Atom-Photon Interactions Basic Processes and Applications

by Cohen-Tannoudji, Claude; Dupont-Roc, Jacques; Grynberg, Gilbert

• ISBN13: 9780471293361
• ISBN10: 0471293369
• Edition: 1st
• Format: Paperback
• Copyright: 1998-03-23
• Publisher: Wiley-VCH

Summary

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.

Author Biography

Claude Cohen-Tannoudji is Professor of Physics at the CollFge de France. He is the coauthor of Quantum Mechanics, published by Wiley. Dr. Cohen-Tannoudji is a member of the French Academy of Sciences and a Foreign Associate of the National Academy of Sciences in the United States. He is a corecipient of the 1997 Nobel Prize in physics.<br> <br> Jacques Dupont-Roc holds a full-time research position at CNRS within the Laboratoire Kastler Brossel at the +cole Normale SupTrieure. Dr. Dupont-Roc earned his PhD in atomic physics at the University of Paris.<br> <br> Gilbert Grynberg is Professor of Physics at +cole Polytechnique and maintains a full-time research position at CNRS. Dr. Grynberg earned his PhD in atomic physics at the University of Paris.

Table of Contents

Preface	xxi
Introduction	1	(4)
I TRANSITION AMPLITUDES IN ELECTRODYNAMICS	5	(62)
Introduction	5	(2)
A. Probability Amplitude Associated with a Physical Process	7	(2)
B. Time Dependence of Transition Amplitudes	9	(6)
1. Coupling between Discrete Isolated States	9	(1)
2. Resonant Coupling between a Discrete Level and a Continuum	10	(2)
3. Couplings inside a Continuum or between Continua	12	(3)
C. Application to Electrodynamics	15	(8)
1. Coulomb Gauge Hamiltonian	15	(1)
2. Expansion in Powers of the Charges q(alpha)	16	(1)
3. Expansion in Powers of the Interaction with the Transverse Field	17	(1)
4. Advantages of Including the Coulomb Interaction in the Particle Hamiltonian	18	(1)
5. Diagrammatic Representation of Transition Amplitudes	19	(4)
COMPLEMENT A(I)--PERTURBATIVE CALCULATION OF TRANSITION AMPLITUDES--SOME USEFUL RELATIONS	23	(15)
Introduction	23	(1)
1. Interaction Representation	23	(2)
2. Perturbative Expansion of Transition Amplitudes	25	(6)
a. Perturbative Expansion of the Evolution Operator
b. First-Order Transition Amplitude
c. Second-Order Transition Amplitude
3. Transition Probability	31	(7)
a. Calculation of the Transition Probability to a Final State Different from the Initial State.
b. Transition Probability between Two Discrete States. Lowest-Order Calculation.
c. Case where the Final State Belongs to an Energy Continuum. Density of States.
d. Transition Rate toward a Continuum of Final States.
e. Case Where both the Initial and Final States Belong to a Continuum
COMPLEMENT B(I)--DESCRIPTION OF THE EFFECT OF A PERTURBATION BY AN EFFECTIVE HAMILTONIAN	38	(11)
1. Introduction--Motivation	38	(3)
2. Principle of the Method	41	(2)
3. Determination of the Effective Hamiltonian	43	(3)
a. Interative Calculation of S.
b. Expression of the Second-Order Effective Hamiltonian.
c. Higher-Order Terms
4. Case of Two Interacting Systems	46	(3)
COMPLEMENT C(I)--DISCRETE LEVEL COUPLED TO A BROAD CONTINUUM: A SIMPLE MODEL	49	(18)
Introduction	49	(1)
1. Description of the Model	50	(1)
a. The Discrete State and the Continuum.
b. Discretization of the Continuum.
c. Simplifying Assumptions
2. Stationary States of the System. Traces of the Discrete State in the New Continuum	51	(5)
a. The Eigenvalue Equation.
b. Graphic Determination of the New Eigenvalues.
c. Probability Density of the Discrete State in the New Continuum
3. A Few Applications of This Simple Model	56	(8)
a. Decay of the Discrete Level.
b. Excitation of the System in the Discrete Level from Another State.
c. Resonant Scattering through a Discrete Level.
d. Fano Profiles
4. Generalization to More Realistic Continua. Diagonalization of the Hamiltonian without Discretization	64	(3)
II A SURVEY OF SOME INTERACTION PROCESSES BETWEEN PHOTONS AND ATOMS	67	(98)
Introduction	67	(2)
A. Emission Process: A New Photon Appears	69	(9)
1. Spontaneous Emission between Two Discrete Atomic Levels. Radiative Decay of an Excited Atomic State	69	(4)
a. Diagrammatic Representation
b. Spontaneous Emission Rate.
c. Nonperturbative Results
2. Spontaneous Emission between a Continuum State and a Discrete State	73	(3)
a. First Example: Radiative Capture.
b. Second Example: Radiative Dissociation of a Molecule
3. Spontaneous Emission between Two States of the Ionization Continuum--Bremsstrahlung	76	(2)
B. Absorption Process: A Photon Disappears	78	(8)
1. Absorption between Two Discrete States	78	(1)
2. Absorption between a Discrete State and a Continuum State	79	(3)
a. First Example: Photoionization
b. Second Example: Photodissociation
3. Absorption between Two States of the Ionization Continuum: Inverse Bremsstrahlung	82	(1)
4. Influence of the Initial State of the Field on the Dynamics of the Absorption Process	83	(3)
C. Scattering Process: A Photon Disappears and Another Photon Appears	86	(12)
1. Scattering Amplitude--Diagrammatic Representation	86	(2)
2. Different Types of Photon Scattering by an Atomic or Molecular System	88	(5)
a. Low-Energy Elastic Scattering: Rayleigh Scattering
b. Low-Energy Inelastic Scattering: Raman Scattering
c. High-Energy Elastic Scattering: Thomson Scattering.
d. High-Energy Inelastic Scattering with the Final Atomic State in the Ionization Continuum: Compton Scattering
3. Resonant Scattering	93	(5)
D. Multiphoton Processes: Several Photons Appear or Disappear	98	(11)
1. Spontaneous Emission of Two Photons	98	(2)
2. Multiphoton Absorption (and Stimulated Emission) between Two Discrete Atomic States	100	(2)
3. Multiphoton Ionization	102	(2)
4. Harmonic Generation	104	(2)
5. Multiphoton Processes and Quasi-Resonant Scattering	106	(3)
E. Radiative Corrections: Photons Are Emitted and Reabsorbed (or Absorbed and Reemitted)	109	(9)
1. Spontaneous Radiative Corrections	109	(5)
a. Case of a Free Electron: Mass Correction.
b. Case of an Atomic Electron: Natural Width and Radiative Shift
2. Stimulated Radiative Corrections	114	(4)
F. Interaction by Photon Exchange	118	(9)
1. Exchange of Transverse Photons between Two Charged Particles: First Correction to the Coulomb Interaction	118	(3)
2. Van der Waals Interaction between Two Neutral Atoms	121	(6)
a. Small Distance: D much less than XXX
b. Large Distance XXX much less than D
COMPLEMENT A(II)--PHOTODETECTION SIGNALS AND CORRELATION FUNCTIONS	127	(20)
Introduction	127	(1)
1. Simple Models of Atomic Photodetectors	128	(1)
a. Broadband Photodetector
b. Narrow-Band Photodetector
2. Excitation Probability and Correlation Functions	129	(8)
a. Hamiltonian. Evolution Operator.
b. Calculation of the Probability That the Atom Has Left the Ground State after a Time delta t.
c. Atomic Dipole Correlation Function.
d. Field Correlation Function
3. Broadband Photodetection	137	(2)
a. Condition on the Correlation Functions.
b. Photoionization Rate
4. Narrow-Band Photodetection	139	(4)
a. Conditions on the Incident Radiation and on the Detector.
b. Excitation by a Broadband Spectrum.
c. Influence of the Natural Width of the Excited Atomic Level
5. Double Photodetection Signals	143	(4)
a. Correlation between Two Photodetector Signals
b. Sketch of the Calculation of W(II)
COMPLEMENT B(II)--RADIATIVE CORRECTIONS IN THE PAULI-FIERZ REPRESENTATION	147	(18)
Introduction	147	(1)
1. The Pauli-Fierz Transformation	148	(4)
a. Simplifying Assumptions.
b. Transverse Field Tied to a Classical Particle.
c. Determination of the Pauli-Fierz Transformation
2. The Observables in the New Picture	152	(5)
a. Transformation of the Transverse Fields
b. Transformation of the Particle Dynamical Variables.
c. Expression for the New Hamiltonian
3. Physical Discussion	157	(8)
a. Mass Correction.
b. New Interaction Hamiltonian between the Particle and the Transverse Field
c. Advantages of the New Representation.
d. Inadequacy of the Concept of a Field Tied to a Particle
III NONPERTURBATIVE CALCULATION OF TRANSITION AMPLITUDES	165	(92)
Introduction	165	(2)
A. Evolution Operator and Resolvent	167	(5)
1. Integral Equation Satisfied by the Evolution Operator	167	(1)
2. Green's Functions--Propagators	167	(3)
3. Resolvent of the Hamiltonian	170	(2)
B. Formal Resummation of the Perturbation Series	172	(11)
1. Diagrammatic Method Explained on a Simple Model	172	(2)
2. Algebraic Method Using Projection Operators	174	(5)
a. Projector onto a Subspace XXX of the Space of States.
b. Calculation of the Projection of the Resolvent in the Subspace XXX
c. Calculation of Other Projections of G(z)
d. Interpretation of the Level-Shift Operator
3. Introduction of Some Approximations	179	(4)
a. Perturbative Calculation of the Level-Shift Operator. Partial Resummation of the Perturbation Series
b. Approximation Consisting of Neglecting the Energy Dependence of the Level-Shift Operator.
C. Study of a Few Examples	183	(30)
1. Evolution of an Excited Atomic State	183	(6)
a. Nonperturbative Calculation of the Probability Amplitude That the Atom Remains Excited.
b. Radiative Lifetime and Radiative Level Shift.
c. Conditions of Validity for the Treatment of the Two Preceding Subsections
2. Spectral Distribution of Photons Spontaneously Emitted by an Excited Atom	189	(8)
a. Relevant Matrix Element of the Resolvent Operator.
b. Generalization to a Radiative Cascade
c. Natural Width and Shift of the Emitted Lines
3. Indirect Coupling between a Discrete Level and a Continuum. Example of the Lamb Transition	197	(8)
a. Introducing the Problem
b. Nonperturbative Calculation of the Transition Amplitude
c. Weak Coupling Limit. Bethe Formula
d. Strong Coupling Limit. Rabi Oscillation
4. Indirect Coupling between Two Discrete States. Multiphoton Transitions	205	(8)
a. Physical Process and Subspace XXX of Relevant States.
b. Nonperturbative Calculation of the Transition Amplitude.
c. Weak Coupling Case. Two-Photon Excitation Rate.
d. Strong Coupling Limit. Two-Photon Rabi Oscillation.
e. Higher-Order Multiphoton Transitions.
f. Limitations of the Foregoing Treatment.
COMPLEMENT A(III)--ANALYTIC PROPERTIES OF THE RESOLVENT	213	(9)
Introduction	213	(1)
1. Analyticity of the Resolvent outside the Real Axis	213	(2)
2. Singularities on the Real Axis	215	(2)
3. Unstable States and Poles of the Analytic Continuation of the Resolvent	217	(3)
4. Contour Integral and Corrections to the Exponential Decay	220	(2)
COMPLEMENT B(III)--NONPERTURBATIVE EXPRESSIONS FOR THE SCATTERING AMPLITUDES OF A PHOTON BY AN ATOM	222	(17)
Introduction	222	(1)
1. Transition Amplitudes between Unperturbed States	222	(7)
a. Using the Resolvent.
b. Transition Matrix.
c. Application to Resonant Scattering.
d. Inadequacy of Such an Approach
2. Introducing Exact Asymptotic States	229	(4)
a. The Atom in the Absence of Free Photons.
b. The Atom in the Presence of a Free Photon
3. Transition Amplitude between Exact Asymptotic States	233	(6)
a. New Definition of the S-Matrix.
b. New Expression for the Transition Matrix. Physical Discussion
COMPLEMENT C(III)--DISCRETE STATE COUPLED TO A FINITE-WIDTH CONTINUUM: FROM THE WEISSKOPF-WIGNER EXPONENTIAL DECAY TO THE RABI OSCILLATION	239	(18)
1. Introduction--Overview	239	(1)
2. Description of the Model	240	(4)
a. Unperturbed States.
b. Assumptions Concerning the Coupling.
c. Calculation of the Resolvent and of the Propagators.
d. Fourier Transform of the Amplitude U(beta) (Tan)
3. The Important Physical Parameters	244	(2)
a. The Function Delta(beta) (E).
b. The Parameter Omega(1) Characterizing the Coupling of the Discrete State with the Whole Continuum.
c. The Function Delta(beta) (E)
4. Graphical Discussion	246	(3)
a. Construction of the Curve XXX(beta) (E).
b. Graphical Determination of the Maxima of XXX(beta) (E). Classification of the Various Regimes
5. Weak Coupling Limit	249	(2)
a. Weisskopf-Wigner Exponential Decay.
b. Corrections to the Exponential Decay
6. Intermediate Coupling. Critical Coupling	251	(2)
a. Power Expansion of XXX(beta) (E) near a Maximum.
b. Physical Meaning of the Critical Coupling
7. Strong Coupling	253	(4)
IV RADIATION CONSIDERED AS A RESERVOIR: MASTER EQUATION FOR THE PARTICLES	257	(96)
A. Introduction--Overview	257	(5)
B. Derivation of the Master Equation for a Small System XXX Interacting with a Reservoir XXX	262	(10)
1. Equation Describing the Evolution of the Small System in the Interaction Representation	262	(1)
2. Assumptions Concerning the Reservoir	263	(3)
a. State of the Reservoir.
b. One-Time and Two-Time Averages for the Reservoir Observables
3. Perturbative Calculation of the Coarse-Grained Rate of Variation of the Small System	266	(3)
4. Master Equation in the Energy-State Basis	269	(3)
C. Physical Content of the Master Equation	272	(6)
1. Evolution of Populations	272	(2)
2. Evolution of Coherences	274	(4)
D. Discussion of the Approximations	278	(4)
1. Order of Magnitude of the Evolution Time for A	278	(1)
2. Condition for Having Two Time Scales	278	(1)
3. Validity Condition for the Perturbative Expansion	279	(1)
4. Factorization of the Total Density Operator at Time t	280	(1)
5. Summary	281	(1)
E. Application to a Two-Level Atom Coupled to the Radiation Field	282	(20)
1. Evolution of Internal Degrees of Freedom	282	(7)
a. Master Equation Describing Spontaneous Emission for a Two-Level Atom.
b. Additional Terms Describing the Absorption and Induced Emission of a Weak Broadband Radiation
2. Evolution of Atomic Velocities	289	(13)
a. Taking into Account the Translational Degrees of Freedom in the Master Equation.
b. Fokker-Planck Equation for the Atomic Velocity Distribution Function.
c. Evolutions of the Momentum Mean Value and Variance.
d. Steady-State Distribution. Thermodynamic Equilibrium
COMPLEMENT A(IV)--FLUCTUATIONS AND LINEAR RESPONSE APPLICATION TO RADIATIVE PROCESSES	302	(20)
Introduction	302	(1)
1. Statistical Functions and Physical Interpretation of the Master Equation	302	(10)
a. Symmetric Correlation Function.
b. Linear Susceptibility.
c. Polarization Energy and Dissipation.
d. Physical Interpretation of the Level Shifts.
e. Physical Interpretation of the Energy Exchanges
2. Applications to Radiative Processes	312	(10)
a. Calculation of the Statistical Functions.
b. Physical Discussion.
c. Level Shifts due to the Fluctuations of the Radiation Field.
d. Level Shifts due to Radiation Reaction.
e. Energy Exchanges between the Atom and the Radiation
COMPLEMENT B(IV)--MASTER EQUATION FOR A DAMPED HARMONIC OSCILLATOR	322	(12)
1. The Physical System	322	(1)
2. Operator Form of the Master Equation	323	(3)
3. Master Equation in the Basis of the Eigenstates of H(A)	326	(3)
a. Evolution of the Populations.
b. Evolution of a Few Average Values
4. Master Equation in a Coherent State Basis	329	(5)
a. Brief Review of Coherent States and the Representation P(N) of the Density Operator.
b. Evolution Equation for P(N)(Beta, Beta*, t).
c. Physical Discussion.
8. COMPLEMENT C(IV)--QUANTUM LANGEVIN EQUATIONS FOR A SIMPLE PHYSICAL SYSTEM	334	(19)
Introduction	334	(1)
1. Review of the Classical Theory of Brownian Motion	334	(6)
a. Langevin Equation.
b. Interpretation of the Coefficient D. Connection between Fluctuations and Dissipation.
c. A Few Correlation Functions
2. Heisenberg-Langevin Equations for a Damped Harmonic Oscillator	340	(13)
a. Coupled Heisenberg Equations.
b. The Quantum Langevin Equation and Quantum Langevin Forces.
c. Connection between Fluctuations and Dissipation.
d. Mixed Two-Time Averages Involving Langevin Forces and Operators of A.
e. Rate of Variation of the Variances V(N) and V(A).
f. Generalization of Einstein's Relation.
g. Calculation of Two-Time Averages for Operators of A. Quantum Regression Theorem
V OPTICAL BLOCH EQUATIONS	353	(54)
Introduction	353	(2)
A. Optical Bloch Equations for a Two-Level Atom	355	(9)
1. Description of the Incident Field	355	(1)
2. Approximation of Independent Rates of Variation	356	(1)
3. Rotating-Wave Approximation	357	(4)
a. Elimination of Antiresonant Terms.
b. Time-Independent Form of the Optical Bloch Equations.
c. Other Forms of the Optical Bloch Equations.
4. Geometric Representation in Terms of a Fictitious Spin 1/2	361	(3)
B. Physical Discussion--Differences with Other Evolution Equations	364	(3)
1. Differences with Relaxation Equations. Couplings between Populations and Coherences	364	(1)
2. Differences with Hamiltonian Evolution Equations	364	(1)
3. Differences with Heisenberg-Langevin Equations	365	(2)
C. First Application--Evolution of Atomic Average Values	367	(12)
1. Internal Degrees of Freedom	367	(3)
a. Transient Regime.
b. Steady-State Regime.
c. Energy Balance. Mean Number of Incident Photons Absorbed per Unit Time
2. External Degrees of Freedom. Mean Radiative Forces	370	(9)
a. Equation of Motion of the Center of the Atomic Wave Packet.
b. The Two Types of Forces for an Atom Initially at Rest.
c. Dissipative Force. Radiation Pressure.
d. Reactive Force. Dipole Force
D. Properties of the Light Emitted by the Atom	379	(9)
1. Photodetection Signals. One- and Two-Time Averages of the Emitting Dipole Moment	379	(3)
a. Connection between the Radiated Field and the Emitting Dipole Moment.
b. Expression of Photodetection Signals.
2. Total Intensity of the Emitted Light	382	(2)
a. Proportionality to the Population of the Atomic Excited State.
b. Coherent Scattering and Incoherent Scattering.
c. Respective Contributions of Coherent and Incoherent Scattering to the Total Intensity Emitted in Steady State
3. Spectral Distribution of the Emitted Light in Steady State.	384	(4)
a. Respective Contributions of Coherent and Incoherent Scattering. Elastic and Inelastic Spectra
b. Outline of the Calculation of the Inelastic Spectrum
c. Inelastic Spectrum in a Few Limiting Cases
COMPLEMENT A(V)--BLOCH-LANGEVIN EQUATIONS AND QUANTUM REGRESSION THEOREM	388	(19)
Introduction	388	(1)
1. Coupled Heisenberg Equations for the Atom and the Field	388	(6)
a. Hamiltonian and Operator Basis for the System.
b. Evolution Equations for the Atomic and Field Observables.
c. Rotating-Wave Approximation. Change of Variables.
d. Comparison with the Harmonic Oscillator Case
2. Derivation of the Heisenberg-Langevin Equations	394	(4)
a. Choice of the Normal Order.
b. Contribution of the Source Field
c. Summary. Physical Discussion
3. Properties of Langevin Forces	398	(9)
a. Commutation Relations between the Atomic Dipole Moment and the Free Field.
b. Calculation of the Correlation Functions of Langevin Forces.
c. Quantum Regression Theorem.
d. Generalized Einstein Relations
VI THE DRESSED ATOM APPROACH	407	(108)
A. Introduction: The Dressed Atom	407	(3)
B. Energy Levels of the Dressed Atom	410	(9)
1. Model of the Laser Beam	410	(2)
2. Uncoupled States of the Atom + Laser Photons System	412	(1)
3. Atom-Laser Photons Coupling	413	(2)
a. Interaction Hamiltonian
b. Resonant and Nonresonant Couplings
c. Local Periodicity of the Energy Diagram
d. Introduction of the Rabi Frequency
4. Dressed States	415	(2)
a. Energy Levels and Wave Functions.
b. Energy Diagram versus hw(L)
5. Physical Effects Associated with Absorption and Induced Emission	417	(2)
C. Resonance Fluorescence Interpreted as a Radiative Cascade of the Dressed Atom	419	(8)
1. The Relevant Time Scales	419	(1)
2. Radiative Cascade in the Uncoupled Basis	420	(3)
a. Time Evolution of the System
b. Photon Antibunching
c. Time Intervals between Two Succesive Spontaneous Emissions
3. Radiative Cascade in the Dressed State Basis	423	(4)
a. Allowed Transitions between Dressed States
b. Fluorescence Triplet.
c. Time Correlations between Frequency Filtered Fluorescence Photons
D. Master Equation for the Dressed Atom	427	(10)
1. General Form of the Master Equation	427	(2)
a. Approximation of Independent Rates of Variation
b. Comparison with Optical Bloch Equations
2. Master Equation in the Dressed State Basis in the Secular Limit	429	(6)
a. Advantages of the Coupled Basis in the Secular Limit
b. Evolution of Populations
c. Evolution of Coherences--Transfer of Coherences
d. Reduced Populations and Reduced Coherences
3. Quasi-Steady State for the Radiative Cascade	435	(2)
a. Initial Density Matrix.
b. Transient Regime and Quasi-Steady State
E. Discussion of a Few Applications	437	(23)
1. Widths and Weights of the Various Components of the Fluorescence Triplet	437	(5)
a. Evolution of the Mean Dipole Moment
b. Widths and Weights of the Sidebands.
c. Structure of the Central Line
2. Absorption Spectrum of a Weak Probe Beam	442	(4)
a. Physical Problem.
b. Case Where the Two Lasers Are Coupled to the Same Transition.
c. Probing on a Transition to a Third Level. The Autler-Townes Effect
3. Photon Correlations	446	(8)
a. Calculation of the Photon-Correlation Signal
b. Physical Discussion.
c. Generalization to a Three-Level System: Intermittent Fluorescence
4. Dipole Forces	454	(6)
a. Energy Levels of the Dressed Atom in a Spatially Inhomogeneous Laser Wave.
b. Interpretation of the Mean Dipole Force.
c. Fluctuations of the Dipole Force
COMPLEMENT A(VI) -- THE DRESSED ATOM IN THE RADIO-FREQUENCY DOMAIN	460	(30)
Introduction	460	(1)
1. Resonance Associated with a Level Crossing or Anticrossing	461	(7)
a. Anticrossing for a Two-Level System.
b. Higher-Order Anticrossing.
c. Level Crossing. Coherence Resonance
2. Spin 1/2 Dressed by Radio-Frequency Photons	468	(5)
a. Description of the System.
b. Interaction Hamiltonian between the Atom and the Radio-Frequency Field
c. Preparation and Detection
3. The Simple Case of Circularly Polarized Photons	473	(6)
a. Energy Diagram.
b. Magnetic Resonance Interpreted as a Level-Anticrossing Resonance of the Dressed Atom.
c. Dressed State Level-Crossing Resonances
4. Linearly Polarized Radio-Frequency Photons	479	(11)
a. Survey of the New Effects.
b. Bloch-Siegert Shift.
c. The Odd Spectrum of Level-Anticrossing Resonances.
d. The Even Spectrum of Level-Crossing Resonances.
e. A Nonperturbative Calculation: The Lande Factor of the Dressed Atom.
f. Qualitative Evolution of the Energy Diagram at High Intensity
COMPLEMENT B(VI)--COLLISIONAL PROCESSES IN THE PRESENCE OF LASER IRRADIATION	490	(25)
Introduction	490	(1)
1. Collisional Relaxation in the Absence of Laser Irradiation	491	(3)
a. Simplifying Assumptions.
b. Master Equation Describing the Effect of Collisions on the Emitting Atom
2. Collisional Relaxation in the Presence of Laser Irradiation	494	(7)
a. The Dressed Atom Approach.
b. Evolution of Populations: Collisional Transfers between Dressed States.
c. Evolution of Coherences. Collisional Damping and Collisional Shift.
d. Explicit Form of the Master Equation in the Impact Limit
3. Collision-Induced Modifications of the Emission and Absorption of Light by the Atom. Collisional Redistribution	501	(9)
a. Taking into Account Spontaneous Emission.
b. Reduced Steady-State Populations.
c. Intensity of the Three Components of the Fluorescence Triplet.
d. Physical Discussion in the Limit Omega(1) much less than Delta(L) much less than XXX
4. Sketch of the Calculation of the Collisional Transfer Rate	510	(5)
a. Expression of the Transfer Rate as a Function of the Collision S-Matrix
b. Case Where the Laser Frequency Becomes Resonant during the Collision. Limit of Large Detunings
EXERCISES	515	(106)
1. Calculation of the Radiative Lifetime of an Excited Atomic Level. Comparison with the Damping Time of a Classical Dipole Moment	515	(3)
2. Spontaneous Emission of Photons by a Trapped Ion. Lamb-Dicke Effect	518	(6)
3. Rayleigh Scattering	524	(3)
4. Thomson Scattering	527	(3)
5. Resonant Scattering	530	(3)
6. Optical Detection of a Level Crossing between Two Excited Atomic States	533	(4)
7. Radiative Shift of an Atomic Level. Bethe Formula for the Lamb Shift	537	(11)
8. Bremsstrahlung. Radiative Corrections to Elastic Scattering by a Potential	548	(9)
9. Low-Frequency Bremsstrahlung. Nonperturbative Treatment of the Infrared Catastrophe	557	(7)
10. Modification of the Cyclotron Frequency of a Particle due to Its Interactions with the Radiation Field	564	(7)
11. Magnetic Interactions between Spins	571	(5)
12. Modification of an Atomic Magnetic Moment due to Its Coupling with Magnetic Field Vacuum Fluctuations	576	(4)
13. Excitation of an Atom by a Wave Packet: Broadband Excitation and Narrow-Band Excitation	580	(5)
14. Spontaneous Emission by a System of Two Neighboring Atoms. Superradiant and Subradiant States	585	(4)
15. Radiative Cascade of a Harmonic Oscillator	589	(7)
16. Principle of the Detailed Balance	596	(1)
17. Equivalence between a Quantum Field in a Coherent State and an External Field	597	(4)
18. Adiabatic Elimination of Coherences and Transformation of Optical Bloch Equations into Relaxation Equations	601	(3)
19. Nonlinear Susceptibility for an Ensemble of Two-Level Atoms. A Few Applications	604	(4)
20. Absorption of a Probe Beam by Atoms Interacting with an Intense Beam. Application to Saturated Absorption	608	(13)
APPENDIX QUANTUM ELECTRODYNAMICS IN THE COULOMB GAUGE--SUMMARY OF THE ESSENTIAL RESULTS	621	(20)
1. Description of the Electromagnetic Field	621	(7)
a. Electric Field E and Magnetic Field B.
b. Vector Potential A and Scalar Potential U. c. Coulomb Gauge.
d. Normal Variables.
e. Principle of Canonical Quantization in the Coulomb Gauge.
f. Quantum Fields in the Coulomb Gauge	621	(7)
2. Particles	628	(1)
3. Hamiltonian and Dynamics in the Coulomb Gauge	629	(4)
a. Hamiltonian
b. Unperturbed Hamiltonian and Interaction Hamiltonian.
c. Equations of Motion
4. State Space	633	(2)
5. The Long-Wavelength Approximation and the Electric Dipole Representation	635	(6)
a. The Unitary Transformation.
b. The Physical Variables in the Electric Dipole Representation.
c. The Displacement Field.
d. Electric Dipole Hamiltonian
References	641	(4)
Index	645