The rapid technological development initiated by the invention of the laser, on the one hand, and the perfection attained in the fabrication of photodetectors, on the other hand, gave birth to a new physical discipline known as quantum optics. A variety of exciting experiments suggested by ingenious quantum theorists were performed that showed specific quantum features of light. What we can learn from those experiments about the miraculous constituents of light, the photons, is a central question in this book. Remarkably, the famous paradox of Einstein, Podolsky and Rosen became a subject of actual experiments too. Here photon pairs produced in entangled states are the actors.

The book gives an account of important achievements in quantum optics. My primary goal was to contribute to a physical understanding of the observed phenomena that often defy the intuition we acquired from our experience with classical physics. So, unlike conventional textbooks, the book contains much more explaining text than formulas. (Elements of the mathematical description can be found in the Appendix.) The translation gave me a welcome opportunity to update the book. In particular, chapters on the Franson experiment and on quantum teleportation have been included.

Quantum mechanical uncertainty

After reviewing the main characteristics of the classical description of light, let us discuss those aspects of the quantization of the electromagnetic field which are of relevance for the analysis of the phenomena we are interested in. It seems a reasonable place to start to make clear the fundamental difference between the classical and the quantum mechanical description of nature; we will come across this difference many times when discussing experiments, and it will often give us a headache. We have to deal with the physical meaning of what is called uncertainty.

The starting point of the classical description is the conviction that natural processes have a “factual” character. This means that physical variables such as the position or momentum of a particle have, in each single case, a well defined (in general, time dependent) value. However, it will not always be possible to measure all the appropriate variables (for instance, the instantaneous electric field strength of a radiation field); furthermore under normal circumstances we are able to measure only with a finite precision. Hence the basic credo of classical physics should be given in the following form: we are justified in imagining a world with variables possessing well defined values which are not known precisely (or not known at all). In doing this we are not forming any conclusions that contradict our everyday experiences.

This is the fundamental concept of classical statistics: we are satisfied with the use of probability distributions for the variables we are interested in, not from fundamental but purely practical reasons.

Most probably all people, even though they belong to different cultures, would agree on the extraordinary role that light – the gift of the Sun-god – plays in nature and in their own existence. Optical impressions mediated by light enable us to form our views of the surrounding world and to adapt to it. The warming power of the sun's rays is a phenomenon experienced in ancient times and still appreciated today. We now know that the sun's radiation is the energy source for the life cycles on Earth. Indeed, it is photosynthesis in plants, a complicated chemical reaction mediated by chlorophyll, that forms the basis for organic life. In photosynthesis carbon dioxide and water are transformed into carbohydrates and oxygen with the help of light. Our main energy resources, coal, oil and gas, are basically nothing other than stored solar energy.

Finally, we should not forget how strongly seeing things influences our concepts of and the ways in which we pursue science. We can only speculate whether the current state of science could have been achieved without sight, without our ability to comprehend complicated equations, or to recognize structures at one glance and illustrate them graphically, and record them in written form.

The most amazing properties, some of which are completely alien to our common experiences with solid bodies, can be ascribed to light: it is weightless; it is able to traverse enormous distances of space with incredible speed (Descartes thought that light spreads out instantaneously); without being visible itself, it creates, in our minds, via our eyes, a world of colors and forms, thus “reflecting” the outside world.

Light waves à la Huygens

Christian Huygens (1629–1695) is rightfully considered to be the founder of the wave theory of light. The fundamental principle enabling us to understand the propagation of light bears his name. It has found its way into textbooks together with the descriptions of reflection and refraction which are based on it.

However, when we make the effort and read Huygens' Treatise of Light (Huygens, 1690) we find to our surprise that his wave concept differs considerably from ours. When we speak of a wave we mean a motion periodic in space and time: at each position the displacement (think about a water wave, for instance) realizes a harmonic oscillation with a certain frequency ν, and an instantaneous picture of the whole wave shows a continuous sequence of hills and valleys. However, this periodicity property which seems to us to be a characteristic of a wave is completely absent in Huygens' wave concept. His waves do not have either a frequency or a wavelength! Huygens' concept of wave generation is that of a (point-like) source which is, at the same time, the wave center inducing, through “collisions” that “do not succeed one another at regular intervals,” a “tremor” of the ether particles.

Beamsplitting

Interference phenomena are certainly among the most exciting phenomena in the whole of physics. In the following we will concentrate mainly on interference of weak fields; i.e. the beams contain, on average, only a few photons.

The principle of classical interference is as follows: a light beam is split by an optical element, for example by a semitransparent mirror or a screen with several very small apertures, into two or more partial beams. These beams will take different paths and are then reunited and form interference patterns. The first step, the splitting of the beam into partial beams, plays a decisive role; light beams coming from different sources (or from different spatial areas of the same source) do not interfere with each other!

We start our discussion of interference with an analysis of the action of a beamsplitter. To form a realistic idea of this device, let us imagine a semitransparent mirror. (Our considerations apply equally well to a screen with two apertures. We could also generalize to cases of unbalanced mirrors, with reflectivity different from 1/2, or screens with apertures of different size.)

The classical wave picture can describe interference phenomena without any great effort: the incoming beam is split into the reflected and the transmitted partial wave, and each of these waves contains half of the energy. The process of splitting becomes conceptually difficult only when we think of the beam as consisting of spatially localized energy packets, or photons.

Polarization entangled photon pairs

Throughout his life, Albert Einstein was never reconciled to quantum theory being an essentially indeterministic description of natural processes, even though he himself contributed fundamental ideas to its development. “God does not play dice” was his inner conviction. In his opinion, quantum theory was only makeshift. His doubts about the completeness of the quantum mechanical description were expressed concisely in a paper published jointly with Podolsky and Rosen (Einstein, Podolsky and Rosen, 1935). This paper analyzes a sophisticated Gedanken experiment, now famous as the Einstein–Podolsky–Rosen paradox, which has excited theoreticians ever since.

The Gedanken experiment was recently realized in a laboratory. The analyzed objects are photon pairs – and this is what has motivated us to dedicate a chapter to this problem which has bearing upon the foundations of quantum mechanics. The photon pairs are formed by two photons generated in sequence (in a so-called cascade transition, as shown in Fig. 11.1). Due to the validity of the angular momentum conservation law (discussed in Section 6.9) for the elementary emission process, the two photons exhibit specifically quantum mechanical correlations, which are incompatible with the classical reality concept, as will be discussed in detail below.

How do the correlations appear in detail? Let us assume the initial state of the atom to be a state with angular momentum (spin) J = 0, the intermediate state to have angular momentum J = 1, and the final state to have again J = 0.

How can we construct a picture of the photon from the wealth of observation material available to us? The photon appears to have a split personality: it is neither a wave nor a particle but something else which, depending on the experimental situation, exhibits a wave- or a particle-like behavior. In other words, in the photon (as in material particles such as the electron) the particle–wave dualism becomes manifest. Whereas classically the wave and the particle pictures are separate, quantum mechanics accomplishes a formal synthesis through a unified mathematical treatment.

Let us look first at the wave aspect familiar from classical electrodynamics, which seems to be the most natural description. It makes all the different interference phenomena understandable, such as the “interference of the photon with itself” on the one hand and the appearance of spatial and temporal intensity correlations in a thermal radiation field on the other (which are obviously brought about by superposition of elementary waves emitted independently from different atoms). It might come as a surprise (at least for those having quantum mechanical preconceptions) that the classical theory is valid down to arbitrarily small intensities: the visibility of the interference pattern does not deteriorate even for very small intensities – the zero point fluctuations of the electromagnetic field advocated by quantum mechanics do not have a disturbing effect – and is valid not only for conventional interference experiments but also for interference between independently generated light beams (in the form of laser light).

Fundamentals of cryptography

The essence of the Einstein–Podolsky–Rosen experiment analyzed in the preceding chapter is our ability to provide two observers with unpolarized light beams, consisting of sequences of photons, which are coupled in a miraculous way. When both observers choose the same measurement apparatus – a polarizing prism with two detectors in the two output ports, whereby the orientation of the prism is set arbitrarily but identically for both observers – their measurement results are identical. The measurement result, characterized, say, by “0” and “1”, is a genuine random sequence – the quantum mechanical randomness rules unrestricted – from which we can form a sequence of random numbers using the binary number system. The experimental setup thus allows us to deliver simultaneously to the two observers an identical series of random numbers. This would be, by itself, not very exciting. Mathematical algorithms can be used to generate random numbers, for example the digit sequence of the number π, which can be calculated up to an arbitrary length. Even though we cannot be completely sure that such a sequence is absolutely random, such procedures are sufficient for all practical purposes. The essential point of the Einstein–Podolsky–Rosen experiment is that “eavesdroppers” cannot listen to the communication without being noticed by the observers. When eavesdroppers perform an observation on the photons sent, they inevitably destroy the subtle quantum mechanical correlations, and this damage is irreparable.

The electromagnetic field and its energy

The conclusion by Maxwell, based on theoretical considerations, that light is, by its character, an electromagnetic process, is surely a milestone in the history of optics. By formulating the equations bearing his name, Maxwell laid the foundations for the apparently precise description of all optical phenomena. The classical picture of light is characterized by the concept of the electromagnetic field. At each point of space, characterized by a vector r, and for each time instant t, we have to imagine vectors describing both the electric and the magnetic field. The time evolution of the field distribution is described by coupled linear partial differential equations: the Maxwell equations.

The electric field strength has a direct physical meaning: if an electrically charged body is placed into the field, it will experience a force given by the product of its charge Q and the electric field strength E. (To eliminate a possible distortion of the measured value by the field generated by the probe body itself, its charge should be chosen to be sufficiently small.) Analogously, the magnetic field strength H, more precisely the magnetic induction B = μH (where μ is the permeability), describes the mechanical force acting on a magnetic pole (which is thought of as isolated). Also, the field has an energy content, or, more correctly (because in a precise field theory we can think only about energy being distributed continuously in space), a spatial energy density.

Light absorption

Whereas receiving radio waves is a macroscopic process and hence belongs to the area of classical electrodynamics – in a macroscopic antenna an electric voltage is induced whereby a large number of electrons follow the electric field strength of the incident wave, in a kind of collective motion – the detection of light, so far as the elementary process is concerned, takes place in microscopic type objects such as atoms and molecules. As a consequence, the response of an optical detector is determined by the microstructure of matter. In particular, it is impossible – due to the enormously high frequency of light (in the region of 1015 Hz) – to measure the electric field strength. What is in fact detectable is the energy transfer from the radiation field to the atomic receiver, and this allows us to draw conclusions about the (instantaneous) intensity of light.

We might ask what we can say about the above-mentioned absorption process from an experimentalist's point of view. Among the basic experiences that provide an insight into the structure of the micro-cosmos is the resonance character of the interaction between light and an atomic system. The atomic system, when hit by light, behaves like a resonator with certain resonance frequencies; i.e. it becomes excited (takes up energy) only when the light frequency coincides with a value that is characteristic for the particular atom. Hence, an incident light wave with an initial broadband frequency spectrum that has passed through a gas exhibits in its spectrum dark zones, the so-called absorption lines.

In this series of lectures I discuss the basic principles and the modelling of the chemical evolution of galaxies. In particular, I present models for the chemical evolution of the Milky Way galaxy and compare them with the available observational data. ¿From this comparison one can infer important constraints on the mechanism of formation of the Milky Way as well as on stellar nucleosynthesis and supernova progenitors. Models for the chemical evolution of elliptical galaxies are also shown in the framework of the two competing scenarios for galaxy formation: monolithic and hierachical. The evolution of dwarf starbursting galaxies is also presented and the connection of these objects with Damped Lyman-α systems is briefly discussed. The roles of supernovae of different type (I, II) is discussed in the general framework of galactic evolution and in connection with the interpretation of high redshift objects. Finally, the chemical enrichment of the intracluster medium as due mainly to ellipticals and S0 galaxies is discussed.

Basic parameters of chemical evolution

Galactic chemical evolution is the study of the evolution in time and space of the abundances of the chemical elements in the interstellar gas in galaxies. This process is influenced by many parameters such as the initial conditions, the star formation and evolution, the nucleosynthesis and possible has flows.

In these lectures I present a highly opinionated review of the observed patterns of metallicity and element abundance ratios in nearby spiral, irregular, and dwarf elliptical galaxies, with connection to a number of astrophysical issues associated with chemical evolution. I also discuss some of the observational and theoretical issues associated with measuring abundances in H II regions and gas and stellar surface densities in disk galaxies. Finally, I will outline a few open questions that deserve attention in future investigations.

Introduction

The measurement of element abundances in galaxies other than our own has a roughly forty-year history, beginning with early attempts to measure helium abundances in giant H II regions in the Magellanic Clouds and M33 (Aller & Faulkner 1962, Mathis 1962) and pioneering studies of heavy element abundances from forbidden lines in extragalactic H II regions (e.g. Peimbert & Spinrad 1970, Searle 1971, Searle & Sargent 1972). Since then this field has grown tremendously, with high quality oxygen abundance data in some 40 nearby spiral galaxies and more than 100 irregular and compact dwarf galaxies. The amount of data for other elements (C, N, Ne, S, and Ar) has also improved tremendously, thanks largely to improvements in visible-wavelength detectors and the launching of spacecraft observatories, such as IUE, HST, and ISO, which have opened up the UV and IR spectral regions for spectroscopy.

The methods of abundance determinations in H ii regions and planetary nebulae are described, with emphasis on the underlying assumptions and inherent problems. Recent results on abundances in Galactic H ii regions and in Galactic and extragalactic Planetary Nebulae are reviewed.

Introduction

H ii regions are ionized clouds of gas associated with zones of recent star formation. They are powered by one, a few, or a cluster of massive stars (depending on the resolution at which one is working). The effective temperatures T* of the ionizing stars lie in the range 35 000 – 50 000 K. The nebular geometries result from the structure of the parent molecular cloud. Stellar winds, at evolved stages, may produce ring-like structures, but the morphology of H ii regions is generally rather complex on all scales. Typical hydrogen densities n are 103 – 104 cm–3 for compact H ii regions. The average densities in giant extragalactic H ii regions are lower, typically 102 cm–3 since giant H ii regions encompass also zones of diffuse material. The total supply of nebular gas is generally large, so that all (or at least a significant fraction) of the ionizing photons are absorbed.

Planetary nebulae (PNe) are evolutionary products of so-called intermediate mass stars (initial masses of 1 – 8 M⊙) as they progress from the asymptotic giant branch (AGB) to the white dwarf stage.