Atom photon interactions: basic processes and applications
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| Sprache: | English French |
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Wiley-VCH
2004
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| Schriftenreihe: | Physics textbook
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| Beschreibung: | XXII, 656 S. graph. Darst. |
| ISBN: | 0471293369 9780471293361 |
Internformat
MARC
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| 020 | |a 9780471293361 |9 978-0-471-29336-1 | ||
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| 100 | 1 | |a Cohen-Tannoudji, Claude |d 1933- |e Verfasser |0 (DE-588)115610340 |4 aut | |
| 240 | 1 | 0 | |a Processus d'interaction entre photons et atomes |
| 245 | 1 | 0 | |a Atom photon interactions |b basic processes and applications |c Claude Cohen-Tannoudji ; Jacques Dupont-Roc ; Gilbert Grynberg |
| 246 | 1 | 3 | |a Atom-photon interactions |
| 264 | 1 | |a Weinheim |b Wiley-VCH |c 2004 | |
| 300 | |a XXII, 656 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Physics textbook | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Photonuclear reactions | |
| 650 | 4 | |a Quantum theory | |
| 650 | 4 | |a Statistical physics | |
| 650 | 0 | 7 | |a Quantentheorie |0 (DE-588)4047992-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Quantenelektrodynamik |0 (DE-588)4047982-1 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Dupont-Roc, Jacques |e Verfasser |4 aut | |
| 700 | 1 | |a Grynberg, Gilbert |e Verfasser |4 aut | |
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Datensatz im Suchindex
| _version_ | 1804134585206833152 |
|---|---|
| adam_text | Contents
Preface
........................................... xxi
Introduction
....................................... 1
I
TRANSITION AMPLITUDES
IN ELECTRODYNAMICS
Introduction
....................................... 5
A.
Probability
Amplitude Associated
with a Physical Process
.... 7
B.
Time Dependence of Transition Amplitudes
.............. 9
1.
Coupling between Discrete Isolated States
............ 9
2.
Resonant Coupling between a Discrete Level and a Contin¬
uum
10
3.
Couplings inside a Continuum or between
Continua
..... 12
C.
Application to Electrodynamics
...................... 15
1.
Coulomb Gauge Hamiltonian
...................... 15
2.
Expansion in Powers of the Charges qa
............... 16
3.
Expansion in Powers of the Interaction with the Transverse
Field
....................................... 17
4.
Advantages of Including the Coulomb Interaction in the
Particle Hamiltonian
............................ 18
5.
Diagrammatic Representation of Transition Amplitudes
... 19
Complement
A¡
—
Perturbative Calculation of
Transition Amplitudes
—
Some Useful Relations
Introduction
....................................... 23
1.
Interaction Representation
......................... 23
v
vi
Contents
2.
Perturbative
Expansion
of Transition Amplitudes
—
a. Pertur¬
bative
Expansion of the Evolution Operator, b. First-Order
Transition Amplitude,
с
Second-Order Transition Amplitude
... 25
3.
Transition Probability
—
a. Calculation of the Transition Proba¬
bility to a Final State Different from the Initial State, b. Transi¬
tion Probability between Two Discrete States. Lowest-Order
Calculation,
с
Case Where the Final State Belongs to an En¬
ergy 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
.................... 31
Complement B,
—
Description of the Effect of a
Perturbation by an Effective Hamiltonian
1.
Introduction
—
Motivation
.......................... 38
2.
Principle of the Method
............................ 41
3.
Determination of the Effective Hamiltonian
—
a. Iterative Cal¬
culation of S. b. Expression of the Second-Order Effective
Hamiltonian.
с
Higher-Order Terms
.................. 43
4.
Case of Two Interacting Systems
..................... 46
Complement Cj
—
Discrete Level Coupled to a Broad
Continuum: A Simple Model
Introduction
:...................................... 49
1.
Description of the Model
—
a. The Discrete State and the Con¬
tinuum, b. Discretization of the Continuum,
с
Simplifying
Assumptions
.................................... 50
2.
Stationary States of the System. Traces of the Discrete State in
the New Continuum
—
a. The Eigenvalue Equation, b. Graphic
Determination of the New Eigenvalues,
с
Probability Density of
the Discrete State in the New Continuum
................. 51
3.
A Few Applications of This Simple Model
—
a. Decay of the
Discrete Level, b. Excitation of the System in the Discrete Level
from Another State,
с
Resonant Scattering through a Discrete
Level, d.
Fano
Profiles
............................ 56
4.
Generalization to More Realistic
Continua. Diagonalization
of
the Hamiltonian without Discretization
................. 64
Contents
vii
II
A SURVEY OF SOME INTERACTION PROCESSES
BETWEEN PHOTONS AND ATOMS
Introduction
....................................... 67
A. Emission Process: A New Photon Appears
............... 69
1.
Spontaneous Emission between Two Discrete Atomic Lev¬
els. Radiative Decay of an Excited Atomic State
—
a. Dia¬
grammatic Representation, b. Spontaneous Emission Rate.
с
Nonperturbative Results
......................... 69
2.
Spontaneous Emission between a Continuum State and
a Discrete State
—
a. First Example: Radiative Capture.
b. Second Example: Radiative Dissociation of a Molecule
... 73
3.
Spontaneous Emission between Two States of the Ioniza-
tion Continuum
—Bremsstrahlung .................. 76
B.
Absorption Process: A Photon Disappears
............... 78
1.
Absorption between Two Discrete States
............. 78
2.
Absorption between a Discrete State and a Continuum
State
—
a. First Example: Photoionization. b. Second Exam¬
ple:
Photodissociation
............................ 79
3.
Absorption between Two States of the Ionization Contin¬
uum: Inverse
Bremsstrahlung...................... 82
4.
Influence of the Initial State of the Field on the Dynamics
of the Absorption Process
........................ 83
С
Scattering Process: A Photon Disappears and Another Photon
Appears
....................................... 86
1.
Scattering Amplitude
—
Diagrammatic Representation
.... 86
2.
Different Types of Photon Scattering by an Atomic or
Molecular System
—
a. Low-Energy Elastic Scattering:
Rayleigh Scattering, b. Low-Energy Inelastic Scattering:
Raman Scattering,
с
High-Energy Elastic Scattering: Thom¬
son Scattering, d. High-Energy Inelastic Scattering with the
Final Atomic State in the Ionization Continuum: Compton
Scattering
.................................... 88
3.
Resonant Scattering
............................ 93
D. Multiphoton Processes: Several Photons Appear or Disappear
98
1.
Spontaneous Emission of Two Photons
............... 98
2.
Multiphoton Absorption (and Stimulated Emission) be¬
tween Two Discrete Atomic States
.................. 100
viii Contents
3. Multiphoton Ionization .......................... 102
4. Harmonie Generation ........................... 104
5.
Multiphoton
Processes
and Quasi-Resonant Scattering
... 106
E. Radiative Corrections: Photons Are Emitted and
Reabsorbed
(or Absorbed and Reemitted)
........................ 109
1.
Spontaneous Radiative Corrections
—
a. Case of a Free Elec¬
tron: Mass Correction, b. Case of an Atomic Electron: Natu¬
ral Width and Radiative Shift
...................... 109
2.
Stimulated Radiative Corrections
................... 114
F. Interaction by Photon Exchange
...................... 118
1.
Exchange of Transverse Photons between Two Charged
Particles: First Correction to the Coulomb Interaction
.... 118
2.
Van
der Waals
Interaction between Two Neutral Atoms
—
a. Small Distance:
D
«:
kab. b. Large Distance
λβΓ
<;/)... 121
Complement An
—
Photodetection Signals and
Correlation Functions
Introduction
....................................... 127
1.
Simple Models of Atomic Photodetectors
—
a. Broadband Pho-
todetector. b. Narrow-Band Photodetector
.............. 128
2.
Excitation Probability and Correlation Functions
—
a. Hamilto-
nian. Evolution Operator, b. Calculation of the Probability That
the Atom Has Left the Ground State after a Time At.
c. Atomic
Dipole
Correlation Function, d. Field Correlation
Function
....................................... 129
3.
Broadband Photodetection
—
a. Condition on the Correlation
Functions, b. Photoionization Rate
.................... 137
4.
Narrow-Band Photodetection
—
a. Conditions on the Incident
Radiation and on the Detector, b. Excitation by a Broadband
Spectrum,
с
Influence of the Natural Width of the Excited
Atomic Level
.................................... 139
5.
Double Photodetection Signals
—
a. Correlation between Two
Photodetector Signals, b. Sketch of the Calculation of
w n
.... 143
Contents ix
Complement
Вп
—
Radiative Corrections in the
Pauli -Fierz
Representation
Introduction
....................................... 147
1.
The Pauli-Fierz Transformation
—
a. Simplifying Assumptions,
b.
Transverse Field Tied to a Classical Particle,
с
Determination
of the Pauli-Fierz Transformation
..................... 148
2.
The
Observables
in the New Picture
—
a. Transformation of the
Transverse Fields, b. Transformation of the Particle Dynamical
Variables,
с
Expression for the New Hamiltonian
......... 152
3.
Physical Discussion—a. Mass Correction, b. New Interaction
Hamiltonian between the Particle and the Transverse Field,
с
Advantages of the New Representation, d. Inadequacy of the
Concept of a Field Tied to a Particle
.................... 157
III
NONPERTURBATIVE CALCULATION OF TRANSITION
AMPLITUDES
Introduction
....................................... 165
A. Evolution Operator and Resolvent
.................... 167
1.
Integral Equation Satisfied by the Evolution Operator
.... 167
2.
Green s Functions
—
Propagators
................... 167
3.
Resolvent of the Hamiltonian
...................... 170
B. Formal Resummation of the Perturbation Series
.......... 172
1.
Diagrammatic Method Explained on a Simple Model
..... 172
2.
Algebraic Method Using Projection Operators
—
a. Projector
onto a Subspace
Jř0
of the Space of States, b. Calculation of
the Projection of the Resolvent in the Subspace Wo.
с
Calcu¬
lation of Other Projections of G(z). d. Interpretation of the
Level-Shift Operator
............................ 174
3.
Introduction of Some Approximations
—
a. Perturbative Cal¬
culation of the Level-Shift Operator. Partial Resummation of
the Perturbation Series, b. Approximation Consisting of Ne¬
glecting the Energy Dependence of the Level-Shift Operator
. . . 179
C. Study of a Few Examples
........................... 183
1.
Evolution of
ал
Excited Atomic State
—
a. Nonperturbative
Calculation of the Probability Amplitude That the Atom Re-
Contents
mains Excited,
b.
Radiative Lifetime and Radiative Level
Shift,
с
Conditions of Validity for the Treatment of the Two
Preceding Subsections
............................ 183
2.
Spectra] Distribution of Photons Spontaneously Emitted by
an Excited Atom
—
a. Relevant Matrix Element of the Resol¬
vent Operator, b. Generalization to a Radiative Cascade.
с
Natural Width and Shift of the Emitted Lines
.......... 189
3.
Indirect Coupling between a Discrete Level and a Contin¬
uum. Example of the Lamb Transition
—
a. Introducing
the Problem, b. Nonperturbative Calculation of the Transi¬
tion Amplitude,
с
Weak Coupling Limit. Bethe Formula.
d. Strong Coupling Limit.
Rabi
Oscillation
............. 197
4.
Indirect Coupling between Two Discrete States. Multi-
photon Transitions
—
a. Physical Process and Subspace Wo
of Relevant States, b. Nonperturbative Calculation of the
Transition Amplitude,
с
Weak Coupling Case. Two-Photon
Excitation Rate. d. Strong Coupling Limit. Two-Photon
Rabi
Oscillation, e. Higher-Order Multiphoton Transitions.
ƒ.
Limitations of the Foregoing Treatment
.............. 205
Complement
Аш
—
Analytic Properties of the
Resolvent
Introduction
....................................... 213
1.
Analyticity of the Resolvent outside the Real Axis
......... 213
2.
Singularities on the Real Axis
........................ 215
3.
Unstable States and Poles of the Analytic Continuation of the
Resolvent
...................................... 217
4.
Contour Integral and Corrections to the Exponential Decay
. . . 220
Complement BnI
—
Nonperturbative Expressions for
the Scattering Amplitudes of a Photon by an Atom
Introduction
....................................... 222
1.
Transition Amplitudes between Unperturbed States
—
a. Using
the Resolvent, b. Transition Matrix,
с
Application to Reso¬
nant Scattering, d. Inadequacy of Such an Approach
....... 222
Contents xi
2.
Introducing Exact Asymptotic States
—
a. The Atom in the Ab¬
sence of Free Photons, b. The Atom in the Presence of a Free
Photon
........................................ 229
3.
Transition Amplitude between Exact Asymptotic States
—
a. New Definition of the S-Matrix. b. New Expression for the
Transition Matrix. Physical Discussion
.................. 233
Complement Cin
—
Discrete State Coupled to a
Finite-Width Continuum: From the
Weisskopf
-Wigner
Exponential Decay to the
Rabi
Oscillation
1.
Introduction
—
Overview
........................... 239
2.
Description of the Model
—
a. Unperturbed States, b. Assump¬
tions concerning the Coupling,
с
Calculation of the Resolvent
and of the Propagators, d. Fourier Transform of the Amplitude
Ub(r)
......................................... 240
3.
The Important Physical Parameters
—
a. The Function
ГЬ(Е).
b.
The Parameter
ß,
Characterizing the Coupling of the Discrete
State with the Whole Continuum,
с
The Function
ЛЬ(Е)
.... 244
4.
Graphical Discussion
—
a. Construction of the Curve
Í¿b(E).
b.
Graphical Determination of the Maxima of Wb(E). Classifica¬
tion of the Various Regimes
.......................... 246
5.
Weak Coupling Limit
—
a.
Weisskopf
-Wigner Exponential De¬
cay, b. Corrections to the Exponential Decay
............. 249
6.
Intermediate Coupling. Critical Coupling
—
a. Power Expansion
of
&b(E)
near a Maximum, b. Physical Meaning of the Critical
Coupling
....................................... 251
7.
Strong Coupling
................................. 253
IV
RADIATION CONSIDERED AS A RESERVOIR: MASTER
EQUATION FOR THE PARTICLES
A. Introduction
—
Overview
........................... 257
B. Derivation of the Master Equation for a Small System s?
Interacting with a Reservoir
Ш
....................... 262
1.
Equation Describing the Evolution of the Small System in
the Interaction Representation
.................... 262
xii Contents
2.
Assumptions Concerning the Reservoir
—
a. State of the
Reservoir, b. One-Time and Two-Time Averages for the
Reservoir
Observables
............................ 263
3.
Perturbative Calculation of the Coarse-Grained Rate of
Variation of the Small System
..................... 266
4.
Master Equation in the Energy-State Basis
............ 269
C. Physical Content of the Master Equation
............... 272
1.
Evolution of Populations
......................... 272
2.
Evolution of Coherences
......................... 274
D. Discussion of the Approximations
..................... 278
1.
Order of Magnitude of the Evolution Time for j/
....... 278
2.
Condition for Having Two Time Scales
............... 278
3.
Validity Condition for the Perturbative Expansion
....... 279
4.
Factorization of the Total Density Operator at Time
t
.... 280
5.
Summary
.................................... 281
E. Application to a Two-Level Atom Coupled to the Radiation
Field
......................................... 282
1.
Evolution of Internal Degrees of Freedom
—
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
....... 282
2.
Evolution of Atomic Velocities
—
a. Taking into Account
the Translational Degrees of Freedom in the Master Equation,
b. Fokker-Planck Equation for the Atomic Velocity Distribu¬
tion Function,
с
Evolutions of the Momentum Mean Value
and Variance, d. Steady-State Distribution. Thermodynamic
Equilibrium
................................... 289
Complement Aiv
—
Fluctuations and Linear Response
Application to Radiative Processes
Introduction
....................... 302
1.
Statistical Functions and Physical Interpretation of the Master
Equation
—
a. Symmetric Correlation Function, b. Linear
Sus-
Contents xiii
ceptibility.
с.
Polarization
Energy
and Dissipation, d. Physical
Interpretation
of the Level Shifts, e. Physical Interpretation of
the Energy Exchanges
.............................. 302
2.
Applications to Radiative Processes
—
a. Calculation of the Sta¬
tistical Functions, b. Physical Discussion,
с
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
.................................... 312
Complement Biv
—
Master Equation for a Damped
Harmonic Oscillator
1.
The Physical System
.............................. 322
2.
Operator Form of the Master Equation
................. 323
3.
Master Equation in the Basis of the Eigenstates of HA
—
a. Evolution of the Populations, b. Evolution of a Few Average
Values
........................................ 326
4.
Master Equation in a Coherent State Basis
—
a. Brief Review of
Coherent States and the Representation PN of the Density Opera¬
tor, b. Evolution Equation for
PN(ß,ß*,t).
с.
Physical Dis¬
cussion
. ................ 329
Complement Civ
—
Quantum
Langevin
Equations
for a Simple Physical System
Introduction
....................................... 334
1.
Review of the Classical Theory of Brownian Motion
—
a. Langevin
Equation, b. Interpretation of the Coefficient D.
Connection between Fluctuations and Dissipation,
с
A Few
Correlation Functions
.............................. 334
2.
Heisenberg-Langevin Equations for a Damped Harmonic Os¬
cillator
—
a. Coupled
Heisenberg
Equations, b. The Quantum
Langevin
Equation and Quantum
Langevin
Forces,
с
Connec¬
tion between Fluctuations and Dissipation, d. Mixed Two-Time
Averages Involving
Langevin
Forces and Operators of
яґ.
e. Rate of Variation of the Variances
5^
and
2^. ƒ.
General¬
ization of Einstein s Rebtion. g. Calculation of Two-Time Aver¬
ages for Operators of sf. Quantum Regression Theorem
...... 340
xiv Contents
v
OPTICAL BLOCH EQUATIONS
Introduction
....................................... 353
A. Optical Bloch Equations for a Two-Level Atom
........... 355
1.
Description of the Incident Field
................... 355
2.
Approximation of Independent Rates of Variation
...... 356
3.
Rotating-Wave Approximation
—
a. Elimination of
Antireso
-
nant Terms, b. Time-Independent Form of the Optical Bloch
Equations, c. Other Forms of the Optical Bloch Equations
... 357
4.
Geometric Representation in Terms of a Fictitious Spin
. . . 361
B. Physical Discussion
—
Differences with Other Evolution Equa¬
tions
......................................... 364
1.
Differences with Relaxation Equations. Couplings between
Populations and Coherences
...................... 364
2.
Differences with Hamiltonian Evolution Equations
...... 364
3.
Differences with Heisenberg-Langevin Equations
....... 365
C. First Application
—
Evolution of
Atomic
Average Values
..... 367
1.
Internal Degrees of Freedom
—
a. Transient Regime,
b. Steady-State Regime,
с
Energy Balance. Mean Number of
Incident Photons Absorbed per Unit Time
.............. 367
2.
External Degrees of Freedom. Mean Radiative Forces
—
a. Equation of Motion of the Center of the Atomic Wave
Packet, b. The Two Types of Forces for an Atom Initially at
Rest,
с
Dissipative Force. Radiation Pressure, d. Reactive
Force.
Dipole
Force
............................. 370
D. Properties of the Light Emitted by the Atom
............. 379
1.
Photodetection Signals. One- and Two-Time Averages of
the Emitting
Dipole
Moment
—
a. Connection between the
Radiated Field and the Emitting
Dipole
Moment, b. Expres¬
sion of Photodetection Signals
...................... 379
2.
Total Intensity of the Emitted Light
—
a. Proportionality to
the Population of the Atomic Excited State, b. Coherent
Scattering and Incoherent Scattering,
с
Respective Contribu¬
tions of Coherent and Incoherent Scattering to the Total
Intensity Emitted in Steady State
.................... 382
3.
Spectral Distribution of the Emitted Light in Steady
Contents
State—
a. Respective Contributions of Coherent and Incoher¬
ent Scattering. Elastic and Inelastic Spectra, b. Outline of
the Calculation of the Inelastic Spectrum,
с
Inelastic Spec¬
trum in a Few Limiting Cases
...................... 384
Complement Av
—
Bloch
-Langevin
Equations and
Quantum Regression Theorem
Introduction
....................................... 388
1.
Coupled
Heisenberg
Equations for the Atom and the Field
—
a. Hamiltonian and Operator Basis for the System, b. Evolution
Equations for the Atomic and Field
Observables,
с.
Rotating-
Wave Approximation. Change of Variables, d. Comparison with
the Harmonic Oscillator Case
........................ 388
2.
Derivation of the Heisenberg-Langevin Equations
—
a. Choice
of the Normal Order, b. Contribution of the Source Field.
с
Summary. Physical Discussion
...................... 394
3.
Properties of
Langevin
Forces
—
a. Commutation Relations
between the Atomic
Dipole
Moment and the Free Field, b. Cal¬
culation of the Correlation Functions of
Langevin
Forces,
с
Quantum Regression Theorem, d. Generalized Einstein
Relations
....................................... 398
VI
THE DRESSED ATOM APPROACH
A. Introduction: The Dressed Atom
...................... 407
B. Energy Levels of the Dressed Atom
.................... 410
1.
Model of the Laser Beam
........................ 410
2.
Uncoupled States of the Atom
+
Laser Photons System
. . . 412
3.
Atom-Laser Photons Coupling
—
a. Interaction Hamiltonian.
b. Resonant and
Nonresonant
Couplings,
с
Local Periodic¬
ity of the Energy Diagram, d. Introduction of the
Rabi
Frequency
.................................... 413
xvi Contents
4.
Dressed
States—
a.
Energy
Levels and Wave Functions.
b. Energy Diagram versus hmL
...................... 415
5.
Physical Effects Associated with Absorption and Induced
Emission
.................................... 417
C. Resonance Fluorescence Interpreted as a Radiative Cascade of
the Dressed Atom
................................ 419
1.
The Relevant Time Scales
........................ 419
2.
Radiative Cascade in the Uncoupled Basis
—
a. Time Evolu¬
tion of the System, b. Photon Antibunching.
с
Time Inter¬
vals between Two Successive Spontaneous Emissions
...... 420
3.
Radiative Cascade in the Dressed State Basis
—
a. Allowed
Transitions between Dressed States, b. Fluorescence Triplet,
с
Time Correlations between Frequency Filtered Fluorescence
Photons
..................................... 423
D. Master Equation for the Dressed Atom
................. 427
1.
General Form of the Master Equation
—
a. Approximation of
Independent Rates of Variation, b. Comparison with Optical
Bloch Equations
............................... 427
2.
Master Equation in the Dressed State Basis in the Secular
Limit
—
a. Advantages of the Coupled Basis in the Secular
Limit, b. Evolution of Populations,
с
Evolution of Coher¬
ences
—
Transfer of Coherences, d. Reduced Populations and
Reduced Coherences
............................. 429
3.
Quasi-Steady State for the Radiative Cascade
—
a. Initial Den¬
sity Matrix, b. Transient Regime and Quasi-Steady State
.... 435
E. Discussion of a Few Applications
..................... 437
1.
Widths and Weights of the Various Components of the
Fluorescence Triplet
—
a. Evolution of the Mean
Dipole
Mo¬
ment, b. Widths and Weights of the Sidebands,
с
Structure
of the Central Line
.............................. 437
2.
Absorption Spectrum of a Weak Probe Beam—a. Physical
Problem, b. Case Where the Two Lasers Are Coupled to the
Same Transition,
с
Probing on a Transition to a Third
Level. The Autler-Townes Effect
.................... 442
3.
Photon Correlations
—
a. Calculation of the Photon-Correla¬
tion Signal, b. Physical Discussion,
с
Generalization to a
Three-Level System: Intermittent Fluorescence
........... 446
4. Dipole
Forces
—
a. Energy Levels of the Dressed Atom in a
Contents xvii
Spatially
Inhomogeneous Laser
Wave. b.
Interpretation
of the
Mean
Dipole
Force,
с.
Fluctuations of the
Dipole
Force
.... 454
Complement Avi
—
The Dressed Atom in the
Radio-Frequency Domain
Introduction
....................................... 460
1.
Resonance Associated with a Level Crossing or Anti-
crossing
—
a. Anticrossing for a Two-Level System, b. Higher-
Order Anticrossing.
с
Level Crossing. Coherence Resonance
. . . 461
2.
Spin Dressed by Radio-Frequency Photons
—
a. Description of
the System, b. Interaction Hamiltonian between the Atom and
the Radio-Frequency Field,
с
Preparation and Detection
..... 468
3.
The Simple Case of Circularly Polarized Photons
—
a. Energy
Diagram, b. Magnetic Resonance Interpreted as a Level-Anti-
crossing Resonance of the Dressed Atom. c. Dressed State
Level-Crossing Resonances
.......................... 473
4.
Linearly Polarized Radio-Frequency Photons
—
a. Survey of the
New Effects, b. Bloch-Siegert Shift,
с
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 Evolu¬
tion of the Energy Diagram at High Intensity
.............. 479
Complement Bvi
—
Collisional Processes in the
Presence of Laser Irradiation
Introduction
....................................... 490
1.
Collisional Relaxation in the Absence of Laser Irradiation
—
a. Simplifying Assumptions, b. Master Equation Describing the
Effect of Collisions on the Emitting Atom
................ 491
2.
Collisional Relaxation in the Presence of Laser Irradiation
—
a. The Dressed Atom Approach, b. Evolution of Populations:
Collisional Transfers between Dressed States, c. Evolution of
Coherences. Collisional Damping and Collisional Shift, d. Ex¬
plicit Form of the Master Equation in the Impact Limit
....... 494
xviii
Contents
3.
Collision-Induced Modifications of the Emission and Absorp¬
tion of Light by the Atom. Collisional Redistribution
—
a. Tak¬
ing into Account Spontaneous Emission, b. Reduced Steady-
State Populations,
с
Intensity of the Three Components of the
Fluorescence Triplet, d. Physical Discussion in the Limit
Ωι
■«
ISzJ«^,1,
..................................... 501
4.
Sketch of the Calculation of the Collisional Transfer Rate
—
a. Expression of the Transfer Rate as a Function of the Collision
S-Matrix. b. Case Where the Laser Frequency Becomes Resonant
during the Collmon. Limit of Large Detunings
............. 510
Exercises
1.
Calculation of the Radiative Lifetime of an Excited Atomic
Level. Comparison with the Damping Time of a Classical
Dipole
Moment
................................. 515
2.
Spontaneous Emission of Photons by a Trapped Ion.
Lamb-Dicke Effect
............................... 518
3.
Rayleigh Scattering
............................... 524
4.
Thomson Scattering
............................... 527
5.
Resonant Scattering
.............................. 530
6.
Optical Detection of a Level Crossing between Two Excited
Atomic States
................................... 533
7.
Radiative Shift of an Atomic Level. Bethe Formula for the
Lamb Shift
..................................... 537
8. Bremsstrahlung.
Radiative Corrections to Elastic Scattering by
a Potential
..................................... 548
9.
Low-Frequency
Bremsstrahlung. Nonperturbative
Treatment
of the Infrared Catastrophe
......................... 557
10.
Modification of the Cyclotron Frequency of a Particle due to
Its Interactions with the Radiation Field
................ 564
11.
Magnetic Interactions between Spins
.................. 571
12.
Modification of an Atomic Magnetic Moment due to Its Cou¬
pling with Magnetic Field Vacuum Fluctuations
........... 576
13.
Excitation of an Atom by a Wave Packet: Broadband Excita¬
tion and Narrow-Band Excitation
..................... 580
14.
Spontaneous Emission by a System of Two Neighboring Atoms.
Superradiant
and
Subradiant
States
................... 585
15.
Radiative Cascade of a Harmonic Oscillator
............. 589
16.
Principle of the Detailed Balance
........ ....... 596
Contents xix
17.
Equivalence
between a Quantum Field in a Coherent State
and an External Field
............................. 597
18.
Adiabatic Elimination of Coherences and Transformation of
Optical Bloch Equations into Relaxation Equations
........ 601
19.
Nonlinear Susceptibility for an Ensemble of Two-Level Atoms.
A Few Applications
............................... 604
20.
Absorption of a Probe Beam by Atoms Interacting with an
Intense Beam. Application to Saturated Absorption
........ 608
APPENDIX
QUANTUM ELECTRODYNAMICS IN THE COULOMB
GAUGE—SUMMARY OF THE ESSENTIAL RESULTS
1.
Description of the Electromagnetic Field
—
a. Electric Field
E
and Magnetic Field B. b. Vector Potential A and Scalar Poten¬
tial
U. c
Coulomb Gauge, d. Normal Variables, e. Principle
of Canonical Quantization in the Coulomb Gauge, f. Quantum
Fields in the Coulomb Gauge
......................... 621
2.
Particles
....................................... 628
3.
Hamiltonian and Dynamics in the Coulomb Gauge
—
a. Hamil-
tonian. b. Unperturbed Hamiltonian and Interaction Hamilto¬
nian.
с
Equations of Motion
........................ 629
4.
State Space
..................................... 633
5.
The Long-Wavelength Approximation and the Electric
Dipole
Representation
—
a. The Unitary Transformation, b. The Phys¬
ical Variables in the Electric
Dipole
Representation,
с
The
Displacement Field, d. Electric
Dipole
Hamiltonian
........ 635
References
......................................... 641
Index
.......................... ............. 645
|
| adam_txt |
Contents
Preface
. xxi
Introduction
. 1
I
TRANSITION AMPLITUDES
IN ELECTRODYNAMICS
Introduction
. 5
A.
Probability
Amplitude Associated
with a Physical Process
. 7
B.
Time Dependence of Transition Amplitudes
. 9
1.
Coupling between Discrete Isolated States
. 9
2.
Resonant Coupling between a Discrete Level and a Contin¬
uum
10
3.
Couplings inside a Continuum or between
Continua
. 12
C.
Application to Electrodynamics
. 15
1.
Coulomb Gauge Hamiltonian
. 15
2.
Expansion in Powers of the Charges qa
. 16
3.
Expansion in Powers of the Interaction with the Transverse
Field
. 17
4.
Advantages of Including the Coulomb Interaction in the
Particle Hamiltonian
. 18
5.
Diagrammatic Representation of Transition Amplitudes
. 19
Complement
A¡
—
Perturbative Calculation of
Transition Amplitudes
—
Some Useful Relations
Introduction
. 23
1.
Interaction Representation
. 23
v
vi
Contents
2.
Perturbative
Expansion
of Transition Amplitudes
—
a. Pertur¬
bative
Expansion of the Evolution Operator, b. First-Order
Transition Amplitude,
с
Second-Order Transition Amplitude
. 25
3.
Transition Probability
—
a. Calculation of the Transition Proba¬
bility to a Final State Different from the Initial State, b. Transi¬
tion Probability between Two Discrete States. Lowest-Order
Calculation,
с
Case Where the Final State Belongs to an En¬
ergy 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
. 31
Complement B,
—
Description of the Effect of a
Perturbation by an Effective Hamiltonian
1.
Introduction
—
Motivation
. 38
2.
Principle of the Method
. 41
3.
Determination of the Effective Hamiltonian
—
a. Iterative Cal¬
culation of S. b. Expression of the Second-Order Effective
Hamiltonian.
с
Higher-Order Terms
. 43
4.
Case of Two Interacting Systems
. 46
Complement Cj
—
Discrete Level Coupled to a Broad
Continuum: A Simple Model
Introduction
:. 49
1.
Description of the Model
—
a. The Discrete State and the Con¬
tinuum, b. Discretization of the Continuum,
с
Simplifying
Assumptions
. 50
2.
Stationary States of the System. Traces of the Discrete State in
the New Continuum
—
a. The Eigenvalue Equation, b. Graphic
Determination of the New Eigenvalues,
с
Probability Density of
the Discrete State in the New Continuum
. 51
3.
A Few Applications of This Simple Model
—
a. Decay of the
Discrete Level, b. Excitation of the System in the Discrete Level
from Another State,
с
Resonant Scattering through a Discrete
Level, d.
Fano
Profiles
. 56
4.
Generalization to More Realistic
Continua. Diagonalization
of
the Hamiltonian without Discretization
. 64
Contents
vii
II
A SURVEY OF SOME INTERACTION PROCESSES
BETWEEN PHOTONS AND ATOMS
Introduction
. 67
A. Emission Process: A New Photon Appears
. 69
1.
Spontaneous Emission between Two Discrete Atomic Lev¬
els. Radiative Decay of an Excited Atomic State
—
a. Dia¬
grammatic Representation, b. Spontaneous Emission Rate.
с
Nonperturbative Results
. 69
2.
Spontaneous Emission between a Continuum State and
a Discrete State
—
a. First Example: Radiative Capture.
b. Second Example: Radiative Dissociation of a Molecule
. 73
3.
Spontaneous Emission between Two States of the Ioniza-
tion Continuum
—Bremsstrahlung . 76
B.
Absorption Process: A Photon Disappears
. 78
1.
Absorption between Two Discrete States
. 78
2.
Absorption between a Discrete State and a Continuum
State
—
a. First Example: Photoionization. b. Second Exam¬
ple:
Photodissociation
. 79
3.
Absorption between Two States of the Ionization Contin¬
uum: Inverse
Bremsstrahlung. 82
4.
Influence of the Initial State of the Field on the Dynamics
of the Absorption Process
. 83
С
Scattering Process: A Photon Disappears and Another Photon
Appears
. 86
1.
Scattering Amplitude
—
Diagrammatic Representation
. 86
2.
Different Types of Photon Scattering by an Atomic or
Molecular System
—
a. Low-Energy Elastic Scattering:
Rayleigh Scattering, b. Low-Energy Inelastic Scattering:
Raman Scattering,
с
High-Energy Elastic Scattering: Thom¬
son Scattering, d. High-Energy Inelastic Scattering with the
Final Atomic State in the Ionization Continuum: Compton
Scattering
. 88
3.
Resonant Scattering
. 93
D. Multiphoton Processes: Several Photons Appear or Disappear
98
1.
Spontaneous Emission of Two Photons
. 98
2.
Multiphoton Absorption (and Stimulated Emission) be¬
tween Two Discrete Atomic States
. 100
viii Contents
3. Multiphoton Ionization . 102
4. Harmonie Generation . 104
5.
Multiphoton
Processes
and Quasi-Resonant Scattering
. 106
E. Radiative Corrections: Photons Are Emitted and
Reabsorbed
(or Absorbed and Reemitted)
. 109
1.
Spontaneous Radiative Corrections
—
a. Case of a Free Elec¬
tron: Mass Correction, b. Case of an Atomic Electron: Natu¬
ral Width and Radiative Shift
. 109
2.
Stimulated Radiative Corrections
. 114
F. Interaction by Photon Exchange
. 118
1.
Exchange of Transverse Photons between Two Charged
Particles: First Correction to the Coulomb Interaction
. 118
2.
Van
der Waals
Interaction between Two Neutral Atoms
—
a. Small Distance:
D
«:
kab. b. Large Distance
λβΓ
<;/). 121
Complement An
—
Photodetection Signals and
Correlation Functions
Introduction
. 127
1.
Simple Models of Atomic Photodetectors
—
a. Broadband Pho-
todetector. b. Narrow-Band Photodetector
. 128
2.
Excitation Probability and Correlation Functions
—
a. Hamilto-
nian. Evolution Operator, b. Calculation of the Probability That
the Atom Has Left the Ground State after a Time At.
c. Atomic
Dipole
Correlation Function, d. Field Correlation
Function
. 129
3.
Broadband Photodetection
—
a. Condition on the Correlation
Functions, b. Photoionization Rate
. 137
4.
Narrow-Band Photodetection
—
a. Conditions on the Incident
Radiation and on the Detector, b. Excitation by a Broadband
Spectrum,
с
Influence of the Natural Width of the Excited
Atomic Level
. 139
5.
Double Photodetection Signals
—
a. Correlation between Two
Photodetector Signals, b. Sketch of the Calculation of
w n
. 143
Contents ix
Complement
Вп
—
Radiative Corrections in the
Pauli -Fierz
Representation
Introduction
. 147
1.
The Pauli-Fierz Transformation
—
a. Simplifying Assumptions,
b.
Transverse Field Tied to a Classical Particle,
с
Determination
of the Pauli-Fierz Transformation
. 148
2.
The
Observables
in the New Picture
—
a. Transformation of the
Transverse Fields, b. Transformation of the Particle Dynamical
Variables,
с
Expression for the New Hamiltonian
. 152
3.
Physical Discussion—a. Mass Correction, b. New Interaction
Hamiltonian between the Particle and the Transverse Field,
с
Advantages of the New Representation, d. Inadequacy of the
Concept of a Field Tied to a Particle
. 157
III
NONPERTURBATIVE CALCULATION OF TRANSITION
AMPLITUDES
Introduction
. 165
A. Evolution Operator and Resolvent
. 167
1.
Integral Equation Satisfied by the Evolution Operator
. 167
2.
Green's Functions
—
Propagators
. 167
3.
Resolvent of the Hamiltonian
. 170
B. Formal Resummation of the Perturbation Series
. 172
1.
Diagrammatic Method Explained on a Simple Model
. 172
2.
Algebraic Method Using Projection Operators
—
a. Projector
onto a Subspace
Jř0
of the Space of States, b. Calculation of
the Projection of the Resolvent in the Subspace Wo.
с
Calcu¬
lation of Other Projections of G(z). d. Interpretation of the
Level-Shift Operator
. 174
3.
Introduction of Some Approximations
—
a. Perturbative Cal¬
culation of the Level-Shift Operator. Partial Resummation of
the Perturbation Series, b. Approximation Consisting of Ne¬
glecting the Energy Dependence of the Level-Shift Operator
. . . 179
C. Study of a Few Examples
. 183
1.
Evolution of
ал
Excited Atomic State
—
a. Nonperturbative
Calculation of the Probability Amplitude That the Atom Re-
Contents
mains Excited,
b.
Radiative Lifetime and Radiative Level
Shift,
с
Conditions of Validity for the Treatment of the Two
Preceding Subsections
. 183
2.
Spectra] Distribution of Photons Spontaneously Emitted by
an Excited Atom
—
a. Relevant Matrix Element of the Resol¬
vent Operator, b. Generalization to a Radiative Cascade.
с
Natural Width and Shift of the Emitted Lines
. 189
3.
Indirect Coupling between a Discrete Level and a Contin¬
uum. Example of the Lamb Transition
—
a. Introducing
the Problem, b. Nonperturbative Calculation of the Transi¬
tion Amplitude,
с
Weak Coupling Limit. Bethe Formula.
d. Strong Coupling Limit.
Rabi
Oscillation
. 197
4.
Indirect Coupling between Two Discrete States. Multi-
photon Transitions
—
a. Physical Process and Subspace Wo
of Relevant States, b. Nonperturbative Calculation of the
Transition Amplitude,
с
Weak Coupling Case. Two-Photon
Excitation Rate. d. Strong Coupling Limit. Two-Photon
Rabi
Oscillation, e. Higher-Order Multiphoton Transitions.
ƒ.
Limitations of the Foregoing Treatment
. 205
Complement
Аш
—
Analytic Properties of the
Resolvent
Introduction
. 213
1.
Analyticity of the Resolvent outside the Real Axis
. 213
2.
Singularities on the Real Axis
. 215
3.
Unstable States and Poles of the Analytic Continuation of the
Resolvent
. 217
4.
Contour Integral and Corrections to the Exponential Decay
. . . 220
Complement BnI
—
Nonperturbative Expressions for
the Scattering Amplitudes of a Photon by an Atom
Introduction
. 222
1.
Transition Amplitudes between Unperturbed States
—
a. Using
the Resolvent, b. Transition Matrix,
с
Application to Reso¬
nant Scattering, d. Inadequacy of Such an Approach
. 222
Contents xi
2.
Introducing Exact Asymptotic States
—
a. The Atom in the Ab¬
sence of Free Photons, b. The Atom in the Presence of a Free
Photon
. 229
3.
Transition Amplitude between Exact Asymptotic States
—
a. New Definition of the S-Matrix. b. New Expression for the
Transition Matrix. Physical Discussion
. 233
Complement Cin
—
Discrete State Coupled to a
Finite-Width Continuum: From the
Weisskopf
-Wigner
Exponential Decay to the
Rabi
Oscillation
1.
Introduction
—
Overview
. 239
2.
Description of the Model
—
a. Unperturbed States, b. Assump¬
tions concerning the Coupling,
с
Calculation of the Resolvent
and of the Propagators, d. Fourier Transform of the Amplitude
Ub(r)
. 240
3.
The Important Physical Parameters
—
a. The Function
ГЬ(Е).
b.
The Parameter
ß,
Characterizing the Coupling of the Discrete
State with the Whole Continuum,
с
The Function
ЛЬ(Е)
. 244
4.
Graphical Discussion
—
a. Construction of the Curve
Í¿b(E).
b.
Graphical Determination of the Maxima of Wb(E). Classifica¬
tion of the Various Regimes
. 246
5.
Weak Coupling Limit
—
a.
Weisskopf
-Wigner Exponential De¬
cay, b. Corrections to the Exponential Decay
. 249
6.
Intermediate Coupling. Critical Coupling
—
a. Power Expansion
of
&b(E)
near a Maximum, b. Physical Meaning of the Critical
Coupling
. 251
7.
Strong Coupling
. 253
IV
RADIATION CONSIDERED AS A RESERVOIR: MASTER
EQUATION FOR THE PARTICLES
A. Introduction
—
Overview
. 257
B. Derivation of the Master Equation for a Small System s?
Interacting with a Reservoir
Ш
. 262
1.
Equation Describing the Evolution of the Small System in
the Interaction Representation
. 262
xii Contents
2.
Assumptions Concerning the Reservoir
—
a. State of the
Reservoir, b. One-Time and Two-Time Averages for the
Reservoir
Observables
. 263
3.
Perturbative Calculation of the Coarse-Grained Rate of
Variation of the Small System
. 266
4.
Master Equation in the Energy-State Basis
. 269
C. Physical Content of the Master Equation
. 272
1.
Evolution of Populations
. 272
2.
Evolution of Coherences
. 274
D. Discussion of the Approximations
. 278
1.
Order of Magnitude of the Evolution Time for j/
. 278
2.
Condition for Having Two Time Scales
. 278
3.
Validity Condition for the Perturbative Expansion
. 279
4.
Factorization of the Total Density Operator at Time
t
. 280
5.
Summary
. 281
E. Application to a Two-Level Atom Coupled to the Radiation
Field
. 282
1.
Evolution of Internal Degrees of Freedom
—
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
. 282
2.
Evolution of Atomic Velocities
—
a. Taking into Account
the Translational Degrees of Freedom in the Master Equation,
b. Fokker-Planck Equation for the Atomic Velocity Distribu¬
tion Function,
с
Evolutions of the Momentum Mean Value
and Variance, d. Steady-State Distribution. Thermodynamic
Equilibrium
. 289
Complement Aiv
—
Fluctuations and Linear Response
Application to Radiative Processes
Introduction
. 302
1.
Statistical Functions and Physical Interpretation of the Master
Equation
—
a. Symmetric Correlation Function, b. Linear
Sus-
Contents xiii
ceptibility.
с.
Polarization
Energy
and Dissipation, d. Physical
Interpretation
of the Level Shifts, e. Physical Interpretation of
the Energy Exchanges
. 302
2.
Applications to Radiative Processes
—
a. Calculation of the Sta¬
tistical Functions, b. Physical Discussion,
с
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
. 312
Complement Biv
—
Master Equation for a Damped
Harmonic Oscillator
1.
The Physical System
. 322
2.
Operator Form of the Master Equation
. 323
3.
Master Equation in the Basis of the Eigenstates of HA
—
a. Evolution of the Populations, b. Evolution of a Few Average
Values
. 326
4.
Master Equation in a Coherent State Basis
—
a. Brief Review of
Coherent States and the Representation PN of the Density Opera¬
tor, b. Evolution Equation for
PN(ß,ß*,t).
с.
Physical Dis¬
cussion
. . 329
Complement Civ
—
Quantum
Langevin
Equations
for a Simple Physical System
Introduction
. 334
1.
Review of the Classical Theory of Brownian Motion
—
a. Langevin
Equation, b. Interpretation of the Coefficient D.
Connection between Fluctuations and Dissipation,
с
A Few
Correlation Functions
. 334
2.
Heisenberg-Langevin Equations for a Damped Harmonic Os¬
cillator
—
a. Coupled
Heisenberg
Equations, b. The Quantum
Langevin
Equation and Quantum
Langevin
Forces,
с
Connec¬
tion between Fluctuations and Dissipation, d. Mixed Two-Time
Averages Involving
Langevin
Forces and Operators of
яґ.
e. Rate of Variation of the Variances
5^
and
2^. ƒ.
General¬
ization of Einstein's Rebtion. g. Calculation of Two-Time Aver¬
ages for Operators of sf. Quantum Regression Theorem
. 340
xiv Contents
v
OPTICAL BLOCH EQUATIONS
Introduction
. 353
A. Optical Bloch Equations for a Two-Level Atom
. 355
1.
Description of the Incident Field
. 355
2.
Approximation of Independent Rates of Variation
. 356
3.
Rotating-Wave Approximation
—
a. Elimination of
Antireso
-
nant Terms, b. Time-Independent Form of the Optical Bloch
Equations, c. Other Forms of'the Optical Bloch Equations
. 357
4.
Geometric Representation in Terms of a Fictitious Spin \
. . . 361
B. Physical Discussion
—
Differences with Other Evolution Equa¬
tions
. 364
1.
Differences with Relaxation Equations. Couplings between
Populations and Coherences
. 364
2.
Differences with Hamiltonian Evolution Equations
. 364
3.
Differences with Heisenberg-Langevin Equations
. 365
C. First Application
—
Evolution of
Atomic
Average Values
. 367
1.
Internal Degrees of Freedom
—
a. Transient Regime,
b. Steady-State Regime,
с
Energy Balance. Mean Number of
Incident Photons Absorbed per Unit Time
. 367
2.
External Degrees of Freedom. Mean Radiative Forces
—
a. Equation of Motion of the Center of the Atomic Wave
Packet, b. The Two Types of Forces for an Atom Initially at
Rest,
с
Dissipative Force. Radiation Pressure, d. Reactive
Force.
Dipole
Force
. 370
D. Properties of the Light Emitted by the Atom
. 379
1.
Photodetection Signals. One- and Two-Time Averages of
the Emitting
Dipole
Moment
—
a. Connection between the
Radiated Field and the Emitting
Dipole
Moment, b. Expres¬
sion of Photodetection Signals
. 379
2.
Total Intensity of the Emitted Light
—
a. Proportionality to
the Population of the Atomic Excited State, b. Coherent
Scattering and Incoherent Scattering,
с
Respective Contribu¬
tions of Coherent and Incoherent Scattering to the Total
Intensity Emitted in Steady State
. 382
3.
Spectral Distribution of the Emitted Light in Steady
Contents
State—
a. Respective Contributions of Coherent and Incoher¬
ent Scattering. Elastic and Inelastic Spectra, b. Outline of
the Calculation of the Inelastic Spectrum,
с
Inelastic Spec¬
trum in a Few Limiting Cases
. 384
Complement Av
—
Bloch
-Langevin
Equations and
Quantum Regression Theorem
Introduction
. 388
1.
Coupled
Heisenberg
Equations for the Atom and the Field
—
a. Hamiltonian and Operator Basis for the System, b. Evolution
Equations for the Atomic and Field
Observables,
с.
Rotating-
Wave Approximation. Change of Variables, d. Comparison with
the Harmonic Oscillator Case
. 388
2.
Derivation of the Heisenberg-Langevin Equations
—
a. Choice
of the Normal Order, b. Contribution of the Source Field.
с
Summary. Physical Discussion
. 394
3.
Properties of
Langevin
Forces
—
a. Commutation Relations
between the Atomic
Dipole
Moment and the Free Field, b. Cal¬
culation of the Correlation Functions of
Langevin
Forces,
с
Quantum Regression Theorem, d. Generalized Einstein
Relations
. 398
VI
THE DRESSED ATOM APPROACH
A. Introduction: The Dressed Atom
. 407
B. Energy Levels of the Dressed Atom
. 410
1.
Model of the Laser Beam
. 410
2.
Uncoupled States of the Atom
+
Laser Photons System
. . . 412
3.
Atom-Laser Photons Coupling
—
a. Interaction Hamiltonian.
b. Resonant and
Nonresonant
Couplings,
с
Local Periodic¬
ity of the Energy Diagram, d. Introduction of the
Rabi
Frequency
. 413
xvi Contents
4.
Dressed
States—
a.
Energy
Levels and Wave Functions.
b. Energy Diagram versus hmL
. 415
5.
Physical Effects Associated with Absorption and Induced
Emission
. 417
C. Resonance Fluorescence Interpreted as a Radiative Cascade of
the Dressed Atom
. 419
1.
The Relevant Time Scales
. 419
2.
Radiative Cascade in the Uncoupled Basis
—
a. Time Evolu¬
tion of the System, b. Photon Antibunching.
с
Time Inter¬
vals between Two Successive Spontaneous Emissions
. 420
3.
Radiative Cascade in the Dressed State Basis
—
a. Allowed
Transitions between Dressed States, b. Fluorescence Triplet,
с
Time Correlations between Frequency Filtered Fluorescence
Photons
. 423
D. Master Equation for the Dressed Atom
. 427
1.
General Form of the Master Equation
—
a. Approximation of
Independent Rates of Variation, b. Comparison with Optical
Bloch Equations
. 427
2.
Master Equation in the Dressed State Basis in the Secular
Limit
—
a. Advantages of the Coupled Basis in the Secular
Limit, b. Evolution of Populations,
с
Evolution of Coher¬
ences
—
Transfer of Coherences, d. Reduced Populations and
Reduced Coherences
. 429
3.
Quasi-Steady State for the Radiative Cascade
—
a. Initial Den¬
sity Matrix, b. Transient Regime and Quasi-Steady State
. 435
E. Discussion of a Few Applications
. 437
1.
Widths and Weights of the Various Components of the
Fluorescence Triplet
—
a. Evolution of the Mean
Dipole
Mo¬
ment, b. Widths and Weights of the Sidebands,
с
Structure
of the Central Line
. 437
2.
Absorption Spectrum of a Weak Probe Beam—a. Physical
Problem, b. Case Where the Two Lasers Are Coupled to the
Same Transition,
с
Probing on a Transition to a Third
Level. The Autler-Townes Effect
. 442
3.
Photon Correlations
—
a. Calculation of the Photon-Correla¬
tion Signal, b. Physical Discussion,
с
Generalization to a
Three-Level System: Intermittent Fluorescence
. 446
4. Dipole
Forces
—
a. Energy Levels of the Dressed Atom in a
Contents xvii
Spatially
Inhomogeneous Laser
Wave. b.
Interpretation
of the
Mean
Dipole
Force,
с.
Fluctuations of the
Dipole
Force
. 454
Complement Avi
—
The Dressed Atom in the
Radio-Frequency Domain
Introduction
. 460
1.
Resonance Associated with a Level Crossing or Anti-
crossing
—
a. Anticrossing for a Two-Level System, b. Higher-
Order Anticrossing.
с
Level Crossing. Coherence Resonance
. . . 461
2.
Spin \ Dressed by Radio-Frequency Photons
—
a. Description of
the System, b. Interaction Hamiltonian between the Atom and
the Radio-Frequency Field,
с
Preparation and Detection
. 468
3.
The Simple Case of Circularly Polarized Photons
—
a. Energy
Diagram, b. Magnetic Resonance Interpreted as a Level-Anti-
crossing Resonance of the Dressed Atom. c. Dressed State
Level-Crossing Resonances
. 473
4.
Linearly Polarized Radio-Frequency Photons
—
a. Survey of the
New Effects, b. Bloch-Siegert Shift,
с
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 Evolu¬
tion of the Energy Diagram at High Intensity
. 479
Complement Bvi
—
Collisional Processes in the
Presence of Laser Irradiation
Introduction
. 490
1.
Collisional Relaxation in the Absence of Laser Irradiation
—
a. Simplifying Assumptions, b. Master Equation Describing the
Effect of Collisions on the Emitting Atom
. 491
2.
Collisional Relaxation in the Presence of Laser Irradiation
—
a. The Dressed Atom Approach, b. Evolution of Populations:
Collisional Transfers between Dressed States, c. Evolution of
Coherences. Collisional Damping and Collisional Shift, d. Ex¬
plicit Form of the Master Equation in the Impact Limit
. 494
xviii
Contents
3.
Collision-Induced Modifications of the Emission and Absorp¬
tion of Light by the Atom. Collisional Redistribution
—
a. Tak¬
ing into Account Spontaneous Emission, b. Reduced Steady-
State Populations,
с
Intensity of the Three Components of the
Fluorescence Triplet, d. Physical Discussion in the Limit
Ωι
■«
ISzJ«^,1,
. 501
4.
Sketch of the Calculation of the Collisional Transfer Rate
—
a. Expression of the Transfer Rate as a Function of the Collision
S-Matrix. b. Case Where the Laser Frequency Becomes Resonant
during the Collmon. Limit of Large Detunings
. 510
Exercises
1.
Calculation of the Radiative Lifetime of an Excited Atomic
Level. Comparison with the Damping Time of a Classical
Dipole
Moment
. 515
2.
Spontaneous Emission of Photons by a Trapped Ion.
Lamb-Dicke Effect
. 518
3.
Rayleigh Scattering
. 524
4.
Thomson Scattering
. 527
5.
Resonant Scattering
. 530
6.
Optical Detection of a Level Crossing between Two Excited
Atomic States
. 533
7.
Radiative Shift of an Atomic Level. Bethe Formula for the
Lamb Shift
. 537
8. Bremsstrahlung.
Radiative Corrections to Elastic Scattering by
a Potential
. 548
9.
Low-Frequency
Bremsstrahlung. Nonperturbative
Treatment
of the Infrared Catastrophe
. 557
10.
Modification of the Cyclotron Frequency of a Particle due to
Its Interactions with the Radiation Field
. 564
11.
Magnetic Interactions between Spins
. 571
12.
Modification of an Atomic Magnetic Moment due to Its Cou¬
pling with Magnetic Field Vacuum Fluctuations
. 576
13.
Excitation of an Atom by a Wave Packet: Broadband Excita¬
tion and Narrow-Band Excitation
. 580
14.
Spontaneous Emission by a System of Two Neighboring Atoms.
Superradiant
and
Subradiant
States
. 585
15.
Radiative Cascade of a Harmonic Oscillator
. 589
16.
Principle of the Detailed Balance
. . 596
Contents xix
17.
Equivalence
between a Quantum Field in a Coherent State
and an External Field
. 597
18.
Adiabatic Elimination of Coherences and Transformation of
Optical Bloch Equations into Relaxation Equations
. 601
19.
Nonlinear Susceptibility for an Ensemble of Two-Level Atoms.
A Few Applications
. 604
20.
Absorption of a Probe Beam by Atoms Interacting with an
Intense Beam. Application to Saturated Absorption
. 608
APPENDIX
QUANTUM ELECTRODYNAMICS IN THE COULOMB
GAUGE—SUMMARY OF THE ESSENTIAL RESULTS
1.
Description of the Electromagnetic Field
—
a. Electric Field
E
and Magnetic Field B. b. Vector Potential A and Scalar Poten¬
tial
U. c
Coulomb Gauge, d. Normal Variables, e. Principle
of Canonical Quantization in the Coulomb Gauge, f. Quantum
Fields in the Coulomb Gauge
. 621
2.
Particles
. 628
3.
Hamiltonian and Dynamics in the Coulomb Gauge
—
a. Hamil-
tonian. b. Unperturbed Hamiltonian and Interaction Hamilto¬
nian.
с
Equations of Motion
. 629
4.
State Space
. 633
5.
The Long-Wavelength Approximation and the Electric
Dipole
Representation
—
a. The Unitary Transformation, b. The Phys¬
ical Variables in the Electric
Dipole
Representation,
с
The
Displacement Field, d. Electric
Dipole
Hamiltonian
. 635
References
. 641
Index
. . 645 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Cohen-Tannoudji, Claude 1933- Dupont-Roc, Jacques Grynberg, Gilbert |
| author_GND | (DE-588)115610340 |
| author_facet | Cohen-Tannoudji, Claude 1933- Dupont-Roc, Jacques Grynberg, Gilbert |
| author_role | aut aut aut |
| author_sort | Cohen-Tannoudji, Claude 1933- |
| author_variant | c c t cct j d r jdr g g gg |
| building | Verbundindex |
| bvnumber | BV020863576 |
| callnumber-first | Q - Science |
| callnumber-label | QC794 |
| callnumber-raw | QC794.8.P4 |
| callnumber-search | QC794.8.P4 |
| callnumber-sort | QC 3794.8 P4 |
| callnumber-subject | QC - Physics |
| classification_rvk | UN 3020 |
| classification_tum | PHY 522f PHY 415f |
| ctrlnum | (OCoLC)221648337 (DE-599)BVBBV020863576 |
| discipline | Physik |
| discipline_str_mv | Physik |
| format | Book |
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| genre | 1\p (DE-588)4123623-3 Lehrbuch gnd-content |
| genre_facet | Lehrbuch |
| id | DE-604.BV020863576 |
| illustrated | Illustrated |
| index_date | 2024-07-02T13:23:47Z |
| indexdate | 2024-07-09T20:26:57Z |
| institution | BVB |
| isbn | 0471293369 9780471293361 |
| language | English French |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-014185435 |
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| physical | XXII, 656 S. graph. Darst. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Wiley-VCH |
| record_format | marc |
| series2 | Physics textbook |
| spelling | Cohen-Tannoudji, Claude 1933- Verfasser (DE-588)115610340 aut Processus d'interaction entre photons et atomes Atom photon interactions basic processes and applications Claude Cohen-Tannoudji ; Jacques Dupont-Roc ; Gilbert Grynberg Atom-photon interactions Weinheim Wiley-VCH 2004 XXII, 656 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Physics textbook Quantentheorie Photonuclear reactions Quantum theory Statistical physics Quantentheorie (DE-588)4047992-4 gnd rswk-swf Quantenelektrodynamik (DE-588)4047982-1 gnd rswk-swf Elektromagnetische Strahlung (DE-588)4014297-8 gnd rswk-swf Kernfotoeffekt (DE-588)4045929-9 gnd rswk-swf Statistische Physik (DE-588)4057000-9 gnd rswk-swf Atom (DE-588)4003412-4 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Atom (DE-588)4003412-4 s Elektromagnetische Strahlung (DE-588)4014297-8 s Quantenelektrodynamik (DE-588)4047982-1 s DE-604 Kernfotoeffekt (DE-588)4045929-9 s 2\p DE-604 Statistische Physik (DE-588)4057000-9 s 3\p DE-604 Quantentheorie (DE-588)4047992-4 s 4\p DE-604 Dupont-Roc, Jacques Verfasser aut Grynberg, Gilbert Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014185435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Cohen-Tannoudji, Claude 1933- Dupont-Roc, Jacques Grynberg, Gilbert Atom photon interactions basic processes and applications Quantentheorie Photonuclear reactions Quantum theory Statistical physics Quantentheorie (DE-588)4047992-4 gnd Quantenelektrodynamik (DE-588)4047982-1 gnd Elektromagnetische Strahlung (DE-588)4014297-8 gnd Kernfotoeffekt (DE-588)4045929-9 gnd Statistische Physik (DE-588)4057000-9 gnd Atom (DE-588)4003412-4 gnd |
| subject_GND | (DE-588)4047992-4 (DE-588)4047982-1 (DE-588)4014297-8 (DE-588)4045929-9 (DE-588)4057000-9 (DE-588)4003412-4 (DE-588)4123623-3 |
| title | Atom photon interactions basic processes and applications |
| title_alt | Processus d'interaction entre photons et atomes Atom-photon interactions |
| title_auth | Atom photon interactions basic processes and applications |
| title_exact_search | Atom photon interactions basic processes and applications |
| title_exact_search_txtP | Atom photon interactions basic processes and applications |
| title_full | Atom photon interactions basic processes and applications Claude Cohen-Tannoudji ; Jacques Dupont-Roc ; Gilbert Grynberg |
| title_fullStr | Atom photon interactions basic processes and applications Claude Cohen-Tannoudji ; Jacques Dupont-Roc ; Gilbert Grynberg |
| title_full_unstemmed | Atom photon interactions basic processes and applications Claude Cohen-Tannoudji ; Jacques Dupont-Roc ; Gilbert Grynberg |
| title_short | Atom photon interactions |
| title_sort | atom photon interactions basic processes and applications |
| title_sub | basic processes and applications |
| topic | Quantentheorie Photonuclear reactions Quantum theory Statistical physics Quantentheorie (DE-588)4047992-4 gnd Quantenelektrodynamik (DE-588)4047982-1 gnd Elektromagnetische Strahlung (DE-588)4014297-8 gnd Kernfotoeffekt (DE-588)4045929-9 gnd Statistische Physik (DE-588)4057000-9 gnd Atom (DE-588)4003412-4 gnd |
| topic_facet | Quantentheorie Photonuclear reactions Quantum theory Statistical physics Quantenelektrodynamik Elektromagnetische Strahlung Kernfotoeffekt Statistische Physik Atom Lehrbuch |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014185435&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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