Chapter
3.3 Field Interaction Representation
3.4 Semiclassical Dressed States
3.5.2 Relaxation Included
3.7 Appendix A: Density Matrix Equations in the Rotating-Wave Approximation
3.7.1 Schrödinger Representation
3.7.2 Interaction Representation
3.7.3 Field Interaction Representation
3.7.5 Semiclassical Dressed-State Representation
3.8 Appendix B: Collision Model
4 Applications of the Density Matrix Formalism
4.1 Density Matrix for an Ensemble
4.2 Absorption Coefficient—Stationary Atoms
4.3 Simple Inclusion of Atomic Motion
5 Density Matrix Equations: Atomic Center-of-Mass Motion, Elementary Atom Optics, and Laser Cooling
5.2 Atom in a Single Plane-Wave Field
5.3.2 Focused Plane Wave: Atom Trapping
5.3.3 Standing-Wave Field: Laser Cooling
5.5 Appendix: Quantization of the Center-of-Mass Motion
5.5.1 Coordinate Representation
5.5.2 Momentum Representation
5.5.3 Sum and Difference Representation
5.5.4 Wigner Representation
6 Maxwell-Bloch Equations
6.1.1 Pulse Propagation in a Linear Medium
6.2 Maxwell-Bloch Equations
6.2.1 Slowly Varying Amplitude and Phase Approximation (SVAPA)
6.3 Linear Absorption and Dispersion—Stationary Atoms
6.4 Linear Pulse Propagation
6.5 Other Problems with the Maxwell-Bloch Equations
6.7 Appendix: Slowly Varying Amplitude and Phase Approximation—Part II
7 Two-Level Atoms in Two or More Fields: Introduction to Saturation Spectroscopy
7.1 Two-Level Atoms and N Fields—Third-Order Perturbation Theory
7.2 N = 2: Saturation Spectroscopy for Stationary Atoms
7.3 N = 2: Saturation Spectroscopy for Moving Atoms in Counterpropagating Fields—Hole Burning
7.3.1 Hole Burning and Atomic Population Gratings
7.3.2 Probe Field Absorption
7.4 Saturation Spectroscopy in Inhomogeneously Broadened Solids
7.6 Appendix A: Saturation Spectroscopy—Stationary Atoms in One Strong and One Weak Field
7.7 Appendix B: Four-Wave Mixing
8 Three-Level Atoms: Applications to Nonlinear Spectroscopy—Open Quantum Systems
8.1 Hamiltonian for Λ, V, and Cascade Systems
8.1.1 Cascade Configuration
8.1.2 V and Λ Configurations
8.2 Density Matrix Equations in the Field Interaction Representation
8.3 Steady-State Solutions—Nonlinear Spectroscopy
8.3.2 Moving Atoms: Doppler Limit
8.4 Autler-Townes Splitting
8.5 Two-Photon Spectroscopy
8.6 Open versus Closed Quantum Systems
9 Three-Level Λ Atoms: Dark States, Adiabatic Following, and Slow Light
9.2 Adiabatic Following—Stimulated Raman Adiabatic Passage
9.4 Effective Two-State Problem for the Λ Configuration
9.6 Appendix: Force on an Atom in the Λ Configuration
10.1 Coherent Transient Signals
10.2 Free Polarization Decay
10.2.1 Homogeneous Broadening
10.2.2 Inhomogeneous Broadening
10.4 Stimulated Photon Echo
10.5 Optical Ramsey Fringes
10.8 Appendix A: Transfer Matrices in Coherent Transients
10.9 Appendix B: Optical Ramsey Fringes in Spatially Separated Fields
11 Atom Optics and Atom Interferometry
11.1 Review of Kirchhoff-Fresnel Diffraction
11.1.1 Electromagnetic Diffraction
11.1.2 Quantum-Mechanical Diffraction
11.2.1 Scattering by an Amplitude Grating
11.2.2 Scattering by Periodic Structures—Talbot Effect
11.2.3 Scattering by Phase Gratings—Atom Focusing
11.3.1 Microfabricated Elements
11.3.2 Counterpropagating Optical Field Elements
12 The Quantized, Free Radiation Field
12.1 Free-Field Quantization
12.2 Properties of the Vacuum Field
12.2.1 Single-Photon State
12.2.2 Single-Mode Number State
12.2.3 Quasiclassical or Coherent States
12.3 Quadrature Operators for the Field
12.4 Two-Photon Coherent States or Squeezed States
12.4.1 Calculation of U[sub(L)](z)
12.7 Appendix: Field Quantization
12.7.2 Longitudinal and Transverse Vector Fields
12.7.3 Transverse Electromagnetic Field
13 Coherence Properties of the Electric Field
13.1 Coherence: Some General Concepts
13.1.1 Time versus Ensemble Averages
13.2 Classical Fields: Correlation Functions
13.2.1 First-Order Correlation Function
13.2.3 Intensity Correlations—Second-Order Correlation Function
13.2.4 Hanbury Brown and Twiss Experiment
13.3 Quantized Fields: Density Matrix for the Field and Photon Optics
13.3.4 Correlation Functions for the Field
14 Photon Counting and Interferometry
14.1.1 Photodetection of Classical Fields
14.1.2 Photodetection of Quantized Fields
14.2 Michelson Interferometer
15 Atom–Quantized Field Interactions
15.1 Interaction Hamiltonian and Equations of Motion
15.1.1 Schrödinger Representation
15.1.2 Heisenberg Representation
15.1.4 Jaynes-Cummings Model
15.3 Generation of Coherent and Squeezed States
16.1 Spontaneous Decay Rate
16.2 Radiation Pattern and Repopulation of the Ground State
16.2.2 Repopulation of the Ground State
16.4 Appendix A: Circular Polarization
16.5 Appendix B: Radiation Pattern
16.5.1 Unpolarized Initial State
16.5.2 z-Polarized Excitation
16.5.3 Other than z-Polarized Excitation
16.6 Appendix C: Quantum Trajectory Approach to Spontaneous Decay
17 Optical Pumping and Optical Lattices
17.1.1 Traveling-Wave Fields
17.1.2 z-Polarized Excitation
17.1.3 Irreducible Tensor Basis
17.1.4 Standing-Wave and Multiple-Frequency Fields
17.2 Optical Lattice Potentials
17.4 Appendix: Irreducible Tensor Formalism
17.4.2 Density Matrix Equations
18 Sub-Doppler Laser Cooling
18.1 Cooling via Field Momenta Exchange and Differential Scattering
18.1.1 Counterpropagating Fields
18.2 Sisyphus Picture of the Friction Force for a G = 1/2 Ground State and Crossed-Polarized Fields
18.3 Coherent Population Trapping
18.5 Appendix: Fokker-Planck Approach for Obtaining the Friction Force and Diffusion Coefficients
18.5.1 Fokker-Planck Equation
18.5.2 G = 1/2; lin⊥lin Polarization
18.5.3 G = 1 to H = 2 Transition; σ[sub(+)] – σ[sub(–)] Polarization
18.5.4 Equilibrium Energy
19 Operator Approach to Atom–Field Interactions: Source-Field Equation
19.1.2 General Problem—n Field Modes
19.3 Source-Field Equation
19.4 Source-Field Approach: Examples
19.4.1 Average Field and Field Intensity in Spontaneous Emission
19.4.2 Frequency Beats in Emission: Quantum Beats
20.1 General Considerations: Perturbation Theory
20.2.1 Dressed-State Approach to Mollow Triplet
20.2.2 Source-Field Approach to Mollow Triplet
20.3 Second-Order Correlation Function for the Radiated Field
20.4 Scattering by a Single Atom in Weak Fields: G ≠ 0
21 Entanglement and Spin Squeezing
21.1 Entanglement by Absorption
21.2 Entanglement by Post-Selection—DLCZ Protocol
21.3.1 General Considerations
21.3.2 Spin Squeezing Using a Coherent Cavity Field
Principles of Laser Spectroscopy and Quantum Optics
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