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Lectures on LightNonlinear and Quantum Optics using the Density Matrix$
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Stephen Rand

Print publication date: 2010

Print ISBN-13: 9780199574872

Published to Oxford Scholarship Online: September 2010

DOI: 10.1093/acprof:oso/9780199574872.001.0001

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Atom—Field Interactions

Atom—Field Interactions

Chapter:
(p.40) 3 Atom—Field Interactions
Source:
Lectures on Light
Author(s):

Stephen C. Rand

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199574872.003.0003

In Chapter 3 the interaction Hamiltonian which determines the way light interacts with matter is derived. Simple perturbative analysis is applied to see if basic dynamics of atoms can be explained. The partial successes of perturbation theory are compared with predictions of an “exact” method of calculating the occupation probabilities of various atomic states. Even the “exact” method is shown to fail, establishing the need for improved approaches that yield correct results in later chapters. Some elementary results for the transition rates, including Fermi's golden rule are covered. Then the density matrix is introduced as a tool for describing not only the populations of atomic energy levels but coherence that can be created and lost during the dynamic evolution of atoms in time. A vector model based on the Bloch vector is presented as a useful way of picturing coherent atom–field interactions in an optical “spin” space, particularly multiple‐pulse interactions. Mechanisms are described that cause line‐broadening in optical spectroscopy, such as the Doppler effect. The chapter closes by showing that it is usually possible to reduce the complexity of real atoms on an experimental basis to facilitate direct comparisons with theoretical calculations based on simple models with only two or three energy levels.

Keywords:   interaction Hamiltonian, perturbation theory, Rabi method, coherence, dephasing, homogeneous and inhomogeneous line‐broadening

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