Atomic Radiative Processes

1st Edition - May 28, 1982
Author: Peter R. Fontana
Language: English
eBook ISBN:
9 7 8 - 0 - 3 2 3 - 1 5 7 5 1 - 3

Atomic Radiative Processes provides a unified treatment of the theory of atomic radiative processes. Fourier transforms are used to obtain solutions of time-dependent Schrödinger… Read more

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Atomic Radiative Processes provides a unified treatment of the theory of atomic radiative processes. Fourier transforms are used to obtain solutions of time-dependent Schrödinger equations, and coupled differential equations are transformed to coupled linear equations that in most cases can be readily solved. This book consists of nine chapters and begins with an overview of some of the properties of the classical field and its interaction with particles, focusing on those aspects needed for a better understanding of quantum theory. The Hamiltonian formalism is used to quantize the field, and the density of states of the radiation field is considered. The following chapters focus on a few Fourier transform techniques and their application to such areas as coherence properties of the field and amplitude and intensity correlations; the theory of angular momentum; the properties of irreducible tensors; quantization of the radiation field; and photon states. The interaction of a two-level atom with single modes of the radiation field is also discussed, along with spontaneous emission and decay processes; the evolution of coupled atomic states; the frequency distribution of emitted radiation; and radiative excitation and fluorescence. This monograph is intended for students and researchers in pure and applied physics.

Preface

Acknowledgments

1. Classical Electrodynamics

1.1 Formal Development

1.2 The Free Field

1.3 Polarization of Radiation

1.4 Density of States in a Cavity

1.5 Single Charged Particle in an Electromagnetic Field

1.6 System of Particles and Fields

References

2. Coherence Properties of Waves

2.1 Fourier Analysis of the Field

2.2 Properties of Fourier Transforms

2.2.1 Convolution

2.3 Fourier Analysis of Wave Trains

2.3.1 Spectrum of a Sinusoidal Pulse of Constant Amplitude

2.3.2 Spectrum of a Decaying Pulse

2.4 Detector Response

2.5 Interference of Two Wave Trains

2.6 Light Beating Spectroscopy

2.7 Intensity Interference

2.7.1 Single Point Source

2.7.2 Extended Source

References

3. Theory of Angular Momentum and Irreducible Tensors

3.1 Coupling of Angular Momenta

3.2 Transformations under Rotation

3.3 Irreducible Tensors

3.4 Expansion of the Interaction Hamiltonian

References

4. Quantization of the Radiation Field

4.1 Introduction

4.2 Eigenstates and Eigenvalues

4.3 Quantization of the Fields

4.4 Phases and Uncertainties

4.5 Interaction Representation

4.6 Coherent States

4.7 Distribution of Photons

4.7.1 Coherent Light

4.7.2 Incoherent Light

4.8 Photon-Atom Interaction

4.9 Higher-Order Coherences

References

5. Interaction Hamiltonian

5.1 Interaction Representation

5.2 Density Operator

5.3 Second Quantization

5.4 Electric Dipole Interaction

References

6. Two-Level Atom Interacting with a Sinusoidal Field

6.1 Introduction

6.2 Rotating Wave

6.2.1 Amplitude Equations

6.2.2 Matrix Elements

6.2.3 Bloch Equations

6.2.4 Distribution of Frequencies

6.3 Linear Wave

6.3.1 Amplitude Equations for a Single Dressed State

6.3.2 Amplitude Equations for a Coherent State

6.3.3 Bloch Equations

6.3.4 Resonances

References

7. Spontaneous Emission

7.1 Introduction

7.2 Weisskopf-Wigner Theory

7.2.1 Amplitudes and Decay Rates

7.2.2 Probabilities

7.3 Fourier Transform Method

7.3.1 Amplitude Equations

7.3.2 Decay Rates

7.3.3 Amplitudes

7.3.4 Reduced Differential Equations for the Initial State

7.4 Density Matrix Equations

7.4.1 Differential Equations and Fourier Transforms

7.4.2 Reduced Density Matrix Equations

7.4.3 Bloch Equations

7.5 Angular Distributions and Decay Rates

References

8. Decay Processes

8.1 Introduction

8.2 Decay of Excited State to Coupled Ground States

8.3 Branching Decay

8.4 Cascade Decay

8.5 Decay of Coherently Excited States

8.6 Decay of Coupled Excited States

8.6.1 Amplitude Equations

8.6.2 Density Matrix Equation

8.6.3 Bloch Equations

8.6.4 Frequency Distributions

8.7 Decay of Interacting Atoms

References

9. Excitation and Fluorescence

9.1 Introduction

9.2 Resonance Fluorescence

9.2.1 Amplitude Equations

9.2.2 Decay Rates

9.2.3 Probabilities

9.3 Level-Crossing and Anti-Crossing Spectroscopy

9.3.1 Amplitudes and Probabilities

9.3.2 Angular Distribution

9.3.3 Level-Crossing Signal in Atomic Hydrogen

9.4 Optical Double Resonance

9.5 Dynamic Stark Effect

9.5.1 Amplitudes and Frequency Distributions

9.5.2 Density Matrix and Bloch Equations

9.5.3 Dipole Moment

References

Appendix A: Glossary of Symbols

Appendix B: Clebsch-Gordan Coefficients

Appendix C: Electric and Magnetic Multi-poles

Appendix D: Properties of the Zeta Function

Index