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CRC Press eBooks

Quantum mechanics in atoms

J Manners

Published Oct 8, 2018• 0 citations
Publisher

Abstract

Lasers are a relatively recent invention. Microwave lasers were in existence in the 1950s and the first visible-light laser appeared in 1960. In the early 1960s some people were of the opinion that lasers were just an interesting curiosity but with no significant use. Nowadays we find lasers in all sorts of everyday situations: CD players, rock concert light shows, bar code scanners, etc. They are also extensively used in technological applications such as eye surgery and welding: modem car plants use robot-controlled lasers to weld sheets of metal together (Figure 3.1) and they are used in experiments at the forefront of research in spectroscopy (Figure 3.2). Lasers have found these many applications because of their particular properties, which are useful in a variety of situations. A laser beam is intense, monochromatic (has a very small range of wavelengths), narrow and well directed. How do these features arise? Laser light originates in the transitions made by electrons in atoms from one energy level to a lower one. Its properties depend on many atoms being stimulated to make the same transition at the same time. So, laser operation depends crucially on the electronic structure of atoms as well as their interaction with electromagnetic radiation. In this chapter, we hope to show you how quantum mechanics can help us to understand atomic structure.

DOI
10.1201/9781315274621-6

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Lasers are a relatively recent invention. Microwave lasers were in existence in the 1950s and the first visible-light laser appeared in 1960. In the early 1960s some people were of the opinion that lasers were just an interesting curiosity but with no significant use. Nowadays we find lasers in all sorts of everyday situations: CD players, rock concert light shows, bar code scanners, etc. They are also extensively used in technological applications such as eye surgery and welding: modem car plants use robot-controlled lasers to weld sheets of metal together (Figure 3.1) and they are used in experiments at the forefront of research in spectroscopy (Figure 3.2). Lasers have found these many applications because of their particular properties, which are useful in a variety of situations. A laser beam is intense, monochromatic (has a very small range of wavelengths), narrow and well directed. How do these features arise? Laser light originates in the transitions made by electrons in atoms from one energy level to a lower one. Its properties depend on many atoms being stimulated to make the same transition at the same time. So, laser operation depends crucially on the electronic structure of atoms as well as their interaction with electromagnetic radiation. In this chapter, we hope to show you how quantum mechanics can help us to understand atomic structure.
Soon after the invention of the laser in the late 1950s many dubbed the discovery as “a solution in search of a problem”. Nowadays lasers are used in an enormous range of scientific and technological applications, thanks to their high intensity and their ability to emit light in an extremely narrow range of wavelengths. Indeed, the laser has revolutionized the whole field of optics and now plays a central role in the world's communications networks. The market for lasers, optical amplifiers and other optoelectronic components is worth billions of dollars every year.
Abstract The calculations of the preceding chapter display some of the inadequacies of the Einstein theory of interaction of light with atoms. The theory itself gives no prescription for computing the values of the A and B coefficients appropriate to a given atomic transition. For this one must look to the quantum-mechanical theory of transition probabilities. As light beams are generated by emission from atoms and measurements on light beams ultimately depend on the absorption of light by atoms, it is essential to cover the theory of the atomic interaction processes, even though the main interest of the book is the quantum nature of the light itself. More seriously, the Einstein theory is applicable only for broad-band illumination of the atom, where the energy in the incident light is distributed smoothly across the frequencies within the linewidth of the atomic transition. By contrast, many experiments with laser sources use light beams whose frequency distributions are much narrower than atomic transition linewidths.
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.
The theory of stimulated emission was put forwarded by A. Einstein (1917), which predicted that as light passed through a substance it could stimulate the emission of more light. In 1954, this phenomenonwas used by Charles Townes andArthur Schawlow in the construction of a microwave amplification by stimulated emission of radiation (maser) using ammonia gas and microwave radiation. Later, this operating principle of maser was put forth to the optical frequencies by them from the Bell Telephone laboratories in 1958, which led to the realization of the device, known as light amplification by stimulated emission of radiation (laser; Townes and Schawlow, 1958). A laser is a quantum optical device that produces a nearly monochromatic (single wavelength), and coherent beam of light by exciting atoms to a higher energy level and causing them to radiate their energy in phase.
All optical oscillators and amplifiers can be analyzed as an electromagnetic structure, such as a cavity or a transmission line, which contains an amplifying medium. The operating characteristics of lasers are governed by both the electromagnetic properties of the structures and the properties of the amplifying medium. Stimulated emission and absorption of radiation from energy states are the physical basis of amplification in all laser materials. In order to study lasers, it is necessary to understand the energy levels of the amplifying medium and the stimulated transitions involving them. Quantum mechanical analysis of the energy states and the stimulated emission and absorption is presented in most books on lasers. However, quantum mechanical analyses cover only the analysis of individual atoms. We need to relate the effects of the quantum mechanical interactions to the macroscopic properties of the materials so that properties of the lasers may be analyzed. Therefore, the macroscopic susceptibility of materials related to stimulated emission and absorption is the focus of discussion in this chapter. It is not the purpose of this book to teach quantum mechanics. There are already many excellent books on this topic. The readers are assumed to have a fundamental knowledge of quantum mechanics. However, it is necessary first to review some of the major steps in order to understand precisely the notation used and the meaning of the results. This is presented in Section 5.1.
… there are certain situations in which the peculiarities of quantum mechanics can come out in a special way on a large scale. Richard Feynman Laser light Nowadays, everyone has heard of lasers, and laser light displays are a frequent ingredient of modern rock concerts. Laser light has many applications, ranging from astronomy to hydrogen fusion. What is the special feature of laser light that makes it so useful? The answer to this question involves a property of wave motion known as ‘coherence’, with light photons acting together in a special form of quantum mechanical co-operation. This type of quantum co-operation will turn out to be vital for an understanding of the peculiar behaviour of quantum ‘superfluids’. To understand the special nature of laser light, however, we must first explain what is meant by coherence. Consider the simple wave motion shown in Fig. 7.1. We see that the pattern repeats itself after one wavelength and the frequency of the wave corresponds to the number of wavelengths sent out per second. If this wave is a wave on a string, each point on the string just moves up and down with a certain amplitude: the maximum distance the point can move out to before it starts to come back. Up to now, this is really all we have needed to know about waves. Now consider two waves of the same wavelength but started at slightly different times, as shown in Fig. 7.2.