Unit 5: the Quantum World
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Unit 5: The Quantum World Unit Overview This unit covers a field of physics that is simultaneously one of the most powerful, transformational, and precise tools for exploring nature and yet for non-physicists one of the most mysterious and misunderstood aspects of all science. Developed early in the 20th century to solve a crisis in understanding the nature of the atom, quantum mechanics has laid the foundation for theoretical and practical advances in 21st century physics. The unit details the reasoning that led to ever deeper awareness of the nature of particles, waves, and their interrelationships, provides a primer on present-day understanding of the field, and outlines ways in which that understanding has led to significant applications today. Content for This Unit Sections: 1. Introduction.............................................................................................................. 2 2. Mysteries of Light....................................................................................................4 3. Waves, Particles, and a Paradox........................................................................... 9 4. Mysteries of Matter............................................................................................... 14 5. Introducing Quantum Mechanics.......................................................................... 19 6. The Uncertainty Principle......................................................................................25 7. Atom Cooling and Trapping.................................................................................. 32 8. Atomic Clocks........................................................................................................39 9. Afterthoughts on a Paradox.................................................................................. 48 10. Further Reading.................................................................................................... 50 Glossary.................................................................................................................51 Unit 5: The Quantum World 1 www.learner.org Section 1: Introduction Figure 1: Thirty-two ions, fluorescing under illumination by laser light in an electrodynamic trap. Source: © R. Blatt at Institut f. Experimentalphysik, Universtaet Innsbruck, Austria. The creation of quantum mechanics in the 1920s broke open the gates to understanding atoms, molecules, and the structure of materials. This new knowledge transformed our world. Within two decades, quantum mechanics led to the invention of the transistor to be followed by the invention of the laser, revolutionary advances in semiconductor electronics, integrated circuits, medical diagnostics, and optical communications. Quantum mechanics also transformed physics because it profoundly changed our understanding of how to ask questions of nature and how to interpret the answers. An intellectual change of this magnitude does not come easily. The founders of quantum mechanics struggled with its concepts and passionately debated them. We are the beneficiaries of that struggle and quantum mechanics has now been developed into an elegant and coherent discipline. Nevertheless, quantum mechanics always seems strange on first acquaintance and certain aspects of it continue to generate debate today. We hope that this unit provides insight into how quantum mechanics works and why people find it so strange at first. We will also sketch some of the recent developments that have enormously enhanced our powers for working in the quantum world. These advances make it possible to manipulate and study quantum systems with a clarity previously achieved only in hypothetical thought experiments. They are so dramatic that some physicists have described them as a second quantum revolution. Unit 5: The Quantum World 2 www.learner.org Figure 2: Neutral rubidium atoms in an optical lattice trap. Source: © M. Greiner. An early step in the second quantum revolution was the discovery of how to capture and manipulate a single ion in an electromagnetic trap, reduce its energy to the quantum limit, and even watch the ion by eye as it fluoresces. Figure 1 shows an array of fluorescing ions in a trap. Then methods were discovered for cooling atoms to microkelvin temperatures (a microkelvin is a millionth of a degree) and trapping them in magnetic fields or with light waves (Figure 2). These advances opened the way to stunning advances such as the observation of Bose-Einstein condensation of atoms, to be discussed in Unit 6, and the creation of a new discipline that straddles atomic and condensed matter physics. The goal of this unit is to convey the spirit of life in the quantum world—that is, to give an idea of what quantum mechanics is and how it works—and to describe two events in the second quantum revolution: atom cooling and atomic clocks. Unit 5: The Quantum World 3 www.learner.org Section 2: Mysteries of Light Figure 3: This furnace for melting glass is nearly an ideal blackbody radiation source. Source: © OHM Equipment, LLC. The nature of light was a profound mystery from the earliest stirrings of science until the 1860s and 1870s, when James Clerk Maxwell developed and published his electromagnetic theory. By joining the two seemingly disparate phenomena, electricity and magnetism, into the single concept of an electromagnetic field, Maxwell's theory showed that waves in the field travel at the speed of light and are, in fact, light itself. Today, most physicists regard Maxwell's theory as among the most important and beautiful theories in all of physics. Maxwell's theory is elegant because it can be expressed by a short set of equations. It is powerful because it leads to powerful predictions—for instance, the existence of radio waves and, for that matter, the entire electromagnetic spectrum from radio waves to x-rays. Furthermore, the theory explained how light can be created and absorbed, and provided a key to essentially every question in optics. Given the beauty, elegance, and success of Maxwell's theory of light, it is ironic that the quantum age, in which many of the most cherished concepts of physics had to be recast, was actually triggered by a problem involving light. Unit 5: The Quantum World 4 www.learner.org Figure 4: The electromagnetic spectrum from radio waves to gamma rays. Source: The spectrum of light from a blackbody—for instance the oven in Figure 3 or the filament of an electric light bulb—contains a broad spread of wavelengths. The spectrum varies rapidly with the temperature of the body. As the filament is heated, the faint red glow of a warm metal becomes brighter, and the peak of the spectrum broadens and shifts to a shorter wavelength, from orange to yellow and then to blue. The spectra of radiation from blackbodies at different temperatures have identical shapes and differ only in the scales of the axes. Figure 5: Spectrum of the cosmic microwave background radiation. Source: © NASA, COBE. Figure 5 shows the blackbody spectrum from a particularly interesting source: the universe. This is the spectrum of thermal radiation from space—the cosmic microwave background—taken by the Cosmic Background Explorer (COBE) satellite experiment. The radiation from space turns out to be the spectrum Unit 5: The Quantum World 5 www.learner.org of a blackbody at a temperature of 2.725 Kelvin. The peak of the spectrum occurs at a wavelength of about one millimeter, in the microwave regime. This radiation can be thought of as an echo of the primordial Big Bang. Enter the quantum In the final years of the 19th century, physicists attempted to understand the spectrum of blackbody radiation but theory kept giving absurd results. German physicist Max Planck finally succeeded in calculating the spectrum in December 1900. However, he had to make what he could regard only as a preposterous hypothesis. According to Maxwell's theory, radiation from a blackbody is emitted and absorbed by charged particles moving in the walls of the body, for instance by electrons in a metal. Planck modeled the electrons as charged particles held by fictitious springs. A particle moving under a spring force behaves like a harmonic oscillator. Planck found he could calculate the observed spectrum if he hypothesized that the energy of each harmonic oscillator could change only by discrete steps. If the frequency of the oscillator is ( is the Greek letter "nu" and is often used to stand for frequency), then the energy had to be 0, 1 , 2 , 3 , ... n , ... where n could be any integer and h is a constant that soon became known as Planck's constant. Planck named the step a quantum of energy. The blackbody spectrum Planck obtained by invoking his quantum hypothesis agreed beautifully with the experiment. But the quantum hypothesis seemed so absurd to Planck that he hesitated to talk about it. Unit 5: The Quantum World 6 www.learner.org Figure 6: Max Planck solved the blackbody problem by introducing quanta of energy. Source: © The Clendening History of Medicine Library, University of Kansas Medical Center. The physical dimension—the unit—of Planck's constant h is interesting. It is either [energy] / [frequency] or [angular momentum]. Both of these dimensions have important physical interpretations. The constant's value in S.I. units, 6.6 x 10-34 joule-seconds, suggests the enormous distance between the quantum world and everyday events. Planck's constant is ubiquitous in quantum physics. The combination h/2 appears so often that it has been given a special symbol