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Cavity Quantum Electrodynamics: The Strange Theory of Light in a Box

Book Description

What happens to light when it is trapped in a box?

Cavity Quantum Electrodynamics addresses a fascinating question in physics: what happens to light, and in particular to its interaction with matter, when it is trapped inside a box? With the aid of a model-building approach, readers discover the answer to this question and come to appreciate its important applications in computing, cryptography, quantum teleportation, and opto-electronics. Instead of taking a traditional approach that requires readers to first master a series of seemingly unconnected mathematical techniques, this book engages the readers' interest and imagination by going straight to the point, introducing the mathematics along the way as needed. Appendices are provided for the additional mathematical theory.

Researchers, scientists, and students of modern physics can refer to Cavity Quantum Electrodynamics and examine the field thoroughly. Several key topics covered that readers cannot find in any other quantum optics book include:

  • Introduction to the problem of the "vacuum catastrophe" and the cosmological constant

  • Detailed up-to-date account of cavity QED lasers and thresholdless lasing

  • Examination of cavities with movable walls

  • First-principles discussion about cavity QED in open cavities

  • Pedagogical account of microscopic quantization in dielectrics

Complementing the coverage of the most advanced theory and techniques, the author provides context by discussing the historical evolution of the field and its discoveries. In that spirit, "recommended reading," provided in each chapter, leads readers to both contemporary literature as well as key historical papers.

Despite being one of many specialties within physics, cavity quantum electrodynamics serves as a window to many of the fundamental issues of physics. Cavity Quantum Electrodynamics will serve as an excellent resource for advanced undergraduate quantum mechanics courses as well as for graduate students, researchers, and scientists who need a comprehensive introduction to the field.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. Acknowledgments
  8. 1: Introduction
    1. 1.1 WHAT IS LIGHT? THE DEVELOPMENT OF OUR MENTAL PICTURE OF LIGHT
    2. 1.2 A BRIEF HISTORY OF CAVITY QED
    3. 1.3 A MAP OF THE BOOK: AN OVERVIEW OF WHAT IS TO COME
    4. 1.4 HOW TO READ THIS BOOK: SUGGESTIONS ON HOW TO FIND YOUR OWN OPTIMAL PATH THROUGH THE CHAPTERS
  9. 2: Fiat Lux! A free tasting of field quantization
    1. 2.1 A BRIEF REVIEW OF QUANTUM MECHANICS: HOW TO QUANTIZE A THEORY
    2. 2.2 WHY THE RADIATION FIELD IS SPECIAL
    3. 2.3 WHAT IS A CAVITY AND HOW DO WE FIND ITS MODES?
    4. 2.4 CANONICAL QUANTIZATION OF THE RADIATION FIELD
    5. 2.5 A PHYSICAL EFFECT DUE TO ZERO-POINT FLUCTUATIONS: THE CASIMIR FORCE
    6. RECOMMENDED READING
    7. Problems
  10. 3: The alternative free tasting: First quantization of light and the photon's wavefunction
    1. 3.1 THE PROBLEM OF THE POSITION OPERATOR IN RELATIVISTIC QUANTUM MECHANICS
    2. 3.2 EXTREME QUANTUM THEORY OF LIGHT WITH A TWIST: PROCA EQUATIONS FOR A MASSIVE PARTICLE OF SPIN 1
    3. 3.3 THE PROBLEM WITH THE WAVEFUNCTION IN CONFIGURATION SPACE
    4. 3.4 BACK TO VECTOR NOTATION
    5. 3.5 THE LIMIT OF VANISHING REST MASS
    6. 3.6 SECOND QUANTIZATION OF THE EXTREME QUANTUM THEORY OF LIGHT
    7. RECOMMENDED READING
    8. Problems
  11. 4: A box of photons
    1. 4.1 THE CLASSICAL LIMIT OF THE QUANTIZED RADIATION FIELD
    2. 4.2 GOING BEYOND THE STANDARD QUANTUM LIMIT: SQUEEZED STATES
    3. RECOMMENDED READING
    4. Problems
  12. 5: Let matter be!
    1. 5.1 A SINGLE POINT DIPOLE
    2. 5.2 AN ARBITRARY CHARGE DISTRIBUTION
    3. 5.3 MATTER–RADIATION COUPLING AS A CONSEQUENCE OF GAUGE INVARIANCE
    4. RECOMMENDED READING
  13. 6: Spontaneous emission: From irreversible decay to Rabi oscillations 1
    1. 6.1 SPONTANEOUS EMISSION IN FREE SPACE
    2. 6.2 SPONTANEOUS EMISSION IN A CAVITY
  14. 7: Macroscopic QED: Quantum electrodynamics in material media
    1. 7.1 A SIMPLE MODEL FOR QED IN MATERIAL MEDIA: THE DIELECTRIC JCM
    2. 7.2 HOPFIELD'S POLARITON–PHOTON DRESSED EXCITATIONS
    3. 7.3 QUANTUM NOISE GENERATED BY MATTER AND MACROSCOPIC AVERAGES: IS A DIELECTRIC PERMITTIVITY ENOUGH?
    4. 7.4 HOW A MACROSCOPIC DESCRIPTION IS POSSIBLE
    5. 7.5 IF THERE IS DISPERSION, THERE MUST ALSO BE ABSORPTION SOMEWHERE: THE KRAMERS–KRONIG DISPERSION RELATION
    6. 7.6 INCLUDING ABSORPTION IN THE DIELECTRIC JCM
    7. 7.7 DIELECTRIC PERMITTIVITY
    8. 7.8 THE FULL QUANTUM THEORY: HUTTNER AND BARNETT'S IMPROVEMENT OF THE HOPFIELD MODEL
    9. RECOMMENDED READING
    10. Problems
  15. 8: The maser, the laser, and their cavity QED cousins
    1. 8.1 THE ASER IDEA: AMPLIFICATION BY STIMULATED EMISSION OF RADIATION
    2. 8.2 HOW TO ADD NOISE: BROWNIAN MOTION; THE LANGEVIN EQUATION; ITO'S AND STRATONOVICH'S STOCHASTIC CALCULUS
    3. 8.3 RATE EQUATIONS WITH NOISE: THE EFFECT OF SPONTANEOUS EMISSION
    4. 8.4 IDEAL LASER LIGHT: WHAT QUANTUM STATE OF LIGHT WOULD BE GENERATED IN AN IDEAL LASER?
    5. 8.5 THE SINGLE-ATOM MASER
    6. 8.6 THE THRESHOLDLESS LASER: A STAGEPOST ON THE ROAD FROM MICROMASER TO LASER
    7. 8.7 THE ONE-AND-THE-SAME ATOM LASER
    8. RECOMMENDED READING
    9. Problems
  16. 9: What is a mode of an open cavity?
    1. 9.1 THE GARDINER–COLLETT HAMILTONIAN
    2. 9.2 SOMMERFELD'S RADIATION CONDITION
    3. 9.3 THOMSON'S NATURAL MODES
    4. 9.4 INCOMING VACUUM MODES AND COMPLETENESS
    5. RECOMMENDED READING
    6. Problems
  17. Appendix A: Modes of a perfectly conducting closed cavity: A quick review
  18. Appendix B: Perfect cavity boundary conditions
  19. Appendix C: Quaternions and special relativity
    1. C.1 WHAT ARE QUATERNIONS?
    2. C.2 QUATERNION CALCULUS
    3. C.3 BIQUATERNIONS AND LORENTZ TRANSFORMATIONS
  20. Appendix D: The Baker–Hausdorff formula
  21. Appendix E: Trade secrets: Tools for dealing with vectors and vector identities
    1. E.1 RELATION BETWEEN VECTOR PRODUCTS AND DETERMINANTS
    2. E.2 VECTOR PRODUCTS AND THE LEVY–CIVITA TENSOR
    3. E.3 THE PRODUCT OF TWO LEVY–CIVITA TENSORS AS A DETERMINANT
    4. E.4 THE VECTOR PRODUCT OF THREE VECTORS
    5. E.5 VECTORIAL EXPRESSIONS INVOLVING DEL
    6. E.6 SOME USEFUL INTEGRAL THEOREMS
  22. Appendix F: The Good, the Bad, and the Ugly: Principal Parts, Step and Delta Functions
    1. F.1 CONNECTION BETWEEN VARIOUS REPRESENTATIONS
    2. F.2 A USEFUL IDENTITY IN FANO DIAGONALIZATION: THE PRODUCT OF TWO PRINCIPAL PARTS
    3. F.3 WHEN THE SAMPLING HAPPENS AT A POINT OF DISCONTINUITY
  23. References
  24. Index