“Why is the sky blue?” or “why are clouds white?” are examples of basic questions that always intrigued the mind of young, and not-so-young, students before their exposure to the fundamentals of light–matter interaction, a phenomenon that occurs anytime and anywhere in our universe and constitutes the main thrust in this chapter. It starts by highlighting the basic aspects of absorption and spontaneous and stimulated emission, described (in terms of quantum mechanics) by using Einstein coefficients and transition moments ; further along, the (classical) macroscopic connection with the Beer–Lambert law is derived. The journey continues by visiting elastic scattering and its two modalities, Rayleigh and Mie scattering , depending on the scattering particle size. In the final step, inelastic Brillouin and Raman scattering are discussed, placing emphasis on the laser-spectroscopic techniques underlying these types of photon–matter interactions. The chapter ends with a brief description how prehistoric humans already knew how to prepare colors for paintings (as exemplified in the Altamira cave in Cantabria, Spain); and a short exposé into state-of-the-art single-molecule spectroscopy using a single photon. This thread of spanning an arc between (historical) breakthroughs and cutting-edge research will be common to all chapters of the book.
“Why is the sky blue?” or “why are clouds white?” are examples of basic questions that always intrigued the mind of young, and not-so-young, students before their exposure to the fundamentals of light–matter interaction, a phenomenon that occurs anytime and anywhere in our universe and constitutes the main thrust in this chapter. It starts by highlighting the basic aspects of absorption and spontaneous and stimulated emission, described (in terms of quantum mechanics) by using Einstein coefficients and transition moments ; further along, the (classical) macroscopic connection with the Beer–Lambert law is derived. The journey continues by visiting elastic scattering and its two modalities, Rayleigh and Mie scattering , depending on the scattering particle size. In the final step, inelastic Brillouin and Raman scattering are discussed, placing emphasis on the laser-spectroscopic techniques underlying these types of photon–matter interactions. The chapter ends with a brief description how prehistoric humans already knew how to prepare colors for paintings (as exemplified in the Altamira cave in Cantabria, Spain); and a short exposé into state-of-the-art single-molecule spectroscopy using a single photon. This thread of spanning an arc between (historical) breakthroughs and cutting-edge research will be common to all chapters of the book.
An impressively comprehensive textbook adopting a phenomenological approach to quantum physics. The chapters cover everything from basic definitions of key concepts to detailed discussions of the underlying theoretical framework, walking students step-by-step through the necessary mathematics and drawing clear connections between the theory and the most important modern research applications including quantum optics, fluids, nanophysics, entanglement, information, and relativity. With this book, students and researchers will have access to hundreds of real-world examples, exercises, and illustrations to support and expand their understanding. Instructors can tailor the content to suit the length and level of their course and will have access to an online solutions manual with fully worked solutions to all 300+ exercises in the book. Other online resources include Python simulations, additional exercises, and detailed appendices.
In this work we shall study the interaction of matter and light. In so doing we shall rely heavily on the description of such processes provided by quantum mechanics. This appears on a number of levels: firstly, a quantum description of matter is indispensable if one wants to understand on the microscopic scale the different kinds of interaction processes that can occur. Secondly, a quantum description of light often turns out to be useful, sometimes necessary, to better understand these processes. We shall study phenomena such as spontaneous emission, which can only be properly treated by a theory taking into account the quantum nature of both light and matter. In the following chapters we shall address, amongst others, the following question: ‘given an atom prepared at a given time in a particular state and subjected from this time onwards to electromagnetic radiation, what is the state of the atom and radiation at any later moment in time?’ In order to be able to answer this question it will be necessary for us to know how to calculate the evolution of a quantum system in a small number of typical situations. These methods we shall demonstrate in the first chapter. The evolution of the coupled atom–light system depends on the temporal dependence of the applied light field, which could, for example, be applied from a given moment and thereafter remain unchanged in intensity, or, perhaps, be appreciable only for a finite period of time (pulsed excitation).
Although the primarily phenomenological theory of absorption and refraction of light by matter, based on classical models as presented in Chapter 4, is very useful, it is incomplete and often inadequate. A more complete and accurate picture of electrodynamics is given by the theory of quantum optics, and that is the topic of this chapter. The models developed in this chapter are more detailed and therefore more complicated than the phenomenological models of Chapter 4. The most robust models, which are applied in Part II, are presented in this chapter. The quantum models accurately represent experimental data and allow extrapolation and interpolation of such data. Many practical computer based models concerning optical propagation are based on this theory. The theory of elastic scatter as presented in Chapter 4 is consistent with quantum optics and is not presented again. (However, inelastic scatter must address the quantum nature of the scattering medium.) Quantum optics is not completely covered in this chapter. Entire textbooks are devoted to this diverse and comprehensive topic covering optics (see Refs. 5.1–5.3). The emphasis of this book is on absorption and reflection spectroscopy. Now details of internal structure of the medium impacting light–matter interaction are examined. The classical oscillator model is upgraded by semiclassical radiation theory and a quantum oscillator model is developed. Semiclassical radiation theory is based on a quantized medium coupled to a classical field. It is often applied to laser theory, where near-line-center stimulated emission dominates. The quantum oscillator model again utilizes the quantized medium and classical field, but with more attention to detailed balance between absorption and emission. It satisfies causality and the fundamental symmetry relationships established in Chapter 2. These quantum optics models are more complete formalisms and provide solutions to the shortcomings of classical electrodynamics. Of particular interest to propagation in gaseous media is the line shape in the far wing. To achieve long path lengths, propagation near line center of a resonance must be avoided. Line shape models in quantum optics accurately represent much of the frequency and temperature dependence observed in experimental data.
Introduction The emission and absorption of radiation, as well as the conversion of radiation into other modes of energy such as heat or electricity, all involve interaction between electromagnetic waves and atoms, molecules, or free electrons. Such daily phenomena as the radiative emission by the sun, the shielding of earth from harmful UV radiation by the ozone layer, the blue color of the sky, and red sunsets are all – despite their celestial magnitude – generated by microscopic particles. Most lasers depend on emission by excited atoms (e.g. the He-Ne laser), ionized atoms (the Ar + laser), molecules (CO or CO 2 lasers), impurities trapped in crystal structures (Nd: YAG or Ti:sapphire lasers), or semiconductors (GaAs diode lasers). Similarly, many scattering processes of interest (e.g., Rayleigh or Mie scattering) result from the exchange of energy and momentum between incident radiation and atomic or molecular species. In the previous chapter we saw that the energy of microscopic particles is quantized: their energy can be acquired, stored, or released only in fixed lumps called quanta . The example of the “particle in the box” (eqn. 8.19) illustrated that these energy quanta are specific not only to the particle itself but to the system to which it belongs. Thus, in the box, the energy of the particle is specified by its own mass and by the dimension of the box; in a different box, the same particle will have an entirely different system of energy levels and the quanta will have different magnitudes.
This chapter provides a brief overview of quantum mechanics and light. It begins with a discussion on the purpose and practice of spectroscopy, which involves the investigation of the interaction of light with matter. It then breaks down the nature of electromagnetic radiation, expounding on the classical theory of light before turning to photons and how they make up light. Next, the chapter elaborates on the properties of lasers and how these same remarkable properties are achieved largely from the process of stimulated emission. Afterward, the chapter presents the wave mechanical description of an atom, and considers the Schrödinger equation and the Hamiltonian operator. Lastly, angular momentum is explored.