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Cambridge University Press eBooks

Catch a falling quantum

Vincent Icke

Published Feb 2, 1995• 0 citations
Publisher

Abstract

An experiment with electrons The preceding chapters described the quantum behaviour of Nature in a general way. In order to show quantum uncertainty at work, it is useful to look at an actual experiment in detail. This demonstrates the practical consequences of the particle–wave duality. To keep things uncluttered, the experiment is only an idealized example, but it will serve to show when quantum interference occurs (wave behaviour) and when it does not (particle behaviour). I will try to demonstrate the intimate connection between the properties of waves and linear superposition, and the consequent uncertainty in the motion of quanta. For once I will try to be precise, so this exposition will be rather more technical than elsewhere. Those who wish to do so, may skip to Chapter 6 without much damage to their education. Before we begin, let me repeat the warning about the generality of analyses such as the one to be given here: I speak about ‘experiments’ or ‘observations’ only in order to make a connection with what a real person could do in a real laboratory, and not because the particle–wave duality is only a laboratory phenomenon that requires a conscious observer. Even though an electron does not wear a lab coat, it is subject to the uncertainty relations when it ‘observes’ other quanta.

DOI
10.1017/cbo9780511622694.007

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An experiment with electrons The preceding chapters described the quantum behaviour of Nature in a general way. In order to show quantum uncertainty at work, it is useful to look at an actual experiment in detail. This demonstrates the practical consequences of the particle–wave duality. To keep things uncluttered, the experiment is only an idealized example, but it will serve to show when quantum interference occurs (wave behaviour) and when it does not (particle behaviour). I will try to demonstrate the intimate connection between the properties of waves and linear superposition, and the consequent uncertainty in the motion of quanta. For once I will try to be precise, so this exposition will be rather more technical than elsewhere. Those who wish to do so, may skip to Chapter 6 without much damage to their education. Before we begin, let me repeat the warning about the generality of analyses such as the one to be given here: I speak about ‘experiments’ or ‘observations’ only in order to make a connection with what a real person could do in a real laboratory, and not because the particle–wave duality is only a laboratory phenomenon that requires a conscious observer. Even though an electron does not wear a lab coat, it is subject to the uncertainty relations when it ‘observes’ other quanta.
Neither particle nor wave The information about the particle behaviour and the wave behaviour of light, presented in the preceding chapter, forms an extremely peculiar combination when taken together. And yet both are true: the experiments have been done as described, with the outcome as stated. There are experiments that tell us clearly that light consists of waves; there are others that tell us, equally clearly, that light consists of particles. Somehow we must find a description of light that incorporates both kinds of behaviour. This is a formidable undertaking, but there is one cheerful fact: in absolutely none of the experiments that have ever been done did the particle and the wave behaviours occur simultaneously . Because this is a fact that covers the entire history of physics, we feel justified in assuming that this is a general feature of Nature, and that there cannot ever be an experiment in which the wave and particle behaviours both occur at the same time. This is a generalization, for we can never expect to do all possible experiments. This generalizing hypothesis was first announced by Bohr, who had the wonderful combination of daring and insight to postulate that the observation of certain quantities excludes the simultaneous observation of certain others.
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The previous chapter surveyed part of the rich variety of physical phenomena that can be understood using the ideas of quantum physics. Now that we are beginning the task of looking more deeply into the subject we shall find it useful to concentrate on examples that are comparatively simple to understand but which still illustrate the fundamental principles and highlight the basic conceptual problems. Some years ago most writers discussing such topics would probably have turned to the example of a ‘particle’ passing through a two-slit apparatus (as in Figure 1.2), whose wave properties are revealed in the interference pattern. Much of the discussion would have been in terms of wave–particle duality and the problems involved in position and momentum measurements, as in the discussion of the uncertainty principle in the last chapter. However, there are essentially an infinite number of places where the particle can be and an infinite number of possible values of its momentum, and this complicates the discussion considerably. We can illustrate all the points of principle we want to discuss by considering situations where a measurement has only a small number of possible outcomes. One such quantity relating to the physics of light beams and photons is known as polarisation . In the next section we discuss it in the context of the classical wave theory of light, and the rest of the chapter extends the concept to situations where the photon nature of light is important.
This chapter discusses the dual nature of small particles, focusing on electrons. It begins by describing how the classical laws of physics, which were mostly established by the start of the twentieth century, did not work very well when applied on the atomic scale. In order to explain the atomic-scale phenomena, a new kind of physics was invented in the 1920s. This new physics was called quantum physics, or quantum mechanics. It applied to the world on the scale of the atom—the microscopic world, or microworld. The discussions then turn to an experiment involving ‘quantum’ coins; the difference between superposition state and mixed state; light, waves, and interference; and interference with electrons.
One of the earliest and most important tenets of quantum mechanics is the wave-particle duality: light behaves sometimes like a wave and at other times as particle and similarly an electron can also behave both like a particle and as a wave. When the formal laws of quantum mechanics are formulated, the central quantity that describes the particles is the wave function. This points to the need for a good understanding of the properties of the waves. This chapter introduces the concepts and most essential applications that are required to follow the discussion of quantum mechanical laws and systems. The basic characteristics of the waves, such as the superposition principle are presented, and the interference and the diffraction phenomena are discussed. The Young’s double slit experiment in analysed and the formation of interference pattern is explicitly shown. The Rayleigh criterion for the microscopic resolution is also derived.
One of the cornerstones of quantum physics is the wave nature of matter. It explains experimentally observed effects like interference and diffraction, occurring when an object moves from one place to another along several indistinguishable ways simultaneously. The wave nature disappears when the individual ways are distinguishable. In this case, the particle nature of the object becomes visible. To determine the particle nature quantitatively, the way of the object has to be measured. Here, large progress has been made recently with new techniques, enabling one to investigate single moving atoms in a controlled manner. Two examples are discussed in the following two sections. The first experiment describes an atom interferometer, where the way of the atom is entangled with its internal state. This allows one to explore the origin of wave-particle duality and perform a quantitative test of this fundamental principle. The second experiment reports on the observation of an atom-photon molecule, a bound state between an atom and a single photon. A fascinating aspect of this system is that it makes possible to monitor the motion of a single neutral atom in real time.