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Quantum Optics

Book Description

In the last decade many important advances have taken place in the field of quantum optics, with numerous potential applications. Ideal for graduate courses on quantum optics, this textbook provides an up-to-date account of the basic principles of the subject. Focusing on applications of quantum optics, the textbook covers recent developments such as engineering of quantum states, quantum optics on a chip, nano-mechanical mirrors, quantum entanglement, quantum metrology, spin squeezing, control of decoherence and many other key topics. Readers are guided through the principles of quantum optics and their uses in a wide variety of areas including quantum information science and quantum mechanics. The textbook features end-of-chapter exercises with solutions available for instructors at www.cambridge.org/9781107006409. It is invaluable to both graduate students and researchers in physics and photonics, quantum information science and quantum communications.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright Page
  4. Dedication
  5. Preface
  6. 1  Quantized electromagnetic field and coherent state representations
    1. 1.1     Quantization of the electromagnetic field
    2. 1.2     State space for the electromagnetic field – Fock space and Fock states
    3. 1.3     Quadratures of the field
    4. 1.4     Coherent states
    5. 1.5     Mixed states of the radiation field
    6. 1.6     Diagonal coherent state representation for electromagnetic fields – P-representation
    7. 1.7     The Wigner function for the electromagnetic field
    8. 1.8     Bosonic systems with finite mass – coherent states and phase-space representations
    9. Exercises
    10. References
  7. 2  Nonclassicality of radiation fields
    1. 2.1     The Mandel QM parameter
    2. 2.2     Phase-dependent measure of nonclassicality – squeezing parameter S
    3. 2.3     Single-mode squeezed states – squeezed vacuum
    4. 2.4     Squeezed coherent state
    5. 2.5     Other measures of nonclassicality
    6. 2.6     Mixed nonclassical states – degradation in squeezing
    7. Exercises
    8. References
  8. 3  Two-mode squeezed states and quantum entanglement
    1. 3.1     The two-mode squeezed states
    2. 3.2     Nonclassicality of the two-mode squeezed vacuum
    3. 3.3     Quantum phase-space distributions and quadrature distributions
    4. 3.4     Cauchy–Schwarz inequalities for nonclassicality in two-mode states
    5. 3.5     Conditional measurements on the two-mode squeezed vacuum
    6. 3.6     Quantum entanglement in the two-mode squeezed vacuum
    7. 3.7     Peres–Horodecki separability criterion for continuous variable systems
    8. 3.8     Generation of two-mode nonclassical and entangled states – optical parametric down-conversion
    9. 3.9     Parametric amplification of signals
    10. 3.10     Type-II optical parametric down-conversion – production of entangled photons
    11. 3.11     Four-photon entanglement using optical parametric down-conversion
    12. 3.12     Two-mode mixed nonclassical states
    13. 3.13     Entanglement in two-mode mixed Gaussian states
    14. 3.14     Application of entanglement to the teleportation of a quantum state
    15. 3.15     Nonclassical fields in optical fibers
    16. Exercises
    17. References
  9. 4  Non-Gaussian nonclassical states
    1. 4.1     Schrödinger cat state and the cat paradox
    2. 4.2     Photon-added and -subtracted states
    3. 4.3     Single-photon-added coherent and thermal states
    4. 4.4     Squeezing and sub-Poissonian properties of single-photon-added states
    5. 4.5     Experimental realization of photon-added nonclassical non-Gaussian states
    6. 4.6     Single-photon-subtracted states
    7. 4.7     Single-photon-subtracted two-mode states with vortex structure
    8. 4.8     Pair-coherent states
    9. Exercises
    10. References
  10. 5  Optical interferometry with single photons and nonclassical light
    1. 5.1     Transformation of quantized light fields at beam splitters
    2. 5.2     Beam splitter transformation equivalent to evolution under a Hamiltonian
    3. 5.3     Transformation of states by the beam splitter
    4. 5.4     Transformation of photon number states by a beam splitter
    5. 5.5     Single photons at beam splitters
    6. 5.6     Pairs of single photons at beam splitters
    7. 5.7     Generalization of the Hong–Ou–Mandel interference to N photons from both ports of the beam splitter
    8. 5.8     Transformation of a two-mode squeezed state by a 50-50 beam splitter
    9. 5.9     Generation of two-mode entangled states by the interference of coherent fields and single photons
    10. 5.10     Beam splitter as an attenuator
    11. 5.11     Transformation of quantized light fields by phase shifters
    12. 5.12     The Mach–Zehnder interferometer
    13. 5.13     Wheeler’s delayed choice gedanken experiment
    14. 5.14     Interaction-free measurements
    15. 5.15     Two-photon Mach–Zehnder interferometer
    16. 5.16     Multiphoton interference and engineering of quantum states
    17. 5.17     Mach–Zehnder interferometer with two-mode squeezed vacuum as input
    18. 5.18     Balanced homodyne interferometers for measuring the squeezing of light
    19. 5.19     Manipulation of quantum states by homodyning and feed-forward
    20. 5.20     Quantum state tomography
    21. 5.21     Sensitivity of an optical interferometer
    22. 5.22     Heisenberg limited sensitivity of interferometers based on parametric amplifiers or four-wave mixers
    23. 5.23     The quantum statistics of fields at the output ports
    24. Exercises
    25. References
  11. 6  Polarization and orbital angular momentum of quantum fields
    1. 6.1     Characterization of the polarization properties of quantized fields
    2. 6.2     Polarization of quantized fields – Stokes operators
    3. 6.3     Action of polarizing devices on quantized fields
    4. 6.4     Description of unpolarized light beyond Stokes parameters
    5. 6.5     Stokes operator tomography
    6. 6.6     Orbital angular momentum of fields – HG and LG modes
    7. 6.7     Orbital Stokes operators and the Poincaré sphere
    8. 6.8     Mixed states of orbital angular momentum
    9. 6.9     Entangled states of the orbital angular momentum
    10. 6.10   Transformation of entanglement between polarization and orbital angular momentum q-plates
    11. Exercises
    12. References
  12. 7  Absorption, emission, and scattering of radiation
    1. 7.1     The interaction of radiation and matter in the electric dipole approximation
    2. 7.2     Rates for the absorption and emission of radiation
    3. 7.3     Single-mode limit – Einstein’s B coefficient and the absorption coefficient α(ω)
    4. 7.4     Scattering of radiation
    5. 7.5     Quantum interferences in scattering
    6. 7.6     Radiative decay of states – Weisskopf–Wigner theory
    7. 7.7    Control of spontaneous emission through the design of the electromagnetic vacuum
    8. Exercises
    9. References
  13. 8  Partial coherence in multimode quantum fields
    1. 8.1     Correlation functions for electromagnetic fields
    2. 8.2     Young’s interferometer and spatial coherence of the field
    3. 8.3     Photon–photon correlations – intensity interferometry
    4. 8.4     Higher-order correlation functions of the field
    5. 8.5     Interferometry in the spectral domain
    6. 8.6     Squeezing spectrum and spectral homodyne measurement
    7. 8.7     Coherence effects in two-photon absorption
    8. 8.8     Two-photon imaging – ghost imaging using G(2)
    9. Exercises
    10. References
  14. 9  Open quantum systems
    1. 9.1     Master equation description of open systems
    2. 9.2     Dissipative dynamics of harmonic oscillators
    3. 9.3     Dissipative dynamics of a two-level system
    4. 9.4     Dissipative dynamics of a multilevel system
    5. 9.5     Time correlation functions for multilevel systems
    6. 9.6     Quantum Langevin equations
    7. 9.7     Exactly soluble models for the dissipative dynamics of the oscillator
    8. 9.8     Exact dissipative dynamics of a two-level system under dephasing
    9. Exercises
    10. References
  15. 10  Amplification and attenuation of quantum fields
    1. 10.1    Quantum theory of optical amplification
    2. 10.2    Loss of nonclassicality in the amplification process
    3. 10.3    Amplification of single-photon states
    4. 10.4    Amplification of entangled fields
    5. 10.5    Realising a phase-insensitive amplifier from a phase-sensitive amplifier
    6. 10.6    Degradation of nonclassicality and entanglement due to the absorption of quantum fields
    7. 10.7    Loss of coherence on interaction with the environment
    8. Exercises
    9. References
  16. 11  Quantum coherence, interference, and squeezing in two-level systems
    1. 11.1    Two-level approximation: atomic dynamics in a monochromatic field
    2. 11.2    Application of atomic coherence – Ramsey interferometry
    3. 11.3    Atomic coherent states
    4. 11.4    Minimum uncertainty states for two-level systems – spin squeezing
    5. 11.5    Atomoc squeezed states by nonlinear unitary transformations
    6. 11.6    Atomic squeezed states produced by supersensitivity of Ramsey interferometers
    7. 11.7    Phase-space representation for a collection of two-level systems
    8. 11.8    Phase-space description of EPR correlations of spin systems
    9. Exercises
    10. References
  17. 12  Cavity quantum electrodynamics
    1. 12.1    Exact solution of the Jaynes–Cummings model: dressed states
    2. 12.2    Collapse and revival phenomena in JCM
    3. 12.3    Dispersive limit of the JCM
    4. 12.4    Dissipative processes in cavity QED – the master equation
    5. 12.5    Spectroscopy of the ladder of dressed states
    6. 12.6    Multi-atom effects in cavity QED
    7. 12.7    Effective dipole–dipole interaction in a dispersive cavity from Lamb shift of the vacuum
    8. 12.8    Atomic cat states using multi-atom dispersive JCM
    9. 12.9    Application of atomic cat states in Heisenberg limited measurements
    10. 12.10    Engineering anti-Jaynes–Cummings interaction
    11. 12.11    QED in coupled cavity arrays – single-photon switch
    12. Exercises
    13. References
  18. 13  Absorption, emission, and scattering from two-level atoms
    1. 13.1    Effects of relaxation: optical Bloch equations
    2. 13.2    Absorption and amplification of radiation by a strongly pumped two-level system
    3. 13.3    Resonance fluorescence from a coherently driven two-level atom
    4. 13.4    Quantum dynamics of the two-level atom and spectrum of fluorescence
    5. Exercises
    6. References
  19. 14  Quantum interference and entanglement in radiating systems
    1. 14.1    Young’s interference with microscopic slits – atoms as slits
    2. 14.2    Spatial bunching and antibunching of photons
    3. 14.3    Interference in radiation from two incoherently excited atoms
    4. 14.4    Atom–photon entanglement
    5. 14.5    Atom–atom entanglement via detection of spontaneously emitted photons
    6. 14.6    Multi-atom entanglement
    7. 14.7    Quantum entanglement in Dicke states and superradiance
    8. 14.8    Multi-path quantum interference as the source of Dicke superradiance
    9. 14.9    Entanglement of photons produced in an atomic cascade
    10. Exercises
    11. References
  20. 15  Near field radiative effects
    1. 15.1    Near field radiative effects – coupling between dipoles
    2. 15.2    Radiative coupling between dipoles and dynamics
    3. 15.3    Vacuum-induced deterministic entanglement
    4. 15.4    Two-photon resonance induced by near field radiative effects
    5. 15.5    The dipole blockade
    6. Exercises
    7. References
  21. 16  Decoherence and disentanglement in two-level systems
    1. 16.1    Decoherence due to the interaction of a two-level system with the environment
    2. 16.2    Disentanglement in two-level systems
    3. 16.3    Decoherence-free subspace
    4. 16.4    Protection of decoherence due to dephasing via dynamical decoupling
    5. 16.5    Control of the spectral density of environment for protection against decoherence
    6. 16.6    Modulation produced protection against disentanglement in cavity QED
    7. Exercises
    8. References
  22. 17  Coherent control of the optical properties
    1. 17.1    A simple model for coherent control
    2. 17.2    Dark states and coherent population trapping
    3. 17.3    EIT in single-atom fluorescence
    4. 17.4    Control of two-photon absorption
    5. 17.5    Vacuum-induced coherence and interference
    6. Exercises
    7. References
  23. 18  Dispersion management and ultraslow light
    1. 18.1    Group velocity and propagation in a dispersive medium
    2. 18.2    Electromagnetically induced waveguides
    3. 18.3    Storage and retrieval of optical pulses
    4. 18.4    Adiabatons and storage and retrieval of pulses
    5. 18.5    Non-EIT mechanisms for ultraslow light
    6. Exercises
    7. References
  24. 19  Single photons and nonclassical light in integrated structures
    1. 19.1    Quantum optics in a coupled array of waveguides
    2. 19.2    The Hong–Ou–Mandel interference in a system of two coupled waveguides
    3. 19.3    Single-photon transport and coherent Bloch oscillations in a coupled array
    4. 19.4    The Anderson localization of quantum fields in coupled waveguide arrays
    5. 19.5    Discrete quantum walks via waveguide couplers on a chip
    6. Exercises
    7. References
  25. 20  Quantum optical effects in nano-mechanical systems
    1. 20.1    The radiation pressure on the nano-mechanical mirror
    2. 20.2    Basic quantum Langevin equations for the coupled system of cavity and NMO
    3. 20.3    Steady-state solution of quantum Langevin equations in the mean field limit and bistability
    4. 20.4    Quantum fluctuations in optomechanical systems
    5. 20.5    Sideband cooling of the nano-mechanical mirror
    6. 20.6    Normal-mode splitting
    7. 20.7    Squeezing of a nano-mechanical oscillator
    8. 20.8    Electromagnetically induced transparency (EIT) in the mechanical effects of light
    9. 20.9    Quantized states of the nano-mechanical mirror coupled to the cavity
    10. Exercises
    11. References
  26. Index