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Introductory Quantum Optics

Book Description

This book provides an elementary introduction to the subject of quantum optics, the study of the quantum mechanical nature of light and its interaction with matter. The presentation is almost entirely concerned with the quantized electromagnetic field. Topics covered include single-mode field quantization in a cavity, quantization of multimode fields, quantum phase, coherent states, quasi-probability distribution in phase space, atom-field interactions, the Jaynes-Cummings model, quantum coherence theory, beam splitters and interferometers, dissipative interactions, nonclassical field states with squeezing etc., 'Schrödinger cat' states, tests of local realism with entangled photons from down-conversion, experimental realizations of cavity quantum electrodynamics, trapped ions, decoherence, and some applications to quantum information processing, particularly quantum cryptography. The book contains many homework problems and an extensive bibliography. This text is designed for upper-level undergraduates taking courses in quantum optics who have already taken a course in quantum mechanics, and for first and second year graduate students.

Table of Contents

  1. Coverpage
  2. Introductory Quantum Optics
  3. Title page
  4. Copyright page
  5. Dedication
  6. Contents
  7. Acknowledgements
  8. 1 Introduction
    1. 1.1 Scope and aims of this book
    2. 1.2 History
    3. 1.3 The contents of this book
      1. References
      2. Suggestions for further reading
  9. 2 Field quantization
    1. 2.1 Quantization of a single-mode field
    2. 2.2 Quantum fluctuations of a single-mode field
    3. 2.3 Quadrature operators for a single-mode field
    4. 2.4 Multimode fields
    5. 2.5 Thermal fields
    6. 2.6 Vacuum fluctuations and the zero-point energy
    7. 2.7 The quantum phase
      1. Problems
      2. References
      3. Bibliography
  10. 3 Coherent states
    1. 3.1 Eigenstates of the annihilation operator and minimum uncertainty states
    2. 3.2 Displaced vacuum states
    3. 3.3 Wave packets and time evolution
    4. 3.4 Generation of coherent states
    5. 3.5 More on the properties of coherent states
    6. 3.6 Phase-space pictures of coherent states
    7. 3.7 Density operators and phase-space probability distributions
    8. 3.8 Characteristic functions
      1. Problems
      2. References
      3. Bibliography
  11. 4 Emission and absorption of radiation by atoms
    1. 4.1 Atom–field interactions
    2. 4.2 Interaction of an atom with a classical field
    3. 4.3 Interaction of an atom with a quantized field
    4. 4.4 The Rabi model
    5. 4.5 Fully quantum-mechanical model; the Jaynes–Cummings model
    6. 4.6 The dressed states
    7. 4.7 Density-operator approach: application to thermal states
    8. 4.8 The Jaynes–Cummings model with large detuning: a dispersive interaction
    9. 4.9 Extensions of the Jaynes–Cummings model
    10. 4.10 Schmidt decomposition and von Neumann entropy for the Jaynes–Cummings model
      1. Problems
      2. References
      3. Bibliography
  12. 5 Quantum coherence functions
    1. 5.1 Classical coherence functions
    2. 5.2 Quantum coherence functions
    3. 5.3 Young’s interference
    4. 5.4 Higher-order coherence functions
      1. Problems
      2. References
      3. Bibliography
  13. 6 Beam splitters and interferometers
    1. 6.1 Experiments with single photons
    2. 6.2 Quantum mechanics of beam splitters
    3. 6.3 Interferometry with a single photon
    4. 6.4 Interaction-free measurement
    5. 6.5 Interferometry with coherent states of light
      1. Problems
      2. References
      3. Bibliography
  14. 7 Nonclassical light
    1. 7.1 Quadrature squeezing
    2. 7.2 Generation of quadrature squeezed light
    3. 7.3 Detection of quadrature squeezed light
    4. 7.4 Amplitude (or number) squeezed states
    5. 7.5 Photon antibunching
    6. 7.6 Schrödinger cat states
    7. 7.7 Two-mode squeezed vacuum states
    8. 7.8 Higher-order squeezing
    9. 7.9 Broadband squeezed light
      1. Problems
      2. References
      3. Bibliography
  15. 8 Dissipative interactions and decoherence
    1. 8.1 Introduction
    2. 8.2 Single realizations or ensembles?
    3. 8.3 Individual realizations
    4. 8.4 Shelving and telegraph dynamics in three-level atoms
    5. 8.5 Decoherence
    6. 8.6 Generation of coherent states from decoherence: nonlinear optical balance
    7. 8.7 Conclusions
      1. Problems
      2. References
      3. Bibliography
  16. 9 Optical test of quantum mechanics
    1. 9.1 Photon sources: spontaneous parametric down-conversion
    2. 9.2 The Hong–Ou–Mandel interferometer
    3. 9.3 The quantum eraser
    4. 9.4 Induced coherence
    5. 9.5 Superluminal tunneling of photons
    6. 9.6 Optical test of local realistic theories and Bell’s theorem
    7. 9.7 Franson’s experiment
    8. 9.8 Applications of down-converted light to metrology without absolute standards
      1. Problems
      2. References
      3. Bibliography
  17. 10 Experiments in cavity QED and with trapped ions
    1. 10.1 Rydberg atoms
    2. 10.2 Rydberg atom interacting with a cavity field
    3. 10.3 Experimental realization of the Jaynes–Cummings model
    4. 10.4 Creating entangled atoms in CQED
    5. 10.5 Formation of Schrödinger cat states with dispersive atom–field interactions and decoherence from the quantum to the classical
    6. 10.6 Quantum nondemolition measurement of photon number
    7. 10.7 Realization of the Jaynes–Cummings interaction in the motion of a trapped ion
    8. 10.8 Concluding remarks
      1. Problems
      2. References
      3. Bibliography
  18. 11 Applications of entanglement: Heisenberg-limited interferometry and quantum information processing
    1. 11.1 The entanglement advantage
    2. 11.2 Entanglement and interferometric measurements
    3. 11.3 Quantum teleportation
    4. 11.4 Cryptography
    5. 11.5 Private key crypto-systems
    6. 11.6 Public key crypto-systems
    7. 11.7 The quantum random number generator
    8. 11.8 Quantum cryptography
    9. 11.9 Future prospects for quantum communication
    10. 11.10 Gates for quantum computation
    11. 11.11 An optical realization of some quantum gates
    12. 11.12 Decoherence and quantum error correction
    13. Problems
    14. References
    15. Bibliography
  19. Appendix A The density operator, entangled states, the Schmidt decomposition, and the von Neumann entropy
    1. A.1 The density operator
    2. A.2 Two-state system and the Bloch sphere
    3. A.3 Entangled states
    4. A.4 Schmidt decomposition
    5. A.5 von Neumann entropy
    6. A.6 Dynamics of the density operator
      1. References
      2. Bibliography
  20. Appendix B Quantum measurement theory in a (very small) nutshell
    1. Bibliography
  21. Appendix C Derivation of the effective Hamiltonian for dispersive (far off-resonant) interactions
    1. References
  22. Appendix D Nonlinear optics and spontaneous parametric down-conversion
    1. References
  23. Index