Advances in atomic physics: an overview
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2011
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| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XXV, 767 S. Ill., graph. Darst. 26 cm |
| ISBN: | 9789812774965 9789812774972 |
Internformat
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| 020 | |a 9789812774965 |c hardcover |9 978-981-277-496-5 | ||
| 020 | |a 9789812774972 |c pbk. |9 978-981-277-497-2 | ||
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| 100 | 1 | |a Cohen-Tannoudji, Claude |d 1933- |e Verfasser |0 (DE-588)115610340 |4 aut | |
| 245 | 1 | 0 | |a Advances in atomic physics |b an overview |c Claude Cohen-Tannoudji ; David Guery-Odelin |
| 264 | 1 | |a New Jersey [u.a.] |b World Scientific |c 2011 | |
| 300 | |a XXV, 767 S. |b Ill., graph. Darst. |c 26 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 0 | 7 | |a Atom-Photon-Wechselwirkung |0 (DE-588)4143332-4 |2 gnd |9 rswk-swf |
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| 650 | 0 | 7 | |a Zwischenatomare Kraft |0 (DE-588)4253455-0 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Atomphysik |0 (DE-588)4003423-9 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Guéry-Odelin, David |e Verfasser |0 (DE-588)1017188181 |4 aut | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020162010&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-020162010 | ||
Datensatz im Suchindex
| _version_ | 1804142738864603136 |
|---|---|
| adam_text | Contents
Fotr
woal
v
AťknowU
(¡(¡ments
xxv
1.
(іічнчаі
introduction
1
(■еікта)
background
ι
2.1
Introduction
............................... 7
2.2
Tlie
two interacting systems: atom and Held
............. 9
2.2.1
External and internal atomic variables
........... 9
2.2.2
Classical versus quantum treatments of atomic variables
. 10
2.2.3
Classical description of field variables
............ 10
2.2.4
Quantum description of field variables
............ 11
2.2.5
Atom-field interaction Hamiltonian in the long wavelength
approximation
......................... 12
2.2.6
Elementary interaction processes
............... 14
2.3
Basic conservation laws
........................ 14
2.3.1
Conservation of the total linear momentum
......... 14
2.3.2
Conservation of the total angular momentum
........ 17
2.4
Two-level atom interacting with a coherent monochromatic field.
The
Rabi
oscillation
.......................... 20
2.4.1
A simple case: magnetic resonance of a spin
1/2...... 20
2.4.2
Extension to any two-level atomic system
.......... 23
2.4.3
Perturbative limit
....................... 25
2.4.4
Two physical pictures for Ramsey fringes
.......... 27
2.5
Two-level atom interacting with a broadband field. Absorption and
emission rates
.............................. 29
2.5.1
Absorption rate deduced from a semiclassical treatment of
the field
............................. 29
2.5.2
Physical discussion. Relaxation time and correlation time
. 31
viii
Advances in atomic physics: an
ouewiew
2.5.3
Sketch of a quantum treatment of the absorption process
. 31
2.5.4
Extension to spontaneous emission
............. 32
2.6
Two-level atom interacting with a coherent monochromatic field in
the presence of damping
........................ 33
Light: a source of information on atoms
35
3.
Optical methods
41
3.1
Introduction
............................... 41
3.2
Double resonance
............................ 43
3.2.1
Principle of the method
.................... 43
3.2.2
Predicted shape for the double resonance curve
...... 44
3.2.3
Experimental results
..................... 45
3.2.4
Interpretation of the
Majorana
reversal
........... 45
3.3
Optical pumping
[Kastler (1950)]................... 46
3.3.1
Principle of the method for a Jg
= 1/2 ->
Je
= 1/2
transition
............................ 47
3.3.2
Angular momentum balance
................. 48
3.3.3
Double role of light
...................... 48
3.4
First experiments on optical pumping
................ 49
3.5
How can optical pumping polarize atomic nuclei?
......... 49
3.5.1
Using hyperfme coupling with polarized electronic spins
. . 49
3.5.2
First example: optical pumping experiments with
mercury-199 atoms
...................... 52
3.5.3
Second example: combining optical pumping with
metastability exchange collisions for helium-3
........ 52
3.5.4
A new application: magnetic resonance imaging of the
lung cavities
.......................... 54
3.6
Brief survey of the main applications of optical methods
...... 55
3.7
Concluding remarks
.......................... 58
4.
Linear superpositions of internal atomic states
61
4.1
Introduction
............................... 61
4.2
First experimental evidence of the importance of
atomic coherences
........................... 62
4.3
Zeeman
coherences in excited states
................. 64
4.3.1
How to prepare
Zeeman
coherences in excited states e?
. . 64
4.3.2
Physical interpretation
.................... 64
4.3.3
How to detect
Zeeman
coherences in e?
........... 66
4.3.4
Equation of motion of
Zeeman
coherences in
e
....... 66
4.3.5
Level crossing resonances in the excited state
є
....... 67
Contents ix
4.3.6
Pulsed excitation. Quantum beats
.............. 69
4.3.7
Excitation with modulated light
............... 70
4.3.8
Modulation of the fluorescence light in a double resonance
experiment. Light beats
.................... 70
4.4
Zeeman
coherences in atomic ground states
............. 71
4.4.1
Hanle effect in atomic ground states
............. 71
4.4.2
Detection of the magnetic resonance in the ground state by
the modulation of the absorbed light
............ 74
4.5
Transfer of coherences
......................... 74
4.6
Dark resonances. Coherent population trapping
........... 79
4.6.1
Discovery of dark resonances
................. 79
4.6.2
First theoretical treatment of dark resonances
....... 80
4.6.3
Interpretation of the Raman resonance condition
...... 81
4.6.4
A few applications of dark resonances
............ 82
4.7
Conclusion
............................... 84
5.
Resonance fluorescence
87
5.1
Introduction
............................... 87
5.2
Low intensity limit. Perturbative approach
............. 88
5.2.1
Lowest order process
..................... 88
5.2.2
Resonant scattering amplitude
............... 89
5.2.3
Scattering of a light wave packet
............... 91
5.2.4
First higher order processes
................. 92
5.3
Optical Bloch equations
........................ 93
5.4
The dressed atom approach
...................... 96
5.4.1
The interacting systems
................... 96
5.4.2
Uncoupled states of the atom-laser system
......... 97
5.4.3
Effect of the coupling. Dressed states
............ 98
5.4.4
Two different situations
................... 99
5.4.5
Radiative cascade in the basis of uncoupled states
..... 101
5.4.6
A new description of quantum dissipative processes
.... 104
5.5
Photon correlations. The quantum jump approach
......... 105
5.5.1
The waiting time distribution
................ 105
5.5.2
From the waiting time distribution to the second order
correlation function
...................... 106
5.5.3
Photon antibunching
..................... 106
5.6
Fluorescence triplet at high laser intensities
............. 108
5.6.1
Limit of large
Rabi
frequency
................ 108
5.6.2
Mollow fluorescence triplet
.................. 108
5.6.3
Widths and weights of the components of the Mollow
triplet
............................. 110
χ
Advances in atomic physics: an orercicw
5.6.4
Time correlations between the photons emitted in the two
sidebands of the fluorescence triplet
.............
Ill
5.7
Conclusion
............................... 112
6.
Advances in high resolution spectroscopy
115
6.1
Introduction
............................... 115
6.2
Saturated absorption
.......................... 117
6.2.1
Principle of the method
.................... 117
6.2.2
Crossover resonances
..................... 118
6.2.3
Recoil doublet
......................... 120
6.3
Two-photon Doppler-free spectroscopy
................ 121
6.3.1
Principle of the method
.................... 121
6.3.2
Examples of results
...................... 122
6.3.3
Comparison between saturated absorption and two-photon
spectroscopy
.......................... 124
6.4
Recoil suppressed by confinement: the Lamb-Dicke effect
..... 124
6.4.1
Intensities of the vibrational lines
.............. 125
6.4.2
Influence of the localization of the ion
............ 127
6.4.3
Case of a harmonic potential
................. 127
6.4.4
Historical perspective
..................... 128
6.5
The shelving method
.......................... 129
6.5.1
Single ion spectroscopy
.................... 130
6.5.2
Intermittent fluorescence
................... 131
6.5.3
Properties of the detected signal
............... 132
6.5.4
Observation of quantum jumps
................ 134
6.6
Quantum logic spectroscopy
...................... 135
6.7
Frequency measurement with frequency combs
........... 137
6.8
Conclusion
............................... 139
Atom-photon interactions: a source of perturbations for
atoms which can be useful
141
7.
Perturbations due to a quasi resonant optical excitation
145
7.1
Introduction
...............................145
7.2
Light shift, light broadening and
Rabi
oscillation
..........147
7.2.1
Effective Hamiltonian
..................... 147
7.2.2
Weak coupling limit. Light shift and light broadening
... 148
7.2.3
High coupling limit.
Rabi
oscillation
............. 149
7.2.4
Absorption rate versus
Rabi
oscillation
........... 151
7.2.5
Semiclassical interpretation in the weak coupling limit
... 151
7.2.6
Generalization to a non-resonant excitation
......... 152
Contents xi
7.2.7
Case of a degenerate ground state
.............. 154
7.3
Perturbation of the field. Dispersion and absorption
........ 155
7.3.1
Atom in a cavity
........................ 155
7.3.2
Frequency shift of the field due to the atom
........ 156
7.3.3
Damping of the field
..................... 157
7.4
Experimental observation of light shifts
............... 158
7.4.1
Principle of the experiment
.................. 158
7.4.2
Examples of results
...................... 159
7.5
Using light shifts for manipulating atoms
.............. 161
7.5.1
Laser traps
........................... 161
7.5.2
Atomic mirrors
........................ 162
7.5.3
Blue detuned traps: a few examples
............. 163
7.5.4
Optical lattices
......................... 164
7.5.5
Internal state dependent optical lattices
........... 165
7.5.6
Coherent transport
...................... 167
7.6
Using light shifts for manipulating fields
............... 167
7.6.1
Linear superposition of two field states with different
phases
............................. 168
7.6.2
Non-destructive detection of photons
............ 168
7.7
Conclusion
............................... 109
8.
Perturbations due to a high frequency excitation
171
8.1
Introduction
............................... 171
8.2
Spin
1/2
coupled to a high frequency RF field
............ 173
8.2.1
Hamiltonian
.......................... 174
8.2.2
Perturbative treatment of the coupling
........... 174
8.2.3
Stimulated corrections
.................... 176
8.2.4
Radiative corrections
..................... 177
8.3
Weakly bound electron coupled to a high frequency field
...... 178
8.3.1
Effective Hamiltonian describing the modifications of the
dynamical properties of the electron
............. 178
8.3.2
Stimulated effects
....................... 180
8.3.3
Spontaneous effects. Vacuum fluctuations and
radiation reaction
....................... 182
8.4
New insights into radiative corrections
................ 183
8.4.1
Examples of spontaneous corrections
............ 183
8.4.2
Interpretation of the Lamb shift
............... 185
8.4.3
Interpretation of the spin anomaly
g
— 2.......... 186
8.5
Conclusion
...............................
igg
xii
Advances in atomic physics: an overview
Atom-photon interactions: a simple system for studying
higher order effects
191
9.
Multiphoton processes between discrete states
195
9.1
Introduction
............................... 195
9.2
Radiofrequency multiphoton processes
................ 196
9.2.1
Multiphoton RF transitions between two
Zeeman
subleveis
mp·
and
TUF
+ 2........................ 196
9.2.2
Experimental observation on sodium atoms
......... 198
9.2.3
Multiphoton resonances between two
Zeeman
subleveis
îuf
and
mr
+ 1 .......................... 199
9.3
Radiative shift and radiative broadening of multiphoton
resonances
................................ 202
9.3.1
Energy levels of the atom+RF photons system.
Transition amplitude
..................... 202
9.3.2
Pure single photon resonance. Simple anticrossing
..... 204
9.3.3
Higher order anticrossing for a p-photon resonance (p
> 1) 205
9.3.4
Application to the case of a spin
1/2
coupled to
a
σ-
polarized RF field
....................... 206
9.4
Optical multiphoton processes between discrete states
....... 211
9.4.1
Introduction
.......................... 211
9.4.2
Radiative shift of Doppler-free two-photon resonances
... 211
9.4.3
Stimulated Raman processes
................. 212
9.4.4
Phase matching condition. Application to degenerate
four-wave mixing
....................... 217
9.5
Conclusion
............................... 219
10.
Photoionization of atoms in intense laser fields
221
10.1
Introduction
............................... 221
10.2
Multiphoton ionization
......................... 223
10.2.1
Parameters influencing the multiphoton ionization rate
. . 223
10.2.2
Quantum interference effects in multiphoton ionization
. . 225
10.2.3
Asymmetric line profiles in resonant multiphoton
ionization
............................ 226
10.3
Above threshold ionization (ATI)
................... 227
10.3.1
Multiphoton transitions between states of the continuum
. 227
10.3.2
Consequences of the oscillatory motion of the electron in
the laser field
.......................... 228
10.3.3
Evidence for non-perturbative effects
............ 229
10.4
Harmonic generation
.......................... 231
10.4.1
Physical interpretation
.................... 231
Contents xiii
10.4.2
High order harmonic generation (HHG). Evidence for non-
perturbative effects
......................232
10.5
Tunnel ionization and
recollision
...................233
10.5.1
The breakdown of perturbation theory
........... 233
10.5.2
Keldysh parameter
...................... 234
10.5.3
Two-step quantum-classical model
.............. 235
10.5.4
Recollision
........................... 237
10.5.5
Full quantum treatments
................... 239
10.6
Conclusion
............................... 239
Atom-photon interactions: a tool for controlling and
manipulating atomic motion
241
11.
Radiative forces exerted on a two-level atom at rest
247
11.1
Introduction
...............................247
11.1.1
Order of magnitude of the force
............... 247
11.1.2
Characteristic times
...................... 248
11.1.3
Validity of the concept of a mean
forco
at a given point
. . 249
11.2
Calculation of the mean radiative force
................ 250
11.2.1
Principle of the calculation
..................250
11.2.2
Hamiltonian and the rotating wave approximation
.....251
11.2.3 Heisenberg
equations for the external variables.
Force operator
.........................252
11.2.4
Approximations. Mean radiative force
............253
11.2.5
The two types of mean radiative forces: dissipative
and reactive
..........................253
11.3
Dissipative force
............................256
11.3.1
Theoretical results
.......................256
11.3.2
Physical interpretation
....................257
11.3.3
Application to the deflection and to the slowing down
of an atomic beam
.......................258
11.3.4
Fluctuations
..........................260
11.4
Reactive force
..............................261
11.4.1
Theoretical results
....................... 262
11.4.2
Physical interpretation
.................... 262
11.4.3
Dressed atom interpretation
................. 263
11.5
Conclusion
............................... 266
12.
Laser cooling of two-level atoms
269
12.1
Introduction
...............................269
12.2
Doppler-induced friction force
.....................271
civ
Advances in atomic physics: an overview
12.2.1
Doppler
effect in a red detuned laser plane wave
...... 271
12.2.2
Low velocity behavior of the force
.............. 272
12.2.3
Idea of
Doppler
cooling for trapped ions
.......... 273
12.2.4
Idea of
Doppler
cooling for neutral atoms
.......... 273
12.3
Two-level atom moving in a weak standing wave.
Doppler
cooling
............................. 275
12.3.1
Perturbative approach for calculating the force
....... 275
12.3.2
Friction coefficient for a red-detuned weak standing wave
. 276
12.3.3
Momentum-energy balance. Entropy balance
........ 276
12.3.4
Limits of
Doppler
cooling. Lowest temperature
....... 277
12.3.5
Consistency of the various approximations
......... 279
12.3.6
Spatial diffusion. Optical molasses
.............. 279
12.4
Beyond the perturbative approach
.................. 280
12.4.1
Optical Bloch equations for a moving atom
......... 280
12.4.2
Time lag of internal variables
................. 281
12.4.3
Low velocity limit (kLv
«Г)
................. 282
12.4.4
Higher velocities
........................ 282
12.5
Dressed atom approach to atomic motion in an intense
.standing wave. Blue cooling
...................... 284
12.5.1
Energy and radiative widths of the dressed states
..... 284
12.5.2
Friction mechanism
...................... 285
12.5.3
High intensity Sisyphus cooling
............... 286
12.5.4
Experimental results
..................... 288
12.6
Conclusion
............................... 289
13.
Sub-Doppler cooling. Sub-recoil cooling
291
13.1
Introduction
............................... 291
13.2
Sub-Doppler cooling
.......................... 293
13.2.1
The basic ingredients of sub-Doppler cooling
........ 293
13.2.2
Laser configuration and atomic transition
.......... 294
13.2.3
Light shifts and optical pumping for an atom at rest
.... 294
13.2.4
Low intensity Sisyphus cooling for a moving atom
..... 296
13.2.5
Characteristics of the friction force. Qualitative discussion
298
13.2.6
Quantum limits of sub-Doppler cooling
........... 300
13.3
Sub-recoil cooling
............................ 302
13.3.1
Physical mechanism
...................... 302
13.3.2
Velocity selective coherent population trapping (VSCPT)
. 304
13.3.3
Sub-recoil Raman cooling
................... 308
13.3.4
Quantitative predictions for sub-recoil cooling
....... 310
13.4
Resolved sideband cooling of trapped ions
.............. 312
13.5
Conclusion
............................... 314
Contents xv
14.
Trapping of particles
317
14.1
Introduction
............................... 317
14.2
Trapping of charged particles
..................... 318
14.2.1
The Earnshaw theorem
.................... 318
14.2.2
The Penning trap
....................... 319
14.2.3
The Paul trap
......................... 321
14.2.4
Cooling of the trapped ions
.................. 323
14.2.5
High precision measurements performed with ultracold
trapped ions
.......................... 324
14.3
Magnetic traps
............................. 325
14.3.1
Introduction
.......................... 325
14.3.2
Quadrupole trap and
Majorana
losses
............ 326
14.3.3
Ioffe-Pritchard trap
...................... 327
14.3.4
Time-averaged orbiting potential (TOP)
.......... 329
14.3.5
Loading neutral atoms in a magnetic trap
......... 330
14.4
Electric
dipole
traps
.......................... 330
14.4.1
Induced
dipole
moment
.................... 330
14.4.2
Application of
dipole
forces to trapping
........... 332
14.4.3
Optical lattices
......................... 335
1-4.5
Artificial orbital magnetism for neutral atoms
............ 338
14.5.1
Introduction
.......................... 338
14.5.2
Rotating a harmonically trapped quantum gas
....... 338
14.5.3
Artificial gauge potential from adiabatie evolution
..... 339
14.0
Magneto-optical trap (MOT)
..................... 341
14.7
Conclusion
............................... 344
Ultracold interactions and their control
347
15.
Two-body interactions at low temperatures
351
15.1
Introduction
............................... 351
15.2
Quantum scattering: a brief reminder
................ 352
15.2.1
Scattering amplitude
..................... 353
15.2.2
Scattering cross section
.................... 355
15.2.3
Partial wave expansion
.................... 355
15.3
Scattering length
............................ 358
15.3.1
Low-energy limit
........................ 358
15.3.2
Scattering amplitude and scattering length
......... 360
15.3.3
Square potential and resonances
............... 361
15.3.4
Effective interactions and the sign of the scattering length
363
15.4
Pseudo-potential
............................ 365
15.4.1
Motivation for introducing this pseudo-potential
...... 365
evi
Advances
in
atomic physics: an overview
15.4.2
Localized pseudo-potential giving the correct
scattering length
........................ 365
15.4.3
Scattering amplitude. Validity of the Born approximation
367
15.4.4
Bound state of the pseudo-potential for a positive
scattering length
........................ 368
15.5
Delta potential truncated in momentum space
............369
15.5.1
Expression of the potential
.................. 369
15.5.2
Determination of the new coupling constant
........ 369
15.5.3
Comparison with the pseudo-potential
........... 370
15.6
Forward scattering
........................... 371
15.6.1
Gaussian incident wave and scattered wave
......... 371
15.6.2
Interference of the incident and scattered waves in the
far-field zone
.......................... 373
15.6.3
Phase shift of the incident wave and mean field energy
. . 375
15.7
Conclusion
............................... 377
16.
Controlling atom-atom interactions
379
16.1
Introduction
...............................379
16.2
Collision channels
............................380
16.2.1
Microscopic interactions
...................380
16.2.2
Quantum numbers of the initial collision state.
Collision channels
....................... 382
16.2.3
Coupled channel equations
.................. 382
16.2.4
Two-channel model
...................... 383
16.3
Qualitative discussion. Analogy between Feshbach resonances and
resonant light scattering
........................ 384
16.4
Scattering states of the two-channel Hamiltonian
.......... 386
16.4.1
Calculation of the dressed scattering states
......... 386
16.4.2
Existence of a resonance in the scattering amplitude
.... 388
16.4.3
Asymptotic behavior of the dressed scattering states
.... 389
16.4.4
Scattering length. Feshbach resonance
............ 391
16.5
Bound states of the two-channel Hamiltonian
............ 393
16.5.1
Calculation of the energy of the bound state
........ 393
16.5.2
Wave function of the bound state
.............. 396
16.5.3
Halo states
........................... 397
16.6
Producing ultracold molecules
..................... 399
16.6.1
Magnetic tuning of a Feshbach resonance
..........399
16.6.2
Photoassociation
of ultracold atoms
.............400
16.7
Conclusion
...............................
4Q2
Contents xvii
Exploring quantum interferences with few atoms and
photons
405
17.
Interference of atomic
de Broglie
waves
409
17.1
Introduction
...............................409
17.2 De
Broglie waves versus optical waves
................410
17.2.1
Dispersion relations. Position and momentum
distributions
.......................... 410
17.2.2
Spatial coherences. Coherence length
............ 411
17.2.3
Fragility of spatial coherences
................ 413
17.3
Young s two-slit interferences with atoms
.............. 414
17.3.1
Important parameters of Young s double-slit interferometer
414
17.3.2
Young s double-slit interferences with supersonic beams
. . 415
17.3.3
Young s double-slit interferences with cold atoms
.....416
17.3.4
Can one determine which slit the atom passes through?
. . 417
17.4
Diffraction of atoms by material structures
.............418
17.5
Diffraction by laser standing waves
..................420
17.5.1
New features compared to the diffraction by
material gratings
....................... 420
17.5.2
Light-atom momentum exchange
............... 422
17.5.3
Raman-Nath regime
...................... 423
17.5.4
Bragg regime
.......................... 424
17.6
Bloch oscillations
............................ 427
17.6.1
Review on the quantum treatment of a particle in a
periodic potential
....................... 427
17.6.2
Implementation with cold atoms
............... 428
17.6.3
Physical interpretations
.................... 430
17.7
Diffraction of atomic
de
Broglie waves by time-dependent
structures
................................ 431
17.7.1
Phase modulation of atomic
de
Broglie waves
.......432
17.7.2
Atomic wave diffraction and interference using
temporal slits
.........................433
17.8
Conclusion
...............................433
18.
Ramsey fringes revisited and atomic
interferometry
435
18.1
Introduction
...............................435
18.2
Microwave atomic clocks with cold atoms
..............437
18.2.1
Principle of an atomic clock
................. 437
18.2.2
Atomic fountains
....................... 437
18.2.3
Performances of atomic fountains
.............. 438
18.2.4
Cold atoms clocks in space
.................. 441
18.2.5
Tests of general relativity
................... 441
xviii
Advances in atomic physics: an over-view
18.3
Extension of Ramsey fringes to the optical domain
.........442
18.3.1
Equivalence of the crossing of a laser beam with a coherent
beam splitter
..........................442
18.3.2
Spatial separation of the two final wave packets. Quenching
of the interference
....................... 443
18.3.3
How to restore the interference signal?
........... 444
18.3.4
Other possible schemes
.................... 448
18.4
Calculation of the phase difference between the two arms of an
atomic interferometer
......................... 449
18.4.1
Quantum propagator and Feynman path integral
.....450
18.4.2
Simple case of quadratic Lagrangians
............451
18.4.3
Phase shift in the absence of external potentials and
inerţial
fields
..........................452
18.4.4
Phase shift due to external potentials and
inerţial
fields in
the perturbative limit
.....................453
18.5
Applications of atomic
interferometry
................454
18.5.1
Measurement of gravitational fields. Gravimeters
..... 454
18.5.2
Measurement of rotational
inerţial
fields
.......... 457
18.5.3
Measurement of h/M and a
................. 459
18.6
New perspectives opened by optical clocks
.............. 461
19.
Quantum correlations. Entangled states
463
19.1
Introduction
...............................463
19.2
Interference effects in double counting rates
.............464
19.2.1
Photodetection signals
.................... 464
19.2.2
Two-mode model for the light field
............. 465
19.2.3
What are the objects which interfere in wjjl
...... 466
19.2.4
Establishment of correlations between the two modes
. . . 467
19.3
Entangled states
............................ 469
19.3.1
Definition
............................ 469
19.3.2
Schmidt decomposition of an entangled state
........ 469
19.3.3
Information content of an entangled state
.......... 471
19.4
Preparing entangled states
....................... 472
19.4.1
Entanglement between one atom and one field mode
.... 472
19.4.2
Entanglement between two atoms
.............. 473
19.4.3
Entanglement between two separate cavity fields
...... 475
19.4.4
Entanglement between two photons
............. 475
19.5
Entanglement and interference
.................... 477
19.6
Entanglement and non-separability
.................. 479
19.6.1
The Einstein-Podolsky-Rosen (EPR) argument [Einstein
et al.
(1935)] .........................479
19.6.2
Belľs
inequalities
.......................480
Contents xix
19.6.3
Experimental
results and conclusion
............. 481
19.7
Entanglement and which-path information
.............. 485
19.8
Entanglement and the measurement process
............. 486
19.8.1 Von
Neumann model of an ideal measurement process
. . . 486
19.8.2
Difficulty associated with macroscopic coherences
..... 487
19.8.3
A possible solution: coupling of
M
with the environment
. 487
19.8.4
Simple example of pointer states
............... 488
19.8.5
The infinite chain of
Von
Neumann
............. 489
19.9
Conclusion
............................... 490
Degenerate quantum gases
491
20.
Emergence of quantum effects in a gas
497
20.1
Introduction
...............................497
20.2
Quantum effects in collisions
.....................499
20.2.1
S-matrix and T-matrix
.................... 499
20.2.2
Interfering scattering amplitudes for identical particles
. . 500
20.2.3
Polarized Fermi gas at low temperature
........... 503
20.2.4
Interference effects in forward and backward scattering
. . 503
20.2.5
Identical spin rotation effect (ISRE)
............. 506
20.2.6
A few examples of effects involving ISRE
.......... 508
20.3
The first prediction of
ВЕС
in a gas
................. 512
20.3.1
A new derivation of Planck s law for black body radiation
512
20.3.2
Extension of
Bose
statistics to atomic particles
....... 513
20.3.3
The condensation phenomenon
................ 514
20.3.4
Critical temperature
...................... 515
20.3.5
Variation of the number N$ of condensed atoms with the
temperature. Thermodynamic limit
............. 518
20.3.6
Influence of dimensionality
.................. 519
20.4
Conclusion
............................... 520
21.
The long quest for Bose-Einstein condensation
523
21.1
Introduction
...............................523
21.2
First attempts on hydrogen
......................524
21.2.1
Spin polarized hydrogen as a quantum gas
......... 524
21.2.2
Production of a spin polarized sample at low temperature
. 525
21.2.3
Difficulties associated with collisions
............. 526
21.2.4
Need for other methods
.................... 527
21.3
Second attempts on hydrogen
.................... 527
21.3.1
Wall free confinement. Magnetic trapping
.........527
21.3.2
Bose-Einstein condensation in a harmonic trap
.......528
xx
Advances in atomic physics: an overview
21.3.3
New cooling method: evaporative cooling
..........529
21.3.4
Need for new detection method of polarized hydrogen
. . . 532
21.4
The quest for
ВЕС
for alkali atoms
..................533
21.4.1
Difficulties associated with alkali atoms
...........533
21.4.2
Advantages of alkali atoms
..................534
21.5
First observation of Bose-Einstein condensation
...........535
21.5.1
Time sequence
......................... 535
21.5.2
Signature of Bose-Einstein condensation
.......... 536
21.5.3
Subsequent observation on hydrogen
............ 538
21.6
Bose-Einstein condensation of other atomic species
......... 538
21.6.1
Experimental improvements
.................538
21.6.2
Review of new condensates
..................540
21.7
The first experiments on quantum degenerate Fermi gases
.....542
21.7.1
Ideal Fermi gas in a three-dimensional harmonic trap
. . . 543
21.7.2
Cooling
fermions
........................ 544
21.7.3
Spatial distribution and Fermi pressure
........... 545
21.7 .4
Pairs of fermionic atoms
................... 545
21.8
Conclusion
............................... 546
22.
Mean field description of a Bose-Einstein condensate
549
22.1
Introduction
...............................549
22.2
Mean field description of the condensate
...............550
22.2.1
Variational calculation of the condensate wave function
. . 550
22.2.2
Stationary Gross-Pitaevskii equation
............551
22.2.3
Expression of the various quantities in terms of the
spatial density
.........................552
22.3
Condensate in a box and healing length
...............553
22.3.1
Condensate in a one-dimensional box
............553
22.3.2
Healing length
........................554
22.4
Condensate in a harmonic trap
....................555
22.4.1
Total energy and the different interaction regimes
..... 555
22.4.2
Condensate with a positive scattering length and the
Thomas-Fermi limit
...................... 556
22.5
Condensate with a negative scattering length
............ 559
22.5.1
Condition of stability in
3D .................559
22.5.2 Solitonic
solution in ID
....................560
22.5.3
Collapse and explosion of a condensate
in
3D
with a negative scattering length
...........560
22.6
Quantum vortex in an homogeneous condensate
...........561
22.6.1
Effective Gross-Pitaevskii equation
.............561
22.6.2
Properties of the velocity field
................562
22.7
Time-dependent problems
.......................563
Contents xxi
22.7.1
Time-dependent Gross-Pitaevskii equation
......... 563
22.7.2
Analogy with hydrodynamic equations
........... 564
22.7.3
The two contributions to the kinetic energy: Thomas-Fermi
approximation for time-dependent problems
........ 565
22.7.4
Harmonic confinement
.................... 567
22.8
Conclusion
............................... 570
22.9
Appendix: Normal modes of a harmonically trapped
condensate
............................... 571
22.9.1 Isotropie
trap
......................... 572
22.9.2
Cylindrically-symmetric trap
................. 575
22.9.3
Scissors mode for anisotropic traps
............. 575
23.
Coherence properties of Bose-Einstein condensates
577
23.1
Introduction
............................... 577
23.2
Atomic field operators and correlation functions
........... 579
23.2.1
Brief reminder on second quantization
........... 579
23.2.2
Atomic field operators
..................... 580
23.2.3
Examples of physical operators. Field correlation functions
581
23.2.4 Heisenberg
equation of the field operator
.......... 583
23.3
Calculation of correlation functions in a few simple cases
..... 583
23.3.1
First-order correlation function for an ideal
Bose
gas in a box
.......................... 583
23.3.2
Higher-order spatial correlation functions for an ideal gas
of bosons above
Гс
....................... 586
23.3.3
Correlation functions for a Bose-Einstein condensate
. . . 587
23.3.4
A few experimental results
.................. 588
23.4
Relative phase of two independent condensates
........... 592
23.4.1
Two condensates in Fock states
............... 593
23.4.2
Phase states
.......................... 593
23.4.3
Conjugate variable of the relative phase
........... 595
23.4.4
Emergence of a relative phase in an interference
experiment
.......................... 596
23.5
Long range order and order parameter
................ 597
23.5.1
Long range order
....................... 597
23.5.2
Order parameter
........................ 598
23.6
New effects in atom optics due to atom-atom interactions
..... 599
23.6.1
Collapse and revival of first-order coherence due
to interactions
......................... 599
23.6.2
An example of nonlinear effects in atom optics: Four-wave
mixing with matter waves
.................. 601
23.7
Conclusion
............................... 602
xxii
Advances in atomic physics: an overview
24.
Elementary excitations and superfluidity in Bose-Einstein condensates
603
24.1
Introduction
............................... 603
24.2
Bogolubov approach for an homogeneous system
.......... 605
24.2.1
Second quantized Hamiltonian
................ 606
24.2.2
Bogolubov quadratic Hamiltonian
.............. 607
24.2.3
Physical discussion
...................... 608
24.2.4
Energy of the ground state
.................. 611
24.2.5
Extension to inhomogeneous systems
............ 612
24.3
Landau criterion for superfluidity in an homogeneous system
. . . 614
24.3.1
Microscopic probe
....................... 614
24.3.2
Macroscopic approach
.................... 616
24.4
Extension of Landau criterion for a condensate in a
rotating bucket
............................. 616
24.4.1
The rotating bucket
...................... 617
24.4.2
Other possible states of the condensate: quantized vortices
617
24.4.3
Various threshold rotation frequencies
............ 620
24.5
Experimental study of vortices in gaseous condensates
....... 621
24.5.1
Introduction
.......................... 621
24.5.2
A few experimental results
.................. 621
24.5.3
Measuring the angular momentum per atom in a
rotating condensate
...................... 623
24.5.4
Routes to vortex nucleation
................. 624
24.6
Conclusion
............................... 628
Frontiers of atomic physics
631
25.
Testing fundamental symmetries. Parity violation in atoms
637
25.1
Introduction
...............................637
25.1.1
Historical perspective
..................... 637
25.1.2
Atomic parity violation
(APV)
................ 639
25.1.3
Organization of this chapter
................. 641
25.2
The first cesium experiment
...................... 641
25.2.1
Principle of the experiment
.................. 641
25.2.2
Transition
dipole
moment
................... 642
25.2.3
Existence of a chiral signal in the re-emitted light
..... 645
25.2.4
Calibration of the parity violation amplitude
........ 647
25.3
Connection between the parity violation amplitude and the
parameters of the electroweak theory
................. 648
25.3.1
Non-relativistic limit of the weak interaction Hamiltonian
. 648
25.3.2
Calculation of the parity violation amplitude
.......649
Contents xxiii
25.3.3
Nuclear
spin-dependent parity violating interactions.
Anapole
moment
....................... 649
25.4
Survey of experimental results
..................... 651
25.4.1
Cesium experiments
...................... 651
25.4.2
Experiments using other atoms
................ 652
25.5
Conclusion about the importance of
APV
experiments
....... 653
25.6
Appendix: Testing time reversal symmetry
by looking for electric
dipole
moments
................ 655
26.
Quantum gases as simple systems for many-body physics
659
26.1
Introduction
............................... 659
26.2
The double well problem for bosonic gases
.............. 661
26.2.1
Introduction
.......................... 661
26.2.2
The Hubbard Hamiltonian
.................. 662
26.2.3
The superfluid regime
..................... 662
26.2.4
The insulator regime
..................... 665
26.2.5
Connection between the superfluid and insulator regimes
. 667
26.2.6
Production of
Sehrödinger
cat states when interactions
are attractive
......................... 668
26.2.7
Controlling the tunnelling rate with a modulation of the
difference of the two potential depths
............ 669
26.3
SuperHuid-Mott insulator transition for a quantum bosonic gas in
an optical lattice
............................ 670
26.3.1
Bose
Hubbard model
.....................
67Ü
26.3.2
Qualitative interpretation of the superfluid-Mott
insulator transition
...................... 670
26.3.3
Experimental observation
................... 672
26.4
Quantum ferniionic gas in an optical lattice
............. 672
26.5
Feshbach resonances and Fermi quantum gases
........... 674
26.5.1
Introduction
.......................... 674
26.5.2
Brief survey of BCS theory
.................. 675
26.5.3
A simple model for the BEC-BCS crossover
........ 682
26.5.4
Experimental investigations
................. 684
26.6
Conclusion
............................... 689
27.
Extreme light
695
27.1
Introduction
............................... 695
27.2
Attosecond science
........................... 697
27.2.1
Mechanism of production of attosecond pulses
....... 697
27.2.2
Multiple-cycle laser pulse. Train of attosecond pulses
. . . 697
27.2.3
Few-cycle laser pulse. Control of the carrier-envelope
phase
.............................. 699
xxiv
Advances in atomic physic.*: an orernrw
27.2.4
Attosecond metrology
..................... 700
27.2.5
A few applications of attosecond pulses
........... 703
27.3
Ultra intense laser pulses
....................... 704
27.3.1
Q-switched lasers
....................... 705
27.3.2
Mode locking techniques
................... 706
27.3.3
Chirped pulse amplification
.................. 709
27.3.4
A few applications of high intensity table-top lasers
.... 709
27.4
Conclusion
............................... 713
28.
General conclusion
715
Bibliography
719
Index
751
|
| any_adam_object | 1 |
| author | Cohen-Tannoudji, Claude 1933- Guéry-Odelin, David |
| author_GND | (DE-588)115610340 (DE-588)1017188181 |
| author_facet | Cohen-Tannoudji, Claude 1933- Guéry-Odelin, David |
| author_role | aut aut |
| author_sort | Cohen-Tannoudji, Claude 1933- |
| author_variant | c c t cct d g o dgo |
| building | Verbundindex |
| bvnumber | BV025562799 |
| classification_rvk | UM 1000 UM 2300 |
| classification_tum | PHY 522f PHY 507f PHY 500f |
| ctrlnum | (OCoLC)698584456 (DE-599)BVBBV025562799 |
| discipline | Physik |
| format | Book |
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| id | DE-604.BV025562799 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:36:33Z |
| institution | BVB |
| isbn | 9789812774965 9789812774972 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-020162010 |
| oclc_num | 698584456 |
| open_access_boolean | |
| owner | DE-11 DE-20 DE-29T DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-522 DE-19 DE-BY-UBM DE-83 DE-210 |
| owner_facet | DE-11 DE-20 DE-29T DE-703 DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-522 DE-19 DE-BY-UBM DE-83 DE-210 |
| physical | XXV, 767 S. Ill., graph. Darst. 26 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Cohen-Tannoudji, Claude 1933- Verfasser (DE-588)115610340 aut Advances in atomic physics an overview Claude Cohen-Tannoudji ; David Guery-Odelin New Jersey [u.a.] World Scientific 2011 XXV, 767 S. Ill., graph. Darst. 26 cm txt rdacontent n rdamedia nc rdacarrier Atom-Photon-Wechselwirkung (DE-588)4143332-4 gnd rswk-swf Kernphysik (DE-588)4030340-8 gnd rswk-swf Elektromagnetisches Feld (DE-588)4014305-3 gnd rswk-swf Zwischenatomare Kraft (DE-588)4253455-0 gnd rswk-swf Atomphysik (DE-588)4003423-9 gnd rswk-swf Atomphysik (DE-588)4003423-9 s DE-604 Kernphysik (DE-588)4030340-8 s Atom-Photon-Wechselwirkung (DE-588)4143332-4 s Zwischenatomare Kraft (DE-588)4253455-0 s Elektromagnetisches Feld (DE-588)4014305-3 s Guéry-Odelin, David Verfasser (DE-588)1017188181 aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020162010&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Cohen-Tannoudji, Claude 1933- Guéry-Odelin, David Advances in atomic physics an overview Atom-Photon-Wechselwirkung (DE-588)4143332-4 gnd Kernphysik (DE-588)4030340-8 gnd Elektromagnetisches Feld (DE-588)4014305-3 gnd Zwischenatomare Kraft (DE-588)4253455-0 gnd Atomphysik (DE-588)4003423-9 gnd |
| subject_GND | (DE-588)4143332-4 (DE-588)4030340-8 (DE-588)4014305-3 (DE-588)4253455-0 (DE-588)4003423-9 |
| title | Advances in atomic physics an overview |
| title_auth | Advances in atomic physics an overview |
| title_exact_search | Advances in atomic physics an overview |
| title_full | Advances in atomic physics an overview Claude Cohen-Tannoudji ; David Guery-Odelin |
| title_fullStr | Advances in atomic physics an overview Claude Cohen-Tannoudji ; David Guery-Odelin |
| title_full_unstemmed | Advances in atomic physics an overview Claude Cohen-Tannoudji ; David Guery-Odelin |
| title_short | Advances in atomic physics |
| title_sort | advances in atomic physics an overview |
| title_sub | an overview |
| topic | Atom-Photon-Wechselwirkung (DE-588)4143332-4 gnd Kernphysik (DE-588)4030340-8 gnd Elektromagnetisches Feld (DE-588)4014305-3 gnd Zwischenatomare Kraft (DE-588)4253455-0 gnd Atomphysik (DE-588)4003423-9 gnd |
| topic_facet | Atom-Photon-Wechselwirkung Kernphysik Elektromagnetisches Feld Zwischenatomare Kraft Atomphysik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020162010&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT cohentannoudjiclaude advancesinatomicphysicsanoverview AT gueryodelindavid advancesinatomicphysicsanoverview |