Advances in technology often rely on a world of photons as the basic units of light. Increasingly one reads of photons as essential to enterprises in Photonics and Quantum Technology, with career and investment opportunities. Notions of photons have evolved from the energy-packet crowds of Planck and Einstein, the later field modes of Dirac, the seeming conflict of wave and particle photons, to the ubiquitous laser photons of today. Readers who take interest in contemporary technology will benefit from learning what photons are now considered to be, and how our views of photons have changed -- in learning about the various operational definitions that have been used for photons and their association with a variety of quantum-state manipulations that include Quantum Information, astronomical sources and crowds of photons, the boxed fields of Cavity Quantum Electrodynamics and single photons on demand, the photons of Feynman and Glauber, and the photon constituents of the Standard Model of Particle Physics. The narrative points to contemporary photons as causers of change to atoms, as carriers of messages, and as subject to controllable creation and alteration -- a considerable diversity of photons, not just one kind.
Our Changing Views of Photons: A Tutorial Memoir presents those general topics as a memoir of the author's involvement with physics and the photons of theoretical Quantum Optics, written conversationally for readers with no assumed prior exposure to science. It offers lay readers a glimpse of scientific discovery -- of how ideas become practical, as a small scientific community reconsiders its assumptions and offers the theoretical ideas that are then developed, revised, and adopted into technology for daily use.
For readers who want a more detailed understanding of the theory, three substantial appendices provide tutorials that, assuming no prior familiarity, proceed from a very elementary start to basics of discrete states and abstract vector spaces; Lie groups; notions of quantum theory and the Schrödinger equation for quantum-state manipulation; Maxwell's equations for electromagnetism, with wave modes that become photons, possibly exhibiting quantum entanglement; and the coupling of atoms and fields to create quasiparticles. The appendices can be seen as a companion to traditional textbooks on Quantum Optics.
Author(s): Bruce W. Shore
Publisher: Oxford University Press
Year: 2020
Language: English
Pages: 512
City: New York
Cover
Our Changing Views of Photons: A Tutorial Memoir
Copyright
Preface
The cartoons
Contents
1 Introduction
1.1 Overview of the Memoir narrative
1.2 Preliminaries: Defining terms
1.3 Models of physical phenomena
1.4 Caveats
2 Basic background: Everyday physics and its math
2.1 Some mathematics
2.1.1 Mathematics of events and actions
2.1.2 Mathematics of numbers and equations
2.2 Particles: Elementary and structured
2.2.1 Indivisibility
2.2.2 Atoms
2.2.3 Electrons
2.2.4 Nuclei and their constituents
2.2.5 Antimatter
2.2.6 Particle sizes
2.2.7 Radiations
2.2.8 Particle spin: Fermions and bosons
2.3 Aggregates: Fluids, flows, waves and granules
2.3.1 Fluids and flows
2.3.2 Matter waves
2.3.3 Electromagnetic waves
2.3.4 Wave character
2.3.5 Granular character
2.4 Free space: The Vacuum
2.5 Forces and vectors
2.5.1 Force
2.5.2 Vectors
2.5.3 Forces from fields
2.6 Energy and heat
2.7 Equations of change: Particles and fluids
2.7.1 Particles: Newtonian mechanics
2.7.2 Wave equations
2.7.3 Wave attributes
2.8 Light: Electromagnetic radiation
2.8.1 Coherence
2.8.2 Incoherent sources
2.8.3 Coherent sources
2.8.4 Visualizing chaotic vs. coherent; Eddington’s photons
2.8.5 Pencil beams; Rays
2.9 Possible radiation granularity; Photons
2.10 Angular momentum: Orbital and spin
2.11 Probabilities
2.11.1 Events
2.11.2 Evaluating probabilities; Classical and quantum
2.11.3 Properties of probabilities
2.11.4 Random variables; Expectation values
2.11.5 Conditional probabilities
2.12 Quantum states
2.12.1 The uncertainty (indeterminacy) principle
2.12.2 Defining a quantum state
3 The photons of Planck, Einstein, and Bohr
3.1 Thermal light: Planck quanta
3.1.1 Planck quanta
3.1.2 Thermal averages and fluctuations
3.2 Spectroscopy; Photons as energy packets
3.3 Discrete energies of atoms
3.4 The Bohr-Einstein emission and absorption photons
3.5 The photoelectric effect; The Einstein photon
3.6 Scattered photons: Doppler and Compton
3.6.1 Photons and Doppler shifts
3.6.2 Compton photons
3.7 The wave-particle photon
3.7.1 Wave-particle duality
3.7.2 Complementarity
3.8 Revised views of Planck, Einstein, and Compton photons
3.9 Beyond emitted and absorbed quanta
3.10 Bohr
4 The photons of Dirac
4.1 Modes: Electron orbitals and cavity radiation; Superpositions
4.1.1 Discrete electron modes
4.1.2 Discrete radiation-field modes
4.1.3 Superpositions and vortices
4.1.4 Knotted fields
4.2 Dirac’s photons: Mode increments
4.2.1 Dirac quantization steps
4.2.2 Photons as field-mode increments
4.2.3 Specifying Dirac photons
4.3 Emission and absorption photons
4.3.1 Emitted photon
4.3.2 Detected photon
4.3.3 Converting between modes
4.4 Comments on Dirac Photons
4.4.1 Next steps
5 Photons as population changers
5.1 Interactions, decoherence, and ensembles
5.1.1 Energies and interactions
5.1.2 The quantum vacuum
5.1.3 The environment; Decoherence
5.1.4 Ensembles
5.2 Einstein-equation populations; Equilibrium
5.3 Einstein-equation photons; Lasers
5.4 Coherent population changes
5.5 Rabi oscillations
5.6 Assured two-state excitation
5.7 Single atoms, single boxed photons
5.8 The Jaynes-Cummings model; Evidence for photons
5.9 Coherent change; Interaction linkages
5.10 Morris-Shore photons
5.11 Pulsed excitation
5.11.1 Pulse timings; Three states
5.11.2 Detuned adiabatic passage; Population return
5.12 Objectives of quantum-state manipulations; Superpositions
6 Photon messengers
6.1 Astronomical photons
6.1.1 Missing photons; Dark matter
6.1.2 Photons in general relativity
6.2 Scattered photons
6.3 Electrical circuits
6.4 Information
6.4.1 Classical information: Bits and bytes
6.4.2 Quantum information: Qubits
6.4.3 Stored and moving information
6.5 Photons as information carriers
6.5.1 Photon time dependence
6.5.2 Characterizing radiation by its coherence
6.6 The no-cloning theorem
6.6.1 Quantum teleportation
6.7 Correlation and entanglement
6.7.1 Correlation
6.7.2 Entanglement
7 Manipulating photons
7.1 Particle conservation
7.2 Creating single photons
7.3 Detecting photons
7.4 Altering photons
7.5 Storing and restoring photons
7.6 Verifying photons
8 Overview; Ways of regarding photons
8.1 Historical photons
8.2 Pulsed photons
8.3 Steady, Feynman photons
8.3.1 Special relativity math
8.3.2 The quaternion photon
8.3.3 The Wigner photon
8.3.4 Gauge photons
8.3.5 Photon uncertainty
8.4 Crowds and singles
8.4.1 Multiple-photon and multiphoton
8.4.2 Creating multiphoton fields
8.4.3 Ultra-high intensity
8.4.4 Mixed-state fields
8.5 Interacting photons
8.5.1 Free-space photons
8.5.2 Photons in matter
8.6 Doing without photons
8.6.1 Semiclassical, photonless fields
8.6.2 Heisenberg equations
8.6.3 Denial of photons
8.6.4 Macroscopic quanta, without photons
8.7 Alternatives to photons
8.8 Contemporary evidence for photons
8.9 Overlooked photons
9 Finale
9.1 A concluding thought
9.2 Basic references
9.3 Acknowledgments
The appendices
Appendix A Atoms and their mathematics
A.1 Classical equations of particle motion
A.1.1 Physical, Euclidean vectors
A.1.2 Newton’s equations
A.1.3 Collective coordinates
A.1.4 Lagrangian dynamics
A.1.5 The principle of least action
A.1.6 Hamiltonian dynamics
A.1.7 Example: The harmonic oscillator
A.1.8 System points and phase space
A.1.9 Summary of particle dynamics
A.1.10 Distributed mass: Fluid equations
A.2 Measurement; Sizes
A.2.1 Electron size
A.2.2 Atom size
A.2.3 Photon size: Resolution and wavelength
A.3 Abstract vector spaces
A.3.1 Property spaces
A.3.2 Normed and metric spaces
A.3.3 Quantum Hilbert space
A.3.4 Coherent superpositions
A.3.5 Matrices and operators; Eigenvectors
A.4 Quantization
A.4.1 Quantum measurement math; Commutators
A.4.2 Uncertainty; Variance
A.4.3 Quantization procedure
A.5 Wave mechanics and wavefunctions
A.6 Phase space
A.7 Matrix mechanics and operators
A.7.1 The harmonic oscillator; Number operator
A.7.2 Angular-momentum operators; Coupling and spin
A.8 The statevector
A.8.1 Abstract-space unit vectors
A.8.2 Degrees of freedom; Multiple particles
A.8.3 Multiparticle states and symmetry; Spin and statistics
A.8.4 Statevector time dependence; Superpositions
A.9 The time-dependent Schr¨odinger equation
A.9.1 The statevector equation of motion
A.9.2 Heisenberg equations
A.9.3 The semiclassical Hamiltonian
A.9.4 The coupled equations for the TDSE
A.9.5 The multipole Hamiltonian
A.9.6 The rotating-wave approximation (RWA)
A.9.7 Probability loss
A.9.8 Detuning shifts
A.9.9 The propagator
A.10 Two-state coherent excitation
A.10.1 Approximations
A.10.2 Rabi oscillations
A.11 Degeneracies and ensembles
A.11.1 Rabi frequency between sublevels
A.11.2 Ensemble averages
A.12 Adiabatic elimination; Multiphoton interaction
A.13 Adiabatic change
A.13.1 Adiabatic states
A.13.2 Adiabatic following
A.14 Density matrices and mixed states
A.14.1 Time dependence
A.14.2 Bloch equations
A.14.3 Rate equation limit
A.14.4 The Lorentz atom
A.14.5 Torque equations; Adiabatic following
A.14.6 Two-state adiabatic following
A.14.7 Two views of excitation: NMR
A.14.8 Multistate adiabatic following
A.15 Three-state pulsed coherent excitation
A.15.1 Multiphoton population cycling
A.15.2 Weak probe field: Autler-Townes splitting
A.15.3 Three-state adiabatic following
A.15.4 The dark adiabatic state
A.15.5 Stimulated-Raman adiabatic passage (STIRAP)
A.16 Radiative rate equations
A.16.1 The Einstein rates
A.16.2 Fermi’s Golden Rule; The Purcell effect
A.16.3 The two-level radiative rate equations
A.17 Algebras
A.18 Group theory
A.18.1 Coordinate transformations
A.18.2 Mathematical groups
A.18.3 Lie groups
A.18.4 Lie algebras
A.18.5 Constants of motion; Noether’s theorem
A.19 The Standard Model of particle physics
A.19.1 The fundamental particles: Leptons and quarks
A.19.2 Quark composites: Hadrons, mesons, baryons
A.19.3 The interactions: Photons, mesons, and gluons
Appendix B Radiation and photons
B.1 Electromagnetic equations in free space
B.1.1 The free-space Maxwell equations
B.1.2 Density of field energy and momentum
B.1.3 Plane-wave fields
B.1.4 The free-space wave equations
B.1.5 Helmholtz equations; Modes
B.1.6 Unit vectors for fields
B.1.7 Polarization and Stokes parameters
B.1.8 Wave-particle complementarity for photons
B.1.9 Vector potentials; Gauge
B.1.10 Field angular momentum
B.1.11 The Riemann-Silberstein (RS) field
B.2 Classical field modes; Examples
B.2.1 Simple beams
B.2.2 Cartesian coordinates: Plane waves
B.2.3 Elaborate beams: Vortices and orbital angular momentum
B.2.4 Cylindrical coordinates: Bessel beams
B.2.5 The paraxial wave equation; Gaussian beams
B.2.6 Spherical coordinates: Multipoles
B.2.7 Spontaneous-emission dipole fields
B.2.8 Multiple-path modes
B.2.9 Summary
B.3 Quantized field modes; Dirac photons
B.3.1 Spatial modes
B.3.2 Field-mode quantization; Photons
B.3.3 Photon-number operator; Number states
B.3.4 Single-photon superpositions
B.3.5 Quantization without photon numbers
B.3.6 The radiation-field Hamiltonian with photons
B.3.7 Traveling-waves, standing-waves, and RS photons
B.3.8 Vector properties
B.3.9 Photon angular momentum
B.4 Photon number-state superpositions
B.4.1 Coherent states
B.4.2 Phase states
B.4.3 Photon distributions
B.4.4 Quadrature operators and squeezed states
B.4.5 Characterizing fields by density matrix
B.5 Temporal variations; Quantum character
B.5.1 Fourier components; Coherence and bandwidth
B.5.2 Pulse shaping
B.5.3 Field correlations
B.5.4 Correlation functions
B.5.5 Characterizing fields by their coherence
B.6 Alternative views of photons
B.7 Thermal equilibrium; Planck photons
B.7.1 The Boltzmann formula
B.7.2 The Planck formula
B.8 Incoherent radiation; Photon crowds
B.8.1 Radiation attenuation
B.8.2 Radiation and scattering theory
B.8.3 Radiation scattering examples
Appendix C Coupled atom and field equations
C.1 Field sources
C.2 The Maxwell equations in matter
C.2.1 Polarization and magnetization fields
C.2.2 Inhomogeneous wave equations in matter
C.3 Bulk-matter steady response
C.3.1 Homogeneous wave equations in linearly-responding matter
C.3.2 Steady paraxial beams; Guided waves
C.3.3 Reflection and refraction
C.3.4 Evanescent fields
C.3.5 Beam splitters
C.3.6 Nonlinear optics
C.4 Bulk-matter transient sources
C.4.1 One dimensional short-pulse propagation
C.4.2 Dark-state polaritons; Spin waves
C.5 The atom-photon Hamiltonian
C.5.1 The two-state atom with photons
C.5.2 Radiative rates with photons
C.6 The Jaynes-Cummings model
C.6.1 JCM solutions
C.6.2 Photon-averaged JCM: Proof of photons
C.7 Cavity STIRAP
C.8 Product spaces; Entanglement
C.8.1 Separability and correlation
C.8.2 Quantifying correlations
C.8.3 Reduced density matrices
C.8.4 Polarization, concurrence, and correlation
C.8.5 Entanglement
Coda
The annual Xmas cartoons
References
Index
