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Introduction to Quantum Optics

Book Description

Covering a number of important subjects in quantum optics, this textbook is an excellent introduction for advanced undergraduate and beginning graduate students, familiarizing readers with the basic concepts and formalism as well as the most recent advances. The first part of the textbook covers the semi-classical approach where matter is quantized, but light is not. It describes significant phenomena in quantum optics, including the principles of lasers. The second part is devoted to the full quantum description of light and its interaction with matter, covering topics such as spontaneous emission, and classical and non-classical states of light. An overview of photon entanglement and applications to quantum information is also given. In the third part, non-linear optics and laser cooling of atoms are presented, where using both approaches allows for a comprehensive description. Each chapter describes basic concepts in detail, and more specific concepts and phenomena are presented in 'complements'.

Table of Contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Contents
  5. Foreword
  6. Preface
  7. Acknowledgements
  8. Part I Semi-classical description of matter-light interaction
    1. 1 The evolution of interacting quantum systems
      1. 1.1 Review of some elementary results of quantum mechanics
      2. 1.2 Transition between discrete levels induced by a time-dependent perturbation
      3. 1.3 Case of a discrete level coupled to a continuum: Fermi’s golden rule
      4. 1.4 Conclusion
    2. Complement 1A A continuum of variable width
    3. Complement 1B Transition induced by a random broadband perturbation
    4. 2 The semi-classical approach: atoms interacting with a classical electromagnetic field
      1. 2.1 Atom-light interaction processes
      2. 2.2 The interaction Hamiltonian
      3. 2.3 Transitions between atomic levels driven by an oscillating electromagnetic field
      4. 2.4 Absorption between levels of finite lifetimes
      5. 2.5 Laser amplification
      6. 2.6 Rate equations
      7. 2.7 Conclusion
    5. Complement 2A Classical model of the atom-field interaction: the Lorentz model
    6. Complement 2B Selection rules for electric dipole transitions. Applications to resonance fluorescence and optical pumping
    7. Complement 2C The density matrix and the optical Bloch equations
    8. Complement 2D Manipulation of atomic coherences
    9. Complement 2E The photoelectric effect
    10. 3 Principles of lasers
      1. 3.1 Conditions for oscillation
      2. 3.2 Description of the amplifying media of some lasers
      3. 3.3 Spectral properties of lasers
      4. 3.4 Pulsed lasers
      5. 3.5 Conclusion: lasers versus classical sources
    11. Complement 3A The resonant Fabry-Perot cavity
    12. Complement 3B The transverse modes of a laser: Gaussian beams
    13. Complement 3C Laser light and incoherent light: energy density and number of photons per mode
    14. Complement 3D The spectral width of a laser: the Schawlow-Townes limit
    15. Complement 3E The laser as energy source
    16. Complement 3F The laser as source of coherent light
    17. Complement 3G Nonlinear spectroscopy
  9. Part II Quantum description of light and its interaction with matter
    1. 4 Quantization of free radiation
      1. 4.1 Classical Hamiltonian formalism and canonical quantization
      2. 4.2 Free electromagnetic field and transversality
      3. 4.3 Expansion of the free electromagnetic field in normal modes
      4. 4.4 Hamiltonian for free radiation
      5. 4.5 Quantization of radiation
      6. 4.6 Quantized radiation states and photons
      7. 4.7 Conclusion
    2. Complement 4A Example of the classical Hamiltonian formalism: charged particle in an electromagnetic field
    3. Complement 4B Momentum and angular momentum of radiation
    4. Complement 4C Photons in modes other than travelling plane waves
    5. 5 Free quantum radiation
      1. 5.1 Photodetectors and semi-reflecting mirrors. Homodyne detection of the quadrature components
      2. 5.2 The vacuum: ground state of quantum radiation
      3. 5.3 Single-mode radiation
      4. 5.4 Multimode quantum radiation
      5. 5.5 One-photon interference and wave-particle duality. An application of the formalism
      6. 5.6 A wave function for the photon?
      7. 5.7 Conclusion
    6. Complement 5A Squeezed states of light: the reduction of quantum fluctuations
    7. Complement 5B One-photon wave packet
    8. Complement 5C Polarization-entangled photons and violation of Bell’s inequalities
    9. Complement 5D Entangled two-mode states
    10. Complement 5E Quantum information
    11. 6 Interaction of an atom with the quantized electromagnetic field
      1. 6.1 Classical electrodynamics and interacting fields and charges
      2. 6.2 Interacting fields and charges and quantum description in the Coulomb gauge
      3. 6.3 Interaction processes
      4. 6.4 Spontaneous emission
      5. 6.5 Photon scattering by an atom
      6. 6.6 Conclusion. From the semi-classical to the quantum treatment of atom-light interaction
    12. Complement 6A Hamiltonian formalism for interacting fields and charges
    13. Complement 6B Cavity quantum electrodynamics
    14. Complement 6C Polarization-entangled photon pairs emitted in an atomic radiative cascade
  10. Part III Applying both approaches
    1. 7 Nonlinear optics. From the semi-classical approach to quantum effects
      1. 7.1 Introduction
      2. 7.2 Electromagnetic field in a nonlinear medium. Semi-classical treatment
      3. 7.3 Three-wave mixing. Semi-classical treatment
      4. 7.4 Quantum treatment of parametric fluorescence
      5. 7.5 Conclusion
    2. Complement 7A Parametric amplification and oscillation. Semi-classical and quantum properties
    3. Complement 7B Nonlinear optics in optical Kerr media
    4. 8 Laser manipulation of atoms. From incoherent atom optics to atom lasers
      1. 8.1 Energy and momentum exchanges in the atom-light interaction
      2. 8.2 Radiative forces
      3. 8.3 Laser cooling and trapping of atoms, optical molasses
      4. 8.4 Gaseous Bose-Einstein condensates and atom lasers
    5. Complement 8A Cooling to sub-recoil temperatures by velocity-selective coherent population trapping
  11. Index