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Atomic and Molecular Physics

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Claude Cohen-Tannoudji

Atomic and Molecular Physics

Inaugural lecture delivered on Tuesday 11 December 1973

Claude Cohen-Tannoudji
Traduction de Liz Libbrecht

Note de l’éditeur

This text has been translated by Liz Libbrecht in collaboration with Céline Surprenant (Collège de France).

Note de l’auteur

This inaugural lecture can obviously not cover all the spectacular breakthroughs in atomic and molecular physics since 1973. Some of them are described in the lectures that were delivered at the Collège de France within the framework of this Chair, transcripts of which are available on the Collège de France website: http://www.phys.ens.fr/cours/college-de-france.

Texte intégral

1Mr Administrator,
My dear colleagues,
Ladies and gentlemen,

2“Explaining complicated visible with simple invisible”: Jean Perrin’s sentence perfectly illustrates the stage that the atomic hypothesis constituted in the development of science. Recognizing that all matter is formed from an aggregate of elementary units called atoms, which mutually attract one another and are in a constant motion of agitation, clarified our view of the world. Although atoms are too small to be directly perceivable by us, their existence makes it possible to interpret, very simply, phenomena as diverse as heat, the behaviour of gases, the fusion of solids, chemical reactions, and so on. And the same atoms are found in an inert rock, a flower, a human being, and a distant star, etc.

3But is the invisible that Jean Perrin talked about as simple as we might first believe it to be? When physicists began to explore the world of atoms more precisely, as they endeavoured to understand its structure and the laws governing its behaviour, they soon encountered serious difficulties. Our intuitive concepts, based on our daily experience of the macroscopic world around us, proved to be completely erroneous on the atomic scale; the atom was incomprehensible within the framework of classical physics. In order to uncover these new mysteries, after a great deal of trial and error, entirely new concepts therefore had to be elaborated: the concepts of quantum physics. Twenty years after the relativist revolution had superseded the notions of absolute time and space, scientific thinking thus underwent a second dramatic upheaval: the idea that an atomic object could at any time have a well-defined position and speed was invalidated, and the notion of trajectory was abandoned.

4Today we are more familiar with quantum concepts. The language that is used to describe atoms is very remote from everyday language; it is more mathematical, more abstract: we talk of energy levels, wave functions, the Hamiltonian, Feynman diagrams, etc. And this theoretical structure allows us to analyse and to understand the innumerable observations carried out on atoms with increasingly elaborate means. What are the main stages that have led us to this modern understanding of the atom? What is the present state of atomic physics? How has it contributed to the development of our knowledge and where is it heading? It seemed to me that this first lecture would be well spent providing a brief overview of these few problems.

***

5Greek philosophers were the first to have the intuition that matter could not be divided indefinitely, and that the atom was the ultimate stage of this partitioning. It took almost twenty-five centuries for this idea to be taken up again scientifically. In fact, it soon became clear that atoms are not indivisible, but are comprised of a massive central nucleus that is highly localized and positively charged, and that attracts around it electrons which are thousands of times lighter than the nucleus and are negatively charged. Like atoms, the nuclei are made up of more elementary particles: nucleons, which are closely linked to one another by nuclear forces. These forces are far more intense than the electromagnetic forces between the nucleus and the electrons. In addition to nucleons, we now know that a very large number of other more or less stable particles exist, which transform into one another, and fall within the scope of elementary particle physics. Certain theories even hold that nucleons have a composite structure. So what is ultimately the final stage of the partitioning of matter? No one can yet answer this question with certainty.

6But let us return to the study of the atom and first lay down a few orders of magnitude. Imagine enlarging an atom one thousand billion times: the electrons would move in a spherical volume with a radius of about one hundred meters; at the centre of the volume, the nucleus would appear as a small sphere with a radius of the order of no more than a millimetre. The first image that came to physicists’ minds was that of a planetary atom, with the light electrons gravitating around the massive central nucleus like the planets around the sun. Though appealing, this image does not withstand serious examination: as they lost energy in the form of electromagnetic radiation, the electrons would gradually get closer to the nucleus and ultimately disappear therein. The atoms would therefore be unstable and could not exist. Such is the absurd conclusion to which classical mechanics and electromagnetism lead.

7It was not easy, however, to give up the image of an electron following a well-defined trajectory around a nucleus. The intuitive idea we have of the movement of a material point is based on our observation of the behaviour of common objects like stones or tennis balls, for example. Perhaps for lack of imagination, we have too much of a tendency simply to transpose our concepts to the new domains we are dealing with. It is therefore hardly surprising to find the image of electronic orbits in the first quantitative outline of an atomic theory, Bohr’s theory. To explain the stability of atoms, Bohr introduced preferred orbits along which he posited that the electron necessarily had to move without being able to radiate. The discrete emission line spectra were interpreted as “quantum jumps” by the electron, from one preferred orbit to another. While this kind of model accounted for the spectrum of the hydrogen atom with remarkable precision, it posed countless thorny problems! Why does the electron not radiate on its orbit at the rotational frequency? What is the nature of this mysterious quantum jump? Bohr was perfectly aware of the flaws in his model and saw it as no more than an intermediate stage towards a more satisfactory understanding of the atom, a first attempt to find a guiding principle with which to navigate through the multitude of experimental facts. On the verge of a profound upheaval of our concepts, how difficult it must have been to link together the new phenomena that foreshadowed this upheaval, in an old language completely unsuited to the situation! One can only admire the founders of atomic theory, considered somewhat as mystics by their most conservative colleagues, for having managed, in spite of everything, to prepare the springboard that would allow physics to make a phenomenal leap forward. The following statement by Bohr, which Heisenberg recalls, eloquently sums up the state of mind that they shared: “We must be clear that when it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images and establishing mental connections”. New languages and new concepts were to see the light of day following the works of de Broglie, Schrödinger, Heisenberg, Born, Dirac and many others.

8We thus learnt to characterize the state of an electron at a certain point in time, not according to its position and speed, but by providing a complex number at each point in space; in other words, again through a wave function whose evolution over time is governed by a partial differential equation called the Schrödinger’s equation. The concept of trajectory, subsequently constituted by the points representing the various successive states of the classical corpuscle, was thus replaced by that of wave propagation.

9Does this mean that we have turned to a purely wave conception of the electron? Assuredly not, as the corpuscular aspect is still present in the localized impacts generated by the electron in a detector. In fact, the point in space where the electron will manifest itself when we seek to detect it cannot be predicted with certainty; we can only give the probability of such an event, based precisely on the wave function.

10This same function can also serve to assess the dispersion of the values of the electron’s speed, and this leads to a surprising finding: if we take a gradually more localized wave function, in other words, one which corresponds to the increasingly weaker degree of dispersion of the position, the dispersion of the speed then becomes gradually greater. This is what prevents us from attributing a simultaneously well-defined position and speed to the electron.

11Could we at least represent an atomic electron as a small bundle of waves whose centre draws a circular or elliptical orbit around the nucleus? This planetary image, which is somewhat blurred by the corpuscle being replaced by a bundle of waves, is inaccurate. In the fundamental state of the hydrogen atom, in other words in the lowest energy state, the wave function is stationary; it does not propagate itself and looks like a spherical cloud centred around a proton, filling the full volume of the atom. The electron is completely delocalized inside this volume.

12We therefore need to think about the various atomic objects in entirely different terms. We must give up projecting our familiar common images onto them and acknowledge that they can have specific and original properties. Quantum concepts thus prevail, as they are the only ones with which to understand and predict the behaviour of these objects in a given situation. Better still, these new concepts encompass the old ones, since any object, as it is made of atoms, obeys the laws of quantum mechanics, even if most of the time the consistently underlying quantum effects are not always apparent at the macroscopic level.

13Around 1930, atomic physics thus experienced a golden age that was to last quite a few years. Quantum mechanics was successfully applied to many problems such as chemical bonding, the absorption and the emission of photons, molecular spectra, ferromagnetism, etc. It seemed that all of the atom’s secrets had been uncovered and that Schrödinger’s equation could explain everything, provided that purely mathematical difficulties were overcome. The atom then lost some of its charm and physicists’ interest gradually shifted to new problems raised by nuclear matter and elementary particles. For atomic physics, this was the beginning of a long period of stagnation that was to last until the end of the Second World War. The post-war years saw the revival of the discipline and the start of continuous growth still witnessed today. An increasing number of physicists devoted themselves to the problems raised by atoms, molecules and ions, and to the study of their mutual interactions and their coupling with photons. Numerous and spectacular applications of this work appeared, such as masers and lasers, in turn affording deeper knowledge in a wide variety of domains.

14Why this renewal and what did it lead to? This is what I will now try to explain using a few examples borrowed from various domains of modern atomic physics. Through them, I would also like to give you an idea of what makes this discipline appealing, of the diversity of intellectual aspirations it fulfils and the talents expressed through it. One physicist may seek the profound harmony that arises from the fundamental laws underlying the phenomena observed, while another might be seduced by the imagination and fantasy guiding the elaboration of a new method or a new device, and yet another might appreciate the frontier domains where a wide variety of techniques and concepts intertwine.

***

15The first example I will discuss pertains to the high-precision experiments carried out on simple atomic systems. These are the experiments that afforded a deeper and more satisfactory understanding of the electromagnetic interactions between charged particles.

16Electronics had made considerable progress by the end of the war, particularly thanks to the development of radar: we had learned to build devices to produce, amplify and detect electromagnetic waves in various frequency bands. Moreover, we knew how to produce jets of atoms in high vacuums and to use sensitive detectors. The circumstances were therefore highly conducive to the appearance of new methods for the exploration of atoms’ structure. The earlier works of Rabi and his students on induced resonances on atomic jets, and the discovery by Bloch, Purcell and Pound of the radio-electric detection of magnetic resonance, opened up a new branch of spectroscopy, Hertzian spectroscopy, also allowing for unmatched precision in the measurement of the fine and hyperfine structure of the atomic and molecular levels. Is this merely a tendency towards perfectionism, a race after decimals? We need to remember that, in physics, a very small anomaly sometimes triggers a complete overhaul of our ideas.

17From this perspective, the value of simple systems becomes apparent. When an anomaly arises, one is less tempted to attribute it to the complexity of the system preventing an exact resolution of equations, and the fundamental laws underpinning these equations are more easily challenged. Take for example the simplest atom, the hydrogen atom, formed from an electron and a proton. The energies of the bound states of these two particles are crucially dependent on the interactions between them. The precise measurement of these energies therefore provides a very strict test of the validity of Coulomb’s law at a very short distance, normally used to describe the attraction between the electron and the proton. One can thus understand the importance of Lamb’s discovery of a slight difference between the first two excited levels of the hydrogen atom. It is impossible to explain this difference on the basis of Dirac’s equation, which calculates the stationary states of a relativistic electron moving in a Coulomb potential. The interpretation of this anomaly stimulated a whole series of studies, from which a new quantum and relativistic theory of the interactions between charged particles and photons was to emerge: quantum electrodynamics.

18In this lecture I cannot go into the details of this theory, which serves as a model for many others, nor discuss the mathematical problems it raises. I would rather give you an idea of the new images that are being suggested to us, particularly by “Feynman diagrams”, small diagrams that physicists use to classify and to visualize various processes that come into play.

19The elementary interactions that appear in the theory and afford an understanding of all the others are the emissions or absorptions of a “quantum of light”, in other words, a photon, by a charged particle. It is possible to calculate the probability amplitudes associated with these processes and those which describe the propagation of a photon or a particle between two elementary acts of emission or absorption.

20Consider, for example, an initially isolated charged particle, on which no photon lands. With nothing to absorb, it can only emit a photon. However, during such a process the energy and momentum cannot be globally preserved. Quantum mechanics indicates that the new situation thereby created cannot last indefinitely: the emitted photon must be reabsorbed by the particle, after a period of time that shortens as the energy defect increases. This is often called a “virtual” photon, as it appears only fleetingly. That is not to suggest, however, that it is not associated with any real effect. The charged particle is surrounded, “dressed”, by the virtual photons it constantly emits and reabsorbs, and its physical properties become different from those of the “bare” particle. It is made heavier by the energy of the cloud of photons it carries; and it can also be shown that its magnetic moment is modified and becomes, so to speak, “abnormal”.

21If another charged particle passes near the first one, a virtual photon emitted by the one may be reabsorbed by the other. The electrostatic and magnetic interactions between two particles are now described through this type of virtual photon exchange. Note that these exchanges are slightly perturbed by the presence of virtual photon clouds that dress each particle. They therefore do not interact in exactly the same way as they would if they were “bare”.

22A photon itself can disintegrate into a particle-antiparticle pair, for example electron-positron, muon+-muon, meson π+-meson π, etc. As above, this type of process cannot preserve the overall energy and momentum. Shortly after its creation, the pair must therefore self-destruct to give birth to the initial photon again. Still, this kind of fleeting metamorphosis occurring on a virtual photon exchanged by two charged particles allows the vacuum that separates them to polarize and to constitute a new source of change for the electromagnetic interactions between them.

23We could therefore analyse increasingly complex Feynman diagrams, in other words which include more and more photons and virtual pairs. It thus becomes clear that there exists no simple law of interaction between two charged particles. Simplicity is found on a deeper level, in the elementary pieces of this new construction set which, fitted together in a certain way, form a Feynman diagram describing a certain process of interaction between the two particles. The greater the experimental precision, the more Feynman diagrams will be needed to account for experimental observations, and the more complex they will be. The fact that atomic physics can validly test quantum electrodynamics, and in this respect can compare favourably with high energy experiments, is therefore owed to the very high precision of its measurements. In order to explain the Lamb shift, for example, all the diagrams need to be calculated to the fourth order included, that is, all the diagrams that involve at least four elementary acts of interaction. Likewise, interpreting measurements of magnetic anomaly on the electron and the muon requires that we calculate diagrams of the sixth order, something which was only recently achieved with the use of computers. Some of these diagrams involve processes of scattering between virtual photons. These processes are thus indirectly detected thanks to the precision of the measurements, whereas the photon-photon scattering cross-section is too weak for such a phenomenon to be directly evidenced on real photons sent onto one another.

24It is also important to see that quantum electrodynamics is not a closed world and that it is impossible to isolate electromagnetic interactions from other known interactions in nature, such as the strong interactions to which nucleons, π-mesons, and hadrons more generally are sensitive. The virtual photons that appear in the Feynman diagrams associated with electrodynamic systems can turn into hadrons for a short while, resulting in “hadronic” corrections, to which measurements may be sensitive if they are sufficiently precise. Following impressive experimental verifications carried out in recent years, the emerging general trend is towards trusting quantum electrodynamics’s ability to calculate the contribution of purely radiative effects, and then to subtract the corrections thus calculated from experimental results so as to obtain and study hadronic effects. In the same line of thought, let me mention the problem of the hyperfine structure of hydrogen which, thanks to the development of the hydrogen maser, is known with twelve significant digits. Such a structure, which as a first approximation is due to the interactions between the magnetic moments of the electron and of the proton, cannot be interpreted theoretically by considering the proton only as a point particle. One must take into account not only its static structure, in other words the charge and magnetization distribution inside the proton, but also its polarizability, which brings the various excited states of the nucleon into play. These problems are the major points of interest of theoretical studies carried out on the hyperfine structure of hydrogen.

25It is also worth highlighting another trend: the study of atomic systems which, while they remain simple and are reminiscent of the hydrogen atom, are less and less common, and gradually more exotic. These are, for example, purely electrodynamic systems like positronium or muonium, bound states formed by an electron with a positron or a muon; highly charged hydrogen-like ions obtained by stripping off all but one of the electrons from accelerated ions going through a thin carbon sheet; muonic atoms resulting from the capture of a negative muon by a nucleus like a proton or a α particle. Why study such systems? First of all, this allows us to analyse the influence of the various parameters such as the mass and charge of the particles. For instance, the mass difference between the electron and the muon causes the average distance between the nucleus and the muon in a muonic atom to be about two hundred times smaller than the distance separating the nucleus from the electron in the corresponding ordinary atom. The vacuum polarization effects then become spectacular, as the Lamb interval drops into the optical domain, providing hope of being able to induce the corresponding transition no longer using a microwave source, but a laser. This work is also motivated by the secret hope that by studying increasingly exotic systems, we will be able to disprove quantum electrodynamics. This is the same perspective in which tests on the major symmetries of physical laws are being carried out. The discovery of the non-conservation of parity in weak interactions, which shows that these interactions give absolute meaning to the left and right, has made physicists very cautious with regard to evidence of the symmetries. Nothing at present allows us to assert that electromagnetic interactions are not invariant through reflection in a mirror or through the reversal of the direction of time. Such invariance, however, is in no way self-evident. Were it to be invalidated by experimentation, this would call for a serious re-examination of our ideas.

***

26I will now turn to what seems to me to be another important component of the atomic physics revival: entirely new structures can be imagined by physicists as they re-examine in a new light known phenomena with well-established rules, and inter-relate these phenomena in an unexpected way; a bit like artists who, through a particular arrangement of simple colours and forms, create original images on their canvas.

27The first example I have chosen to illustrate such a situation is optical pumping, as it clearly shows the variety of problems that can be tackled by the elegant combination of very simple phenomena, in this case optical resonance, discovered by Wood in 1905, and the global conservation of angular momentum during interactions between matter and radiation, established by Rubinowicz in 1918. The second example I will consider is lasers, instruments which still have surprises in store for us and which make very ingenious use of induced emission properties, laid down by Einstein as early as 1917.

28I will therefore first look at another one of atoms’ characteristics: their angular momentum – a term which is reminiscent of a spinning top’s rotation around its axis, or of an ice skating figure. However, these images do not apply well to the quantum objects that are atoms. The projection of their angular momentum onto any given axis in space does not vary continuously and can only take on a discrete sequence of values at equally spaced intervals. In fact, each of these states corresponds to a different value of the projection of the atomic magnetic moment, and consequently also to a different coupling energy with a magnetic field that applied along this direction. This explains the Zeeman effect, that is, the fact that in the presence of a magnetic field an atomic level decomposes into a finite number of slightly different energy sublevels, called Zeeman sublevels.

29If we consider a set of atoms in thermodynamic equilibrium, we can easily show that for a given level, the populations of the various Zeeman sublevels are equal in a zero field, so that no orientation of the angular momentum is preferred over the others. We say the sample is not polarized. The container holding the atoms would have to be maintained at an extremely low temperature and held in a very high magnetic field to obtain a slight overpopulation of the lowest Zeeman sublevels. Of course, other techniques such as the action of field gradients on atomic jets could be used, but all these methods are difficult to implement. It is not easy to polarize a collection of atoms.

30The difference with photons is striking. Photons’ angular momentum is closely linked to the polarization of the wave with which they are associated. For example, a light wave with right-handed circular polarization corresponds to photons which carry a unit of angular momentum along their propagation direction. A polarizing plate, very easy to make, therefore simply needs to be placed on the path of a light beam to obtain a jet of photons, all with a well-defined angular momentum, after it has gone through the plate.

31The optical methods imagined by Kastler and Brossel around 1950 and since developed in many French and foreign laboratories use resonant energy and angular momentum exchanges between polarized atoms and photons to transfer to atoms part of the angular momentum that we are able to introduce so simply onto photons. During the resonant absorption of a polarized optical photon the atom acquires not only the photon’s energy, allowing it to shift from the fundamental level A to the excited level B, but also the angular momentum carried by this photon. When it then drops back into the fundamental state, the atom does not entirely lose the angular momentum it has acquired, as the photon reemitted can have several states of polarization. The overall balance of the cycle of optical resonance, absorption and then reemission of a photon is therefore not equal to zero. To describe this set of processes we often use the image of an “optical pump” which empties certain Zeeman sublevels of A into other sublevels, by making atoms go via certain sublevels of B. Even if it leaks a little, this pump is effective as it can concentrate up to 90% of the atoms in certain sublevels, that we can actually pick and choose by playing on the polarization of the incident wave.

32Furthermore, the optical methods provide a very practical means of detecting the atomic polarization they allow, which is important if we then wish to use these oriented atoms to study other physical problems. The characteristics of the light absorbed or emitted by atoms, such as the intensity or degree of polarization for instance, depend on the distribution of the populations between the various Zeeman sublevels of the fundamental or excited state. One therefore simply needs to observe this light to obtain precise information on the atomic polarization, to monitor how it is built and evolves.

33I will now give you an idea of the problems that can be addressed by these methods.

34First, it is possible to study the return to thermodynamic equilibrium, in other words to identify and analyse the so-called thermal relaxation processes behind the establishment of this equilibrium. To do so, one must start off by accumulating the atoms in a well-defined Zeeman sublevel, and then suddenly turn off the optical pumping beam. The populations then equalize under the effect of the collisions between the atoms or against the sides of their container. If, with a detection beam, we can determine the time constants of this return to thermodynamic equilibrium, we obtain valuable information regarding the collision processes, and it is possible to choose between several possible mechanisms. Many phenomena have thus been evidenced and studied in detail: for example, the fact that an atom does not bounce elastically off a glass wall, but remains absorbed therein for a certain amount of time which can be measured; or yet the formation of krypton-rubidium molecules when a three-body collision occurs between two krypton atoms and a rubidium atom, etc.

35The optical methods also serve to determine small energetic differences with great precision. Once the atoms have been accumulated in a certain Zeeman sublevel A1, they can be moved to a neighbouring sublevel A2 by making them absorb the corresponding energy in the form of a Hertzian photon. The measurement of this photon’s energy, in other words, still that of the associated Hertzian wave frequency, directly provides the A1 A2 difference. We recognize here the principle of Hertzian spectroscopy. The optical methods of magnetic resonance further contribute sensitivity. Instead of monitoring the atoms as they shift from A1 to A2 through sensitive radio-electric processes counting the Hertzian photons that disappear, as we normally would, the observation focuses on the optical photons absorbed by the atoms and whose polarization changes, depending on whether the atoms are in A1 or A2. The absorption of a Hertzian photon is therefore indirectly detected on an optical photon which can transport energy a billion times greater, and which is subsequently much easier to reveal. This sensitivity increase allows us to operate on highly diluted atomic vapours, avoiding the disruptions associated with the interactions found in a condensed medium.

36These measurements thus afford access to the physical quantities characteristic of the isolated atom: magnetic moments, fine and hyperfine structures, etc. with a precision which, in some cases, can reach the ten millionth. It also becomes possible to study the interactions between atoms and incident photons in more depth and to reveal new effects. It has thus been established that such interactions can have observable consequences, even though they are non-resonant, in other words even though the energy of the incident photons does not coincide with that of an atomic transition. For example, a non-resonant light irradiation shifts the various Zeeman sublevels Ai of the fundamental state by an amount which is proportional to the light intensity and may vary from one sublevel to the next, and which translates into a modification of the Hertzian differences Ai Aj. The optical pumping beam, which generally always contains non-resonant frequencies, therefore perturbs the atoms it orients and detects. Likewise, a non-resonant Hertzian irradiation can modify an atomic magnetic moment, rendering it anisotropic, even cancelling it out in some cases. In certain respects, these effects are reminiscent of those of quantum electrodynamics, for instance the Lamb shift and the anomaly of the electron’s magnetic moment. They conjure up similar images, of an atom virtually absorbing and immediately re-emitting the non-resonant photons sent onto it, in a way “dressed” with these photons, and thereby acquiring new properties. Furthermore, the atoms are not the only ones affected by these processes: for example, the propagation of the photon is stopped for an instant, when it is virtually snatched by the atom. We deduce from this that the propagation of light energy is slowed down in a transparent medium, in other words in a medium formed from atoms for which light is non-resonant. This is a well-known phenomenon, usually described by a refractive index.

37To conclude this brief review of the tribulations that an atom can undergo with optical methods, I shall mention the transversal pumping experiments where the atom is subjected to two somewhat contradictory temptations: a magnetic field parallel to a certain direction, which encourages states of angular momentum that are well-defined in relation to this direction, and a transversal optical pumping beam, perpendicular to the field, which tends to orient the atoms in this new direction. What do atoms do in such conditions? In a zero field, they head along the light beam. If the field is slowly increased from zero, the light beam’s orienting effect is increasingly upset by the field, and completely disappears in a sufficiently strong field. We can show that the variation of the atomic orientation thus obtained with the field gives rise to resonances centred in a zero field which, in some cases, are so fine that they can serve to detect fields as weak as a billionth of the terrestrial field, far smaller even than the field created by the functioning of the human heart. Such an experiment actually raises a far more general problem, that of a linear superposition of states. A given atom does not necessarily occupy a well-defined energy sublevel; it can very well find itself in what we call a coherent superposition of sublevels, with physical properties which do not simply result from the juxtaposition of the properties of each sublevel with certain statistical weights. As in the interference effects, observed in optics or acoustics, these new physical properties associated with coherent superpositions of sublevels involve the intensity of a wave obtained by superposing two elementary waves, which is not just the sum of the two waves’ intensities. The variations of these interference effects, which are obtained with the static field, explain the resonances in a zero field described above, as well as several other effects observed in atomic physics. We thus see how the corpuscular and wave concepts are closely intertwined at quantum level.

38I will now discuss the problem of lasers and of their impact in atomic and molecular physics. I will begin by analysing another property of the interactions between atoms and photons, which underpins these instruments’ functioning. Let us start from an atom that has been carried into an excited level B in some way or another. If it is isolated, after some time it generally drops back onto an inferior level A by spontaneously emitting a photon that can have several propagation directions and several different polarization states. Suppose now that this atom, in state B, is also irradiated by N photons that are identical and resonate for the transition BA. A new process of so-called induced or stimulated emission is superposed onto the process of spontaneous emission previously described: the incident N photons stimulate the atom to emit a photon in all points identical to themselves, with the same energy, the same propagation direction, the same polarization. The more of these photons there are and the more efficient this process is. This reveals a fundamental property of photons, and bosons more generally: their somewhat gregarious tendency to gather as much as possible in the same quantum state, whereas electrons, and fermions more generally, demonstrate on the contrary staunch individualism that causes them to mutually exclude one another.

39Now consider an atomic medium in which we have carried out what we call a population inversion, in other words a medium in which the proportion of atoms occupying the superior level B is greater than that of the inferior level A. The optical pumping described above has already familiarized us with such situations, which visibly fall out of thermodynamic equilibrium. We send a resonant photon for the BA transition onto this medium. This photon has more chances of stimulating the emission of a second photon identical to itself by an excited atom than of being absorbed by an atom in the state A. We thus obtain two photons which, in turn, can stimulate the emission of a third photon twice as efficiently, and so on and so forth. Such a multiplication process is limited by the time it takes the light to cross the amplifying atomic medium. This time can easily be increased by enclosing the atoms between two parallel mirrors. If the photons propagate themselves perpendicular to the mirrors, they come and go many times between the two and can interact for longer times with the atoms, provided however that the distance between the two mirrors is suitably chosen, to avoid a destructive interference between the light waves. It is actually not necessary to send photons from the outside and the system can function as an oscillator rather than as an amplifier: the excited atoms’ spontaneous emission provides the initial photons which can trigger the multiplication process. If the medium’s gain is greater than its loss, for example due to the poor quality of the mirrors or to the diffraction, and if the population inversion between levels A and B is successfully maintained throughout, thanks to a suitable pumping device, a source of photons with a very well-defined energy and propagation direction is obtained: the laser.

40The image I have just painted of it is of course very schematic and highly qualitative. The development of lasers has generated many problems for physicists, thereby very effectively stimulating certain research work in atomic and molecular physics. For example, we had to imagine mechanisms of selective population and depopulation of energy levels likely to lead to population inversions. This also involved analysing a wide variety of excitation processes, such as radiative and non-radiative transfers, collisions with electrons, energy exchanges between distinct atoms, chemical reactions, etc. The systems studied were not only atoms in gaseous phase, but also molecules, ions, semi-conductors, insulating crystals, liquid dyes, etc. We also had to achieve greater precision in our description of the electromagnetic field, and to synthesize the wave language employed by optical and electronic engineers, as well as the corpuscular one in which high-energy physicists generally discuss γ photons. Various types of quantum states were introduced to describe the radiation coming from a laser, to analyse the statistical properties of a light beam, and to provide simpler interpretations of photon coincidence experiments. The very functioning of the laser is a complex problem of atomic physics, quantum mechanics and statistical mechanics. How can we calculate exactly the synchronization phenomenon, the width and the shape of the line emitted, the angular dispersion of the beam, the competition between the various modes inherent to the cavity defined by the two mirrors, and the effect of the movement of thermal agitation of the atoms? Several theoretical models had to be developed. They have shown the power and richness of the basic equations underpinning them all: Schrödinger’s equation and Maxwell’s equations.

41Finally, it is important to realize that the interest of lasers not only lies in drawing attention to the physics problems posed by their functioning. They are light sources with completely original properties and are increasingly considered as new tools that will be used to open up and explore new research domains.

42A first interesting characteristic these sources present is their instantaneous power, which can be very high and exceed that of usual sources by several orders of magnitude. It thus becomes possible to subject the electrons of an atom to electromagnetic fields comparable to and even greater than those that keep them linked to the nucleus. The atom’s behaviour is then no longer the same as that at low intensities, and new phenomena appear. For example, a red light beam from a ruby laser falling on a quartz crystal turns into an ultraviolet light beam. This transformation is explained by the fact that at high intensities an atom of crystal becomes able to convert two red photons that arrive on it into a single ultraviolet photon with twice as much energy. Many other non-linear effects similar to these are now being studied by a new branch of optics, non-linear optics: addition and subtraction of frequencies, simultaneous absorption of several photons, stimulated Raman effect, self-focusing of the light in a non-linear medium whose index varies with the intensity. Improved power lasers are currently allowing us to near the 1012 watts. To have an idea of what such power represents, consider a 100 watt lamp which is more than enough to light a room at night, and imagine gathering 10 billion such lamps and concentrating the light they emit into a pen so narrow that, arriving on the moon, it would render a spot with a radius of only a few kilometres. Such power, which actually corresponds to the power of the entire world’s electricity plants put together, obviously cannot be maintained for very long; in these conditions the laser can only provide a very brief flash. This leads me to another interesting characteristic of these sources: their ability to function by pulses.

43Such pulses can be used to excite very briefly an atom or a molecule, and then to study the system’s subsequent evolution when it is left to its own devices. For example, if a laser pulse has carried a set of atoms in a coherent superposition of two excited levels close to each other, the light they then spontaneously re-emit is modulated at a frequency which corresponds to the difference between these two levels. The observation of these quantum beats constitutes a new spectroscopic method of study. Light pulses can also be used to excite a well-defined molecular level, and then study the way in which this energy subsequently transfers to the other degrees of freedom of the molecule, or to a neighbouring molecule. This provides direct access to the kinetics of atomic and intra-molecular processes. The faster these processes are, the briefer the exciting pulse must be. We are now able to produce 10-12 second pulses, allowing us to study relaxation in a condensed medium, where the time constants are very short.

44Laser sources present yet other characteristics that make them interesting for atomic and molecular physics, essentially monochromaticity and frequency stability, as well as the possibility, which dye lasers have recently afforded, to sweep this frequency over an extended range.

45Consider molecular spectra for instance. Their complexity stems from the very high number of levels the molecules have, due to their additional degrees of vibrational and rotational freedom. The interpretation of these spectra is considerably simplified if we manage to excite selectively only one energy level, so as to obtain only the lines emitted from this level. We can also study the systematic variation, from one level to the next, of physical units such as the lifetime, the magnetic moment, etc., to collect precise information regarding the molecule’s structure and its internal couplings. Another interesting application concerns the study of the Doppler broadening and the demonstration of non-linear effects that cancel it out. Say we send two monochromatic waves with the same frequency in opposite directions onto an atom or molecule gas: one very intense wave, perturbing the atoms, and the other very weak, probing them. The intense wave is absorbed by only some of the atoms, those with a Doppler effect that allows them to resonate with it. All these atoms are characterized by the same motion speed along the direction of the intense wave. The probe wave, which propagates in the opposite direction, detects another class of atoms, those that propagate with the same speed but in the opposite direction. The two waves therefore do not interact with the same atoms, except if their common frequency is such that it requires a zero Doppler effect, in which case the atoms concerned are the ones that move perpendicular to the two waves’ propagation. Let us therefore sweep the two waves’ common frequency. On the probe wave’s absorption, a large Doppler profile will characterize the distribution of the speed of the absorbing atoms, and at its centre there will be a much narrower peak, reflecting the fact that for this frequency and this frequency alone, the probe wave detects atoms that are also perturbed by the intense wave. This narrow peak of so-called saturated absorption can be used to stabilize the frequency of a laser, to lock it in at the centre of an atomic line with much greater precision than if we used only the Doppler profile. We thus reach frequency stabilities and reproducibilities greater than 10-11. Such a performance, transposed to the domain of lengths, would amount to setting a distance of the order of that separating the Earth from the Moon, with a precision of the order of the millimetre. It is easy to imagine the progress that will stem from these methods in optical spectroscopy and frequency standards.

***

46To conclude this brief overview of the major currents driving atomic and molecular physics, I would now like to mention another important characteristic of this discipline: its opening to other branches of physics and other sciences, notably chemistry and biology.

47This opening first translates into a growing exchange of ideas and experimental techniques. For example, it is becoming more and more common to see atomic physics experiments using ion accelerators, coincidence devices and scalers, thereby increasingly resembling nuclear physics experiments. Conversely, by using the radiation emitted by charged particles turning into a synchrotron, atomic and molecular physicists are considerably expanding the domain of application of these instruments. Another important example, providing a good illustration of this new state of mind, is the collision between atomic jets. So as to study the interactions between atoms, molecules, ions and electrons in detail, atomic and molecular physicists now readily cause such particles to collide after having communicated a well-defined energy and speed to them. They then study the scattered particles stemming from the reaction, measure their energy and their angular distribution, and determine the variation of the various cross-sections according to the energy of the incident particles. These studies are far more complex than those of the same reaction in gaseous or liquid phase, which can supply only global information. They afford precision about the intimate mechanism of the reaction, the important intermediate states, the various potential curves the system follows to move from the entrance channel to the exit one. It is also worth mentioning lasers’ recent contribution to other domains, like microsurgery for the treatment of retinal detachment for instance, or biology, for the study of reaction speeds and of the vibration and torsion movements of biological macromolecules and membranes. In the latter case we study the angular and spectral distribution of the diffused laser radiation, which has a wavelength of the same order of magnitude as the dimensions of the studied objects.

48More important still than the exchange of ideas and techniques, seems to me to be the fact that, thanks to its multidisciplinary contacts, atomic and molecular physics is finding new motivations for its studies. Progress in the other branches of science translate into an increased need for information and data on the high number of atomic and molecular processes underlying the observed phenomena, and atomic and molecular physicists are constantly called upon to supply this information and data.

49For example, the interpretation of the X-rays and ultraviolet rays emitted by stars raises a whole new series of problems: determining the energy levels and oscillator strengths of highly ionized atoms, finding the preponderant mode from among several modes of radiative de-excitation of metastable ions, understanding how H– ions are formed through the capture of electrons around hydrogen atoms, then destroyed through photo-detachment, etc. I could also mention the recent discovery of dozens of molecular species in interstellar space that radio-astronomers were able to detect and identify thanks to the microwave and Herztian radiation they emit or absorb. We are still staggered by the complexity of these molecules, which can include up to eight atoms. How do they form? Is it when atoms collide or through a catalytic reaction on the surface of dust specks that exist in space? The brilliance, line thinness and directivity of certain emissions, like those of the OH radical, is such that only a maser effect could explain them. What then are the radiative or collisional processes likely to produce the corresponding population inversion?

50I prefer not to continue with this long list of problems for fear of boring you. However, I hope to have convinced you of the current vitality of atomic and molecular physics and of its multiple facets. Excepting the nuclear reactions at the root of the energy emitted by stars, we can say that atoms, molecules, ions and electrons are at the centre of all the physical, chemical and biological phenomena of our universe. Hence, allow me to draw on the image Feynman used right at the beginning of his famous physics lectures. Imagine that all our scientific knowledge were destroyed in a cataclysm and that only one sentence could be passed down to future generations; what message should the bottle we threw into the sea contain? I believe it would be that all things are made of atoms.

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51Finally, I would like to conclude by mentioning a last point to which I am personally particularly sensitive. Despite the growing sophistication of experimental techniques, atomic and molecular physics still lends itself to the constitution of small research teams, carrying out experiments on a human scale, studying both the theoretical and the experimental aspects of the problems addressed. At a time when the specialization of tasks is intensifying, and when management and administrative problems absorb a growing proportion of precious time, the possibility of working in small teams appears to me to be an essential factor for balance, allowing us to retain the availability and open mindedness so fundamental to research.

52I was fortunate to learn to do research in a small team. Words cannot express the gratitude I feel towards the two men who enabled me to discover and love physics, Alfred Kastler and Jean Brossel. Their laboratory, which I joined in September 1955 to do my post-graduate degree followed by my doctoral dissertation [thèse d’État], and which I ultimately never left, had only six or seven researchers at the time, but offered an exceptional atmosphere. A research theme of great simplicity and elegance had just been uncovered, and many experimental ideas were forming and being discussed with intense enthusiasm. I have particularly fond memories of this period of my life when, free of all material concerns thanks to a CNRS scholarship, I was able to devote all my time to the in-depth study of a physics problem, learning to design and carry out an experiment, to build a theoretical model, to draw out the physical significance of a calculation, and to draft a scientific article. More precious yet than the results obtained seems to be how personally enriching that human contact was. Thanks to it, I understood better what modesty, the passion for truth, the spirit of tolerance, and respect for others meant.

53We are all marked by the teachers we had. I still remember some of my high-school teachers and my parents’ constant interest in my studies. What attracted me to atomic physics was a lecture Kastler gave to the students of the École normale supérieure. Neither have I forgotten the modern physics classes provided at the École des Houches and at Saclay at a time when post-doctoral studies had not yet made their appearance in the Faculties, nor some of the lectures and seminars at the Collège de France, particularly yours, my dear Abragam, which revealed to us the mysteries of magnetic resonance, of the Mössbauer effect, of thermal relaxation, etc. You showed interest in my work from the outset, and you are behind my being at the Collège de France. You know just how grateful I am.

54For some fifteen years now I have in turn had to teach different subjects at the Faculties, either at postgraduate level or at the physics Master’s level. I have thus been able to constitute a small team of young researchers around me and to discover another fascinating aspect of our work, that is, initiation into research. Today I would like to tell all the members of this team how pleased I have been to be able to work with them, and how much I value their friendship. Everything we have achieved together is the fruit of collective work and represents far more than the sum of individual contributions. I sincerely hope that we will be able to pursue this close and friendly collaboration for a long time to come.

55As I set out to undertake this new teaching, I am driven by two crucial concerns: first, that of staying in contact with an audience of students and young researchers who encourage the teacher to formulate clear and simple guiding ideas, and constantly to move onto new ground without becoming too specialized; and second, that of fostering fruitful contact between laboratories, particularly through seminars, and of giving as faithful an image as possible of physics in action, with its imperfections, its hopes, its successes, and its failures.

56My dear colleagues, I do not know whether I will be able to achieve such a goal; I very often have my doubts. However, I can assure you that I will devote myself to it as best I can, strengthened by the trust you have put in me.

Auteur

Honorary professor, Collège de France
Liz Libbrecht (Traducteur)

© Collège de France, 2015

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

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