantum: it is the wavelength of the matter waves associated with the atoms, which we have already discussed. Cooling the atoms increases this wavelength.

Figure 8

Figure 8

On the left: a hot and diluted gas; the wavelength of the matter wave is shorter than the distance between particles. On the right: this is the reverse situation, where the quantum properties of matter are strongly pronounced.

62When the gas is hot and diluted, the wavelength is shorter than the distance between particles. The behaviour of the atom gas is then similar to what is expected of a set of billiard balls knocking together; our fluid is classical, in the sense that the effects linked to the wave character of matter are negligible.

  • 14 Quantum particles, when identical, must therefore be treated as indiscernible. As a result, they ar (...)
  • 15 For a review of the properties of this quantum matter formed from atomic gases, see for example: I. (...)

63When the gas is cooled down, on the other hand, the wavelength matter exceeds the distance between particles. The waves associated with the atoms overlap and mix. The atoms lose their individuality: even with measurement tools with an arbitrarily high-resolution power, it becomes impossible to follow their individual trajectories.14 To describe the whole range of phases, which can then appear, with properties that are radically different from the classical matter we encounter in daily life, we use the term “quantum matter”.15

64Let me offer two examples of this quantum matter, discovered in the first half of the twentieth century and therefore known well before the arrival of cold atoms. The first is the superconductivity phenomenon: at a very low temperature, certain materials can conduct electricity without the slightest dissipation. This property allows for the levitation of magnetic bodies, for example, without energy constantly having to be provided. The second example relates to the superfluidity of liquid helium, in other words, to the fact that this liquid can run without the slightest viscosity through microtubes or rise through capillary action along the sides of a container.

65These are two fascinating phenomena; over the last ten years many teams working on cold atoms have sought to transpose them to the field of diluted gases. In a personal capacity, I would like to point out that each of these subjects has led to encounters, linked to the Collège de France, which have been extremely fruitful for me. I would like to take this opportunity first to tell Philippe Nozière how grateful I am for his teaching and advice when our team was trying to understand what a superfluid was. I would also like to thank Antoine Georges who patiently explained some of the subtleties of superconductive materials to me when we were working on a project together. On the subject of superconductivity, I would also like to mention another famous professor at the Collège de France, Pierre-Gilles de Gennes, whose name has remained associated with the modelling of these materials, among many other discoveries.

66Let us look more closely at superfluidity: as the emblematic illustration of the quantum properties of liquid helium, does it also exist for cold atom gases? The path to follow for answering this question is not an easy one. As our atom gases are trapped in cages of light that do not contain microtubes and that do not have material walls, most of the diagnoses developed by the physics of liquid helium cannot be used. One nevertheless remains, which consists in making the fluid rotate, as a superfluid cannot rotate like an ordinary fluid.

67In order to illustrate this point, first consider a bowl full of an ordinary liquid, which is set in rotation with a spoon. The surface of the liquid curves under the effect of the rotation, with the liquid’s velocity increasing as it gets further from the centre. In mathematical terms, the product velocity*distance from the centre continuously varies, from zero at the middle of the bowl to a possibly high value on the sides.

68In a bowl filled with a superfluid, the result of triggering a rotation is very different, for in quantum mechanics the product velocity*distance can only take discrete values. This result is the strict analogue, on a macroscopic level, of Bohr’s rule, which prioritized certain orbits of an electron rotating around an atomic nucleus.

69To respect the discrete character of this product, the fluid can be set in motion only by means of quantum vortices. When the rotational velocity is increased, it must host one, then two, then an increasingly large number of identical vortices. Each new vortex corresponds to the increase of the product velocity*distance by one unit. These vortices can be visualized as their centre holds no matter: the fluid’s density therein is zero.

Figure 9

Figure 9

Quantum vortices in rotating Bose-Einstein condensates. The rotational velocity is slow on the left hand side picture and increases from left to right.

Photograph: LKB-CNRS-ENS, 2000.

  • 16 K. W. Madison, F. Chevy, W. Wohlleben and J. Dalibard, “Vortex Formation in a Stirred Bose-Einstein (...)

70My team has devoted a great deal of effort to observing these quantum vortices and understanding their properties. Starting with a still Bose-Einstein condensate, we set it in rotation. To do so, we used not a material spoon but an agitator formed of a laser beam with a rapidly varying direction in space. Our observations, represented in Figure 9, confirmed the expected scenario for a superfluid16: a critical rotation frequency exists below which nothing happens; then, rotating a little faster, a vortex appears at the centre of the condensate, and finally a network of vortices forms when the rotational velocity becomes truly high. Gas condensates are therefore indeed superfluids.

  • 17 Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier and J. Dalibard, “Berezinskii–Kosterlitz–Thoules (...)

71We recently showed that the superfluidity property extended to a two-dimensional atom gas. To do so, we used the light of a laser to flatten our gas and transform it into a sheet of extremely fine matter. We then agitated this sheet with another light beam and checked that it also presented the property of superfluidity.17

  • 18 J. M. Kosterlitz and D. J. Thouless, “Ordering, Metastability and Phase Transitions in Two-Dimensio (...)

72The fact that this superfluid state would survive the shift from three to two dimensions was not straightforward at first. Since Peierls’ pioneering work in the 1930s and 1940s, we know that the equilibrium phases of matter strongly depend on the dimension of space in which they are prepared. For example, if we lived in a two-dimensional world, crystals would not exist as thermal agitation would destroy the regular arrangement of atom lattices. The fact that superfluidity is still present in a two-dimensional gas shows that it stems from a special transition phase, discovered by Kosterlitz and Thouless18: when they become superfluid, planar gases acquire an order that is qualified as topological, which is more robust than the crystalline order.

Towards a quantum simulator

  • 19 See for example the April 2012 special issue of Nature Physics (vol. 8, no. 4), with the contributi (...)

73Over the course of this lecture I have highlighted several research paths linked to the manipulation of atoms using laser. I will mention one more highly promising such path, relating to the use of cold atom fluids as quantum simulators.19

  • 20 R. P. Feynman, “Simulating Physics with Computers”, International Journal of Theoretical Physics, v (...)

74The 2012 Nobel Prize in physics, awarded to Serge Haroche and David Wineland, rewarded spectacular progress in the control of individual quantum systems, an atom or a photon. In a visionary text written in the eighties, the physicist Richard Feynman explained the value of having equivalent control of a large number of particles.20 The artificial matter thus produced would allow for some major fundamental and practical unanswered questions to be addressed. I will mention two here: by better understanding the superconductivity phenomenon, can we design materials to transport electricity without loss for daily life applications? By using quantum concepts wisely, can we produce new devices able to store far more information than our current hard drives?

Figure 10

Figure 10

Above, the state of a classical magnetic memory, comprised of a chain of spins, is described by indicating the orientation of each magnetic moment. Below, the quantum version of the state of the chain of spins is the superposition of all possible states.

75The challenge raised by these systems with large numbers of particles lies in the complexity of their description within the framework of quantum physics. To illustrate this complexity, consider a magnetic memory comprised of a chain of spins, in other words microscopic magnets that can exist in two configurations, the North Pole either on top or at the bottom. In classical physics, the state of this chain is described by specifying the orientation of each spin. In the drawing that makes up the upper part of Figure 10 for example, the first spin points upwards, the second and the third downwards, the fourth and the fifth upwards, etc.

76In quantum physics, any given state of the chain of spins is a superposition of all possible classical states. Just as Schrödinger’s cat is both in a living and in a dead state, so too the chain of spins is at once in the state where the spins point upwards, the one where they point downwards, and any of the intermediary classical states. For an assembly of a hundred particles, simply writing this state with its 2100 coefficients would require a computer larger than any currently in operation. And performing computations on this quantum state would be even more unrealistic…

77The path proposed by Feynman consists in simulating rather than calculating. This approach is not new. From the eleventh to the sixteenth century, many astronomical clocks were built: their movements, performed with great precision, made it possible to predict the position of the planets, the moon’s phases and solar and lunar eclipses, without any computation. The simulation of interest to us here is based on the universality of quantum physics; two seemingly different systems can be described by a similar formalism if they share certain parameters, like the relationship between their interaction energy and their temperature. The quantum system we are basing ourselves on is of course a cold atom gas. Thanks to light beams, the atoms are organized in a “landscape” which simulates another environment. We saw with Sisyphus cooling that a stationary light wave could be used to create a periodic potential, which is an environment well-suited to modelling the motion of electrons in a crystal. It is also possible to create disordered landscapes with which to study wave propagation in a random environment. By forming an alignment of a hundred atoms, it is possible to simulate the chain of spins described above.

78In any case, our cold atom gas is prepared in a known initial state, it is left to evolve for a set period of time, and its final state is measured. Nature does the calculation for us, and the universality of quantum physics ensures that the result obtained for our atoms also holds true for the modelled system.

Conclusion

79The atoms we manipulate and observe individually bear little resemblance to the ultimate, indivisible object invented by Greek and Latin philosophers. Nevertheless, as we have seen, the physics of atoms and light can contribute to elucidating the laws of nature. A possible dissymmetry between matter and antimatter, and a potential drift of fundamental constants, are examples of what may potentially be observed in atomic physics, thanks to the precision of the measurements that we carry out. Progress in the control of light and its interaction with matter also has spin-offs and applications in domains as varied as telecommunication, image analysis or the measurement of time and space.

80The collective behaviour of atoms in these cold gases has paved the way for our field of physics towards the study of complex systems. This is a customized complexity, in which both the atoms’ environment and their mutual interactions are controlled. Many bridges have now been drawn with the physics of condensed matter; the perspectives established are particularly promising as our systems allow for the exploration of new situations that were out of reach with real materials.

81The links between our research field and neighbouring disciplines like mathematics and chemistry are also very real. In the non-linear equations governing these gases’ behaviour, mathematicians have found a new field of application for tools developed in other contexts. Chemists are utilizing the real-time observation of the formation of small molecular constructs with two, three or four bodies under unprecedented temperatures and densities, to shed new light on the notion of reactional dynamics.

82Everyone in our field therefore senses the great promise this research topic has to offer. One possible barrier to their fulfilment is the difficulty of establishing a common language, of making an inventory of open questions. My wish is that the Chair will to contribute to lifting that barrier and to bring all these communities together.

83A first lecture is as much the elaboration of a programme as an outline of a personal review. This review shows me everything for which I am indebted to many people, and I would like to conclude this presentation by expressing my gratitude to them individually and collectively, albeit very briefly.

84I have already said just how grateful I am to Claude Cohen-Tannoudji for the way in which he guided my first steps in research. I discovered experimental physics thanks to Alain Aspect and Bill Phillips, who each hosted me in their laboratory. For years, Christophe Salomon showered me with advice virtually on a daily basis. Claude, Alain, Bill and Christophe, please know how much our discussions meant to me, in terms both of pure physics and of scientific ethics. In more distant times, I was fortunate to have high school teachers who truly gave me the taste for science. Two of them, Nicole Tuffreau and Eusèbe Redondo, did me the kindness of attending this lecture, thus exchanging our roles after forty years.

85Teaching has been an essential factor of well-being for me. As a researcher at the CNRS, I was fortunate that the volume of teaching remained low enough not to stall my research – quite the opposite. I would here like to salute all those who accompanied me in these different courses, particularly Jean-Louis Basdevant, who patiently and benevolently showed me the ropes at the École polytechnique, and who introduced me to the pleasure of its large lecture theatres.

86For over twenty years now, our team at the Kastler-Brossel laboratory has brought together exceptionally motivated young academic researchers, students and post-docs. While I cannot mention them all here, I want them to know how indebted I am to them for their determination and spirit of initiative.

87These cold atom experiments are highly technical. While the concepts are relatively simple to explain, their implementation requires complicated equipment. The technical, mechanical, electronic and informatics services play a crucial role in this development. I would like to thank them for all their help. I also wish to thank the administrative services that ensure the livelihood of our teams, both literally and figuratively speaking.

88Finally, with the launch of this Chair, in a few months my team will be settling into the new premises of the Collège’s physics building. This new research space is opening unprecedented possibilities to us, I would like to say here how grateful I am to those who made this great construction project possible, especially Jacques Glowinski, its tireless orchestrator.

Notes

1 Johannes Kepler, De cometis libelli tres. I. Astronomicus… II. Physicus… III. Astrologicus…, Augustae Vindelicorum, Augsbourg, 1619; translation by H. Flaugergues in the Journal de physique, de chimie et d’histoire naturelle, vol. LXXXV, September 1817, pp. 193-216.

2 Nicolas Hartsoeker, Principes de physique, published in Paris by Jean Anisson, Head of the Imprimerie royale, 1696.

3 For details on Niels Bohr’s approach, see Max Jammer’s book The Conceptual Development of Quantum Mechanics, New-York, McGraw-Hill, 1966.

4 A. Kastler, “Quelques suggestions concernant la production optique et la détection optique d’une inégalité de population des niveaux de quantification spatiale des atomes. Application à l'expérience de Stern et Gerlach et à la résonance magnétique”, Journal de physique et le radium, vol. 11, no. 6, 1950, pp. 255-265, DOI: 10.1051/jphysrad:01950001106025500; J. Brossel, A. Kastler and J. Winter, “Création optique d’une inégalité de population entre les sous-niveaux Zeeman de l’état fondamental des atomes”, Journal de physique et le radium, vol. 13, no. 12, 1952, p. 668, DOI: 10.1051/jphysrad:019520013012066800.

5 C. Cohen-Tannoudji, “Observation d’un déplacement de raie de résonance magnétique causé par l’excitation optique”, Comptes rendus hebdomadaires des séances de l’Académie des sciences, vol. 252, 1961, pp. 394-396.

6 J. Dalibard and C. Cohen-Tannoudji, “Dressed-Atom Approach to Atomic Motion in Laser Light: the Dipole Force Revisited”, Journal of the Optical Society of America B, vol. 2, no. 11, 1985, pp. 1707-1720, DOI: 10.1364/JOSAB.2.001707; “Laser Cooling below the Doppler Limit by Polarization Gradients: Simple Theoretical Models”, vol. 6, no. 11, 1989, pp. 2023-2045, DOI: 10.1364/JOSAB.6.002023.

7 See for example the Nobel lectures: S. Chu, “The Manipulation of Neutral Particles”, Reviews of Modern Physics, vol. 70, no. 3, 1998, pp. 685-706, DOI: 10.1103/RevModPhys.70.685; C. Cohen-Tannoudji, “Manipulating Atoms with Photons”, Reviews of Modern Physics, vol. 70, no. 3, 1998, pp. 707-719, DOI: 10.1103/RevModPhys.70.707; W. D. Phillips, “Laser Cooling and Trapping of Neutral Atoms”, Reviews of Modern Physics, vol. 70, no. 3, 1998, pp. 721-741, DOI: 10.1103/RevModPhys.70.721.

8 A. Clairon, C. Salomon, S. Guellati et W. D. Phillips, “Ramsey resonance in a Zacharias fountain”, Europhysics Letters, vol. 16, no. 2, 1991, p. 165-170, DOI : 10.1209/0295-5075/16/2/008.

9 C. Salomon, N. Dimarcq, M. Abgrall, A. Clairon, P. Laurent et al., “Cold Atoms in Space and Atomic Clocks: ACES”, Comptes rendus de l’Académie des sciences (Paris), Series IV (Physique), vol. 2, no. 9, 2001, pp. 1313-1330, DOI: 10.1016/S1296-2147(01)01274-4.

10 J. C. Berengut and V. V. Flambaum, “Astronomical and Laboratory Searches for Space-Time Variation of Fundamental Constants”, Journal of Physics: Conference Series, vol. 264 [Proceedings of the 22nd International Conference on Atomic Physics, 25-30 July 2010; Cairns, Australia], 2011, DOI: 10.1088/1742-6596/264/1/012010.

11 For a recent review of matter-wave interferometers, see the article by A. D. Cronin, J. Schmiedmayer and D. E. Pritchard, “Optics and Interferometry with Atoms and Molecules”, Reviews of Modern Physics, vol. 81, no. 3, 2009, pp. 1051-1129, DOI: 10.1103/RevModPhys.81.1051.

12 For the description of the most precise measurement of the electron’s rotundity to date, see the article by J. J. Hudson, D. M. Kara, I. J. Smallman, B. E. Sauer, M. R. Tarbutt and E. A. Hinds, “Improved Measurement of the Shape of the Electron”, Nature, vol. 473, 2011, pp. 493-496, DOI: 10.1038/nature10104.

13 See for example the Nobel lectures of E. A. Cornell and C. E. Wieman, “Bose-Einstein Condensation in a Dilute Gas, the First 70 Years and Some Recent Experiments”, Reviews of Modern Physics, vol. 74, no. 3, 2002, pp. 875-893, DOI: 10.1103/RevModPhys.74.875; W. Ketterle, “When Atoms Behave as Waves: Bose-Einstein Condensation and the Atom Laser”, Reviews of Modern Physics, vol. 74, no. 4, 2002, pp. 1131-1151, DOI: 10.1103/RevModPhys.74.1131.

14 Quantum particles, when identical, must therefore be treated as indiscernible. As a result, they are organized into two categories: bosons, for which the probability of having several particles in the same individual state is increased compared to the case of discernible particles, and fermions, for which an individual quantum state is occupied at most by one particle. While Bose-Einstein condensation concerns bosons, fermions also give rise to spectacular quantum matter, of which superconductivity is one example.

15 For a review of the properties of this quantum matter formed from atomic gases, see for example: I. Bloch, J. Dalibard and W. Zwerger, “Many-Body Physics with Ultracold Gases”, Reviews of Modern Physics, vol. 80, no. 3, 2008, pp. 885-964, DOI: 10.1103/RevModPhys.80.885.

16 K. W. Madison, F. Chevy, W. Wohlleben and J. Dalibard, “Vortex Formation in a Stirred Bose-Einstein Condensate”, Physical Review Letters, vol. 84, no. 5, 2000, pp. 806-809, DOI: 10.1103/PhysRevLett.84.806.

17 Z. Hadzibabic, P. Krüger, M. Cheneau, B. Battelier and J. Dalibard, “Berezinskii–Kosterlitz–Thouless Crossover in a Trapped Atomic Gas”, Nature, vol. 441, 2006, pp. 1118-1121, DOI: 10.1038/nature04851; R. Desbuquois, L. Chomaz, T. Yefsah, J. Léonard, J. Beugnon, C. Weitenberg and J. Dalibard, “Superfluid Behaviour of a Two-Dimensional Bose Gas”, Nature Physics, vol. 8, no. 9, 2012, pp. 645-648, DOI: 10.1038/nphys2378.

18 J. M. Kosterlitz and D. J. Thouless, “Ordering, Metastability and Phase Transitions in Two-Dimensional Systems”, Journal of Physics C: Solid State Physics, vol. 6, no. 7, 1973, pp. 1181-1203, DOI: 10.1088/0022-3719/6/7/010.

19 See for example the April 2012 special issue of Nature Physics (vol. 8, no. 4), with the contributions of J. I. Cirac and P. Zoller, “Goals and Opportunities in Quantum Simulation” (pp. 264-266, DOI: 10.1038/nphys2275); I. Bloch, J. Dalibard and S. Nascimbène, “Quantum Simulations with Ultracold Quantum gases” (pp. 267-276, DOI: 10.1038/nphys2259); R. Blatt and C. F. Roos, “Quantum Simulations with Trapped Ions” (pp. 277-284, DOI: 10.1038/nphys2252). Although atoms are neutral, this simulation can extend to charged particle systems thanks to the production of artificial gauge potentials; see for example J. Dalibard, F. Gerbier, G. Juzeliūnas and P. Öhberg, “Colloquium: Artificial Gauge Potentials for Neutral Atoms”, Reviews of Modern Physics, vol. 83, no. 4, 2011, pp. 1523-1543, DOI: 10.1103/RevModPhys.83.1523.

20 R. P. Feynman, “Simulating Physics with Computers”, International Journal of Theoretical Physics, vol. 21, no. 6-7, 1982, pp. 467-488, DOI: 10.1007/BF02650179.

Table des illustrations

Titre Figure 1
Légende Process of absorption by an atom. To the left, a photon with energy E3E1 arrives on an atom prepared in its fundamental state, with energy E1. To the right, the atom has absorbed the photon and has shifted to the energy state E3.
URL http://books.openedition.org/cdf/docannexe/image/3695/img-1.png
Fichier image/png, 17k
Titre Figure 2
Légende Optical pumping principle. At the top, an assembly of six atoms is randomly distributed across the energy states E1 and E2. At the bottom, after light has been focused on the atoms with photons with energy E3E2, all the atoms have been accumulated in the energy state E1. The initial disorder has been removed.
URL http://books.openedition.org/cdf/docannexe/image/3695/img-2.png
Fichier image/png, 23k
Titre Figure 3
Légende Sisyphus cooling principle. In a stationary light wave, the energy levels are modulated in space. Configurations exist such that the atom constantly ascends hills of potential, with optical pumping placing it at the bottom of a valley as soon as it reaches a hilltop. When its energy becomes too weak, the atom is trapped at the bottom of a well of potential.
URL http://books.openedition.org/cdf/docannexe/image/3695/img-3.png
Fichier image/png, 43k
Titre Figure 4
Légende (Logarithmic) scale of temperatures. Cold atomic gases correspond to the lowest kinetic temperatures ever measured.
URL http://books.openedition.org/cdf/docannexe/image/3695/img-4.png
Fichier image/png, 17k
Titre Figure 5
Légende Image of a sodium optical molasses containing a few million sodium atoms at the intersection of three pairs of laser beams.
Crédits Photography: W. D. Phillips, NIST, 1987.
URL http://books.openedition.org/cdf/docannexe/image/3695/img-5.png
Fichier image/png, 292k
Titre Figure 6
Légende Block diagram of an atomic clock.
URL http://books.openedition.org/cdf/docannexe/image/3695/img-6.png
Fichier image/png, 60k
Titre Figure 7
Légende Diagram of a two-path matter-wave interferometer (Young’s holes).
URL http://books.openedition.org/cdf/docannexe/image/3695/img-7.png
Fichier image/png, 56k
Titre Figure 8
Légende On the left: a hot and diluted gas; the wavelength of the matter wave is shorter than the distance between particles. On the right: this is the reverse situation, where the quantum properties of matter are strongly pronounced.
URL http://books.openedition.org/cdf/docannexe/image/3695/img-8.png
Fichier image/png, 75k
Titre Figure 9
Légende Quantum vortices in rotating Bose-Einstein condensates. The rotational velocity is slow on the left hand side picture and increases from left to right.
Crédits Photograph: LKB-CNRS-ENS, 2000.
URL http://books.openedition.org/cdf/docannexe/image/3695/img-9.png
Fichier image/png, 50k
Titre Figure 10
Légende Above, the state of a classical magnetic memory, comprised of a chain of spins, is described by indicating the orientation of each magnetic moment. Below, the quantum version of the state of the chain of spins is the superposition of all possible states.
URL http://books.openedition.org/cdf/docannexe/image/3695/img-10.png
Fichier image/png, 62k

Auteur

Liz Libbrecht (Traducteur)

© Collège de France, 2015

Conditions d’utilisation : http://www.openedition.org/6540

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