Atom-Photon Interactions: Basic Processes and Applications

✍ Scribed by Claude Cohen-Tannoudji, Jacques Dupont-Roc, Gilbert Grynberg

• Publisher: Wiley-VCH
• Year: 1998
• Tongue: English
• Leaves: 679
• Category: Library

✦ Synopsis

Atom-Photon Interactions: Basic Processes and Applications allows the reader to master various aspects of the physics of the interaction between light and matter. It is devoted to the study of the interactions between photons and atoms in atomic and molecular physics, quantum optics, and laser physics. The elementary processes in which photons are emitted, absorbed, scattered, or exchanged between atoms are treated in detail and described using diagrammatic representation. The book presents different theoretical approaches, including:

• Perturbative methods
• The resolvent method
• Use of the master equation
• The Langevin equation
• The optical Bloch equations
• The dressed-atom approach

Each method is presented in a self-contained manner so that it may be studied independently. Many applications of these approaches to simple and important physical phenomena are given to illustrate the potential and limitations of each method.

✦ Table of Contents

Front cover
Title page
Date-line
Contents
Preface
Introduction
I TRANSITION AMPLITUDES IN ELECTRODYNAMICS
Introduction
A. Probability Amplitude Associated with a Physical Process
B. Time Dependence of Transition Amplitudes
1. Coupling between Discrete Isolated States
2. Resonant Coupling between a Discrete Level and a Continuum
3. Couplings inside a Continuum or between Continua
C. Application to Electrodynamics
1. Coulomb Gauge Hamiltonian
2. Expansion in Powers of the Charges $q_\alpha$
3. Expansion in Powers of the Interaction with the Transverse Field
4. Advantages of Including the Coulomb Interaction in the Particle Hamiltonian
5. Diagrammatic Representation of Transition Amplitudes
Complement A_I — Perturbative Calculation of Transition Amplitudes — Some Useful Relations
Introduction
1. Interaction Representation
2. Perturbative Expansion of Transition Amplitudes
3. Transition Probability
Complement B_I — Description of the Effect of a Perturbation by an Effective Hamiltonian
1. Introduction—Motivation
2. Principle of the Method
3. Determination of the Effective Hamiltonian
4. Case of Two Interacting Systems
Complement C_I — Discrete Level Coupled to a Broad Continuum: A Simple Model
Introduction
1. Description of the Model
2. Stationary States of the System. Traces of the Discrete State in the New Continuum
3. A Few Applications of This Simple Model
4. Generalization to More Realistic Continua. Diagonalization of the Hamiltonian without Discretization
II A SURVEY OF SOME INTERACTION PROCESSES BETWEEN PHOTONS AND ATOMS
Introduction
A. Emission Process: A New Photon Appears
1. Spontaneous Emission between Two Discrete Atomic Levels. Radiative Decay of an Excited Atomic State
2. Spontaneous Emission between a Continuum State and a Discrete State
3. Spontaneous Emission between Two States of the Ionization Continuum—Bremsstrahlung
B. Absorption Process: A Photon Disappears
1. Absorption between Two Discrete States
2. Absorption between a Discrete State and a Continuum State
3. Absorption between Two States of the Ionization Continuum: Inverse Bremsstrahlung
4. Influence of the Initial State of the Field on the Dynamics of the Absorption Process
C. Scattering Process: A Photon Disappears and Another Photon Appears
1. Scattering Amplitude—Diagrammatic Representation
2. Different Types of Photon Scattering by an Atomic or Molecular System
3. Resonant Scattering
D. Multiphoton Processes: Several Photons Appear or Disappear
1. Spontaneous Emission of Two Photons
2. Multiphoton Absorption (and Stimulated Emission) between Two Discrete Atomic States
3. Multiphoton Ionization
4. Harmonic Generation
5. Multiphoton Processes and Quasi-Resonant Scattering
E. Radiative Corrections: Photons Are Emitted and Reabsorbed (or Absorbed and Reemitted)
1. Spontaneous Radiative Corrections
2. Stimulated Radiative Corrections
F. Interaction by Photon Exchange
1. Exchange of Transverse Photons between Two Charged Particles: First Correction to the Coulomb Interaction
2. Van der Waals Interaction between Two Neutral Atoms
Complement A_II — Photodetection Signals and Correlation Functions
Introduction
1. Simple Models of Atomic Photodetectors
2. Excitation Probability and Correlation Functions
3. Broadband Photodetection
4. Narrow-Band Photodetection
5. Double Photodetection Signals
Complement B_II — Radiative Corrections in the Pauli-Fierz Representation
Introduction
1. The Pauli-Fierz Transformation
2. The Observables in the New Picture
3. Physical Discussion
III NONPERTURBATTVE CALCULATION OF TRANSITION AMPLITUDES
Introduction
A. Evolution Operator and Resolvent
1. Integral Equation Satisfied by the Evolution Operator
2. Green's Functions—Propagators
3. Resolvent of the Hamiltonian
B. Formal Resummation of the Perturbation Series
1. Diagrammatic Method Explained on a Simple Model
2. Algebraic Method Using Projection Operators
3. Introduction of Some Approximations
C. Study of a Few Examples
1. Evolution of an Excited Atomic State
2. Spectral Distribution of Photons Spontaneously Emitted by an Excited Atom
3. Indirect Coupling between a Discrete Level and a Continuum. Example of the Lamb Transition
4. Indirect Coupling between Two Discrete States. Multi-photon Transitions
Complement A_III — Analytic Properties of the Resolvent
Introduction
1. Analyticity of the Resolvent outside the Real Axis
2. Singularities on the Real Axis
3. Unstable States and Poles of the Analytic Continuation of the Resolvent
4. Contour Integral and Corrections to the Exponential Decay
Complement B_III — Nonperturbative Expressions for the Scattering Amplitudes of a Photon by an Atom
Introduction
1. Transition Amplitudes between Unperturbed States
2. Introducing Exact Asymptotic States
3. Transition Amplitude between Exact Asymptotic States
Complement C_III - Discrete State Coupled to a Finite-Width Continuum: From the Weisskopf-Wigner Exponential Decay to the Rabi Oscillation
1. Introduction—Overview
2. Description of the Model
3. The Important Physical Parameters
4. Graphical Discussion
5. Weak Coupling Limit
6. Intermediate Coupling. Critical Coupling
7. Strong Coupling
IV RADIATION CONSIDERED AS A RESERVOIR: MASTER EQUATION FOR THE PARTICLES
A. Introduction—Overview
B. Derivation of the Master Equation for a Small System $\mathcal{A}$ Interacting with a Reservoir $\mathcal{R}$
1. Equation Describing the Evolution of the Small System in the Interaction Representation
2. Assumptions Concerning the Reservoir
3. Perturbative Calculation of the Coarse-Grained Rate of Variation of the Small System
4. Master Equation in the Energy-State Basis
C. Physical Content of the Master Equation
1. Evolution of Populations
2. Evolution of Coherences
D. Discussion of the Approximations
1. Order of Magnitude of the Evolution Time for $\mathcal{A}$
2. Condition for Having Two Time Scales
3. Validity Condition for the Perturbative Expansion
4. Factorization of the Total Density Operator at Time $t$
5. Summary
E. Application to a Two-Level Atom Coupled to the Radiation Field
1. Evolution of Internal Degrees of Freedom
2. Evolution of Atomic Velocities
Complement A_IV — Fluctuations and Linear Response Application to Radiative Processes
Introduction
1. Statistical Functions and Physical Interpretation of the Master Equation
2. Applications to Radiative Processes
Complement B_IV — Master Equation for a Damped Harmonic Oscillator
1. The Physical System
2. Operator Form of the Master Equation
3. Master Equation in the Basis of the Eigenstates of $H_A$
4. Master Equation in a Coherent State Basis
Complement C_IV — Quantum Langevin Equations for a Simple Physical System
Introduction
1. Review of the Classical Theory of Brownian Motion
2. Heisenberg-Langevin Equations for a Damped Harmonic Oscillator
V OPTICAL BLOCH EQUATIONS
Introduction
A. Optical Bloch Equations for a Two-Level Atom
1. Description of the Incident Field
2. Approximation of Independent Rates of Variation
3. Rotating-Wave Approximation
4. Geometric Representation in Terms of a Fictitious Spin
B. Physical Discussion—Differences with Other Evolution Equations
1. Differences with Relaxation Equations. Couplings between Populations and Coherences
2. Differences with Hamiltonian Evolution Equations
3. Differences with Heisenberg-Langevin Equations
C. First Application—Evolution of Atomic Average Values
1. Internal Degrees of Freedom
2. External Degrees of Freedom. Mean Radiative Forces
D. Properties of the Light Emitted by the Atom
1. Photodetection Signals. One- and Two-Time Averages of the Emitting Dipole Moment
2. Total Intensity of the Emitted Light
3. Spectral Distribution of the Emitted Light in Steady State
Complement A_V — Bloch-Langevin Equations and Quantum Regression Theorem
Introduction
1. Coupled Heisenberg Equations for the Atom and the Field
2. Derivation of the Heisenberg-Langevin Equations
3. Properties of Langevin Forces
VI THE DRESSED ATOM APPROACH
A. Introduction: The Dressed Atom
B. Energy Levels of the Dressed Atom
1. Model of the Laser Beam
2. Uncoupled States of the Atom + Laser Photons System
3. Atom-Laser Photons Coupling
4. Dressed States
5. Physical Effects Associated with Absorption and Induced Emission
C. Resonance Fluorescence Interpreted as a Radiative Cascade of the Dressed Atom
1. The Relevant Time Scales
2. Radiative Cascade in the Uncoupled Basis
3. Radiative Cascade in the Dressed State Basis
D. Master Equation for the Dressed Atom
1. General Form of the Master Equation
2. Master Equation in the Dressed State Basis in the Secular Limit
3. Quasi-Steady State for the Radiative Cascade
E. Discussion of a Few Applications
1. Widths and Weights of the Various Components of the Fluorescence Triplet
2. Absorption Spectrum of a Weak Probe Beam
3. Photon Correlations
4. Dipole Forces
Complement A_VI — The Dressed Atom in the Radio-Frequency Domain
Introduction
1. Resonance Associated with a Level Crossing or Anti-crossing
2. Spin $\frac{1}{2}$ Dressed by Radio-Frequency Photons
3. The Simple Case of Circularly Polarized Photons
4. Linearly Polarized Radio-Frequency Photons
Complement B_VI — Collisional Processes in the Presence of Laser Irradiation
Introduction
1. Collisional Relaxation in the Absence of Laser Irradiation
2. Collisional Relaxation in the Presence of Laser Irradiation
3. Collision-Induced Modifications of the Emission and Absorption of Light by the Atom. Collisional Redistribution
4. Sketch of the Calculation of the Collisional Transfer Rate
Exercises
1. Calculation of the Radiative Lifetime of an Excited Atomic Level. Comparison with the Damping Time of a Classical Dipole Moment
2. Spontaneous Emission of Photons by a Trapped Ion. Lamb-Dicke Effect
3. Rayleigh Scattering
4. Thomson Scattering
5. Resonant Scattering
6. Optical Detection of a Level Crossing between Two Excited Atomic States
7. Radiative Shift of an Atomic Level. Bethe Formula for the Lamb Shift
8. Bremsstrahlung. Radiative Corrections to Elastic Scattering by a Potential
9. Low-Frequency Bremsstrahlung. Nonperturbative Treatment of the Infrared Catastrophe
10. Modification of the Cyclotron Frequency of a Particle due to Its Interactions with the Radiation Field
11. Magnetic Interactions between Spins
12. Modification of an Atomic Magnetic Moment due to Its Coupling with Magnetic Field Vacuum Fluctuations
13. Excitation of an Atom by a Wave Packet: Broadband Excitation and Narrow-Band Excitation
14. Spontaneous Emission by a System of Two Neighboring Atoms. Superradiant and Subradiant States
15. Radiative Cascade of a Harmonic Oscillator
16. Principle of the Detailed Balance
17. Equivalence between a Quantum Field in a Coherent State and an External Field
18. Adiabatic Elimination of Coherences and Transformation of Optical Bloch Equations into Relaxation Equations
19. Nonlinear Susceptibility for an Ensemble of Two-Level Atoms. A Few Applications
20. Absorption of a Probe Beam by Atoms Interacting with an Intense Beam. Application to Saturated Absorption
APPENDIX QUANTUM ELECTRODYNAMICS IN THE COULOMB GAUGE—SUMMARY OF THE ESSENTIAL RESULTS
1. Description of the Electromagnetic Field
2. Particles
3. Hamiltonian and Dynamics in the Coulomb Gauge
4. State Space
5. The Long-Wavelength Approximation and the Electric Dipole Representation
References
Index
Back cover