Mendonça / Terças Physics of Ultra-Cold Matter

Atomic Clouds, Bose-Einstein Condensates and Rydberg Plasmas
2013
ISBN: 978-1-4614-5413-7
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 70, 398 Seiten

Reihe: Springer Series on Atomic, Optical, and Plasma Physics

The advent of laser cooling of atoms led to the discovery of ultra-cold matter, with temperatures below liquid Helium, which displays a variety of new physical phenomena. Physics of Ultra-Cold Matter gives an overview of this recent area of science, with a discussion of its main results and a description of its theoretical concepts and methods.
Ultra-cold matter can be considered in three distinct phases: ultra-cold gas, Bose Einstein condensate, and Rydberg plasmas. This book gives an integrated view of this new area of science at the frontier between atomic physics, condensed matter, and plasma physics. It describes these three distinct phases while exploring the differences, as well as the sometimes unexpected similarities, of their respective theoretical methods.
This book is an informative guide for researchers, and the benefits are a result from an integrated view of a very broad area of research, which is limited in previous books about this subject. The main unifying tool explored in this book is the wave kinetic theory based on Wigner functions. Other theoretical approaches, eventually more familiar to the reader, are also given for extension and comparison. The book considers laser cooling techniques, atom-atom interactions, and focuses on the elementary excitations and collective oscillations in atomic clouds, Bose-Einstein condensates, and Rydberg plasmas. Linear and nonlinear processes are considered, including Landau damping, soliton excitation and vortices. Atomic interferometers and quantum coherence are also included.

J.T. Mendonça, Instituto Superior Tecnico, Lisbon, Portugal, [e-mail]
Hugo Terças, Université Blaise Pascal, Aubière, France, [e-mail]

Autoren/Hrsg.

Mendonça, J. T.

Terças, Hugo

Inhaltsverzeichnis

1;Physics of Ultra-Cold Matter;3
1.1;Preface;5
1.2;Contents;7
1.3;List of Figures;13
1.4;List of Tables;21
1.5;Chapter 1: Introduction;23
1.5.1;1.1 Three Phases of Ultra-cold Matter;23
1.5.2;1.2 Historical Perspective;25
1.5.3;1.3 Book Overview;26
1.5.4;References;28
1.6;Part I Atomic Clouds ;29
1.6.1;Chapter 2: Laser Cooling;30
1.6.1.1;2.1 Atom in the Laser Field;30
1.6.1.2;2.2 Laser Cooling Force;35
1.6.1.3;2.3 Doppler Limit;38
1.6.1.4;2.4 Magnetic Traps;39
1.6.1.4.1;2.4.1 Multipolar Field Configuration;40
1.6.1.4.2;2.4.2 Helmholtz Configuration;41
1.6.1.4.3;2.4.3 Ioffe Configuration;41
1.6.1.4.4;2.4.4 Anti-Helmholtz Configuration;42
1.6.1.5;2.5 Sisyphus Cooling;44
1.6.1.6;2.6 Evaporative Cooling;46
1.6.1.7;2.7 Sympathetic Cooling;50
1.6.1.8;References;54
1.6.2;Chapter 3: Wave Kinetic Approach;56
1.6.2.1;3.1 Wigner-Moyal Procedure;56
1.6.2.1.1;3.1.1 Quasi-distributions;57
1.6.2.1.2;3.1.2 Weyl Transformation;60
1.6.2.1.3;3.1.3 Wave Kinetic Equation;62
1.6.2.1.4;3.1.4 The Quasi-classical Limit;64
1.6.2.2;3.2 Center-of-Mass Equation;65
1.6.2.3;3.3 Wave Kinetic Description of the Laser-Atom Interaction;68
1.6.2.4;3.4 Two-Level Atom;69
1.6.2.5;3.5 Links with Dynamics and Statistics;71
1.6.2.5.1;3.5.1 Quasi-classical Limit;71
1.6.2.5.2;3.5.2 Momentum Diffusion and the Doppler Limit;72
1.6.2.6;3.6 Lambda Configuration;74
1.6.2.7;3.7 Two Coupled Radiative Transitions;76
1.6.2.8;3.8 Influence of a Blue-Detuned Pump;79
1.6.2.9;References;81
1.6.3;Chapter 4: Atomic Clouds;83
1.6.3.1;4.1 Atom-Atom Collisions;84
1.6.3.2;4.2 Feshbach Resonances;89
1.6.3.3;4.3 Collective Forces;94
1.6.3.4;4.4 Equilibrium Profiles;99
1.6.3.4.1;4.4.1 Qualitative Discussion;100
1.6.3.4.2;4.4.2 Quantitative Model;102
1.6.3.5;4.5 Coulomb Expansion;104
1.6.3.6;References;108
1.6.4;Chapter 5: Waves and Oscillations in Clouds;109
1.6.4.1;5.1 Hybrid Sound;109
1.6.4.1.1;5.1.1 Fluid Description;109
1.6.4.1.2;5.1.2 Kinetic Approach;111
1.6.4.2;5.2 Tonks-Dattner Modes;116
1.6.4.3;5.3 Large Scale Oscillations;119
1.6.4.3.1;5.3.1 The Centre-of-Mass Oscillation;119
1.6.4.3.2;5.3.2 Normal Modes;120
1.6.4.4;5.4 Nonlinear Mode Coupling;123
1.6.4.5;5.5 Quasi-linear Diffusion;127
1.6.4.6;5.6 Phaser, the Phonon Laser;130
1.6.4.7;References;134
1.6.5;Chapter 6: Photons in the Ultra-cold Gas;135
1.6.5.1;6.1 Optical Properties;136
1.6.5.2;6.2 Modulational Instability;138
1.6.5.3;6.3 Photon Bubbles;140
1.6.5.4;6.4 Roton Instability;145
1.6.5.5;6.5 Density Fluctuations;151
1.6.5.6;6.6 Collective Laser Scattering;155
1.6.5.7;References;158
1.7;Part II The Physics of Bose-Einstein Condensates;160
1.7.1;Chapter 7: Bose Einstein Condensates;161
1.7.1.1;7.1 Uniform Gas;162
1.7.1.2;7.2 Trapped Gas;163
1.7.1.3;7.3 Atom Correlations;167
1.7.1.4;7.4 Mean Field Approximation;171
1.7.1.5;7.5 Thomas-Fermi Approximation;173
1.7.1.6;7.6 Fluid and Kinetic Formulations;176
1.7.1.6.1;7.6.1 Quantum Fluid Equations;176
1.7.1.6.2;7.6.2 Wave Kinetic Equation;178
1.7.1.7;References;179
1.7.2;Chapter 8: Elementary Excitations in BECs;181
1.7.2.1;8.1 Sound Waves;181
1.7.2.2;8.2 Global Oscillations;183
1.7.2.3;8.3 Kinetic Processes;186
1.7.2.4;8.4 Landau Damping;187
1.7.2.5;8.5 Dynamical Instabilities;189
1.7.2.6;8.6 Wakefields in Bose-Einstein Condensates;192
1.7.2.7;References;198
1.7.3;Chapter 9: Solitons;199
1.7.3.1;9.1 Effective One-Dimensional Gross-Pitaevskii Equation;200
1.7.3.2;9.2 One-Dimensional Dark and Grey Solitons;202
1.7.3.2.1;9.2.1 Energy of the Soliton;205
1.7.3.3;9.3 The Inverse Scattering Transform;206
1.7.3.4;9.4 Interaction Between Two Dark Solitons;207
1.7.3.5;9.5 Bright Solitons;211
1.7.3.6;9.6 Dark Solitons in Harmonic Traps;212
1.7.3.7;9.7 The Soliton Gas;215
1.7.3.8;9.8 Solitons in Two Dimensions;218
1.7.3.9;References;220
1.7.4;Chapter 10: Quantum Field Theory of BECs;222
1.7.4.1;10.1 Bogoliubov Theory;222
1.7.4.2;10.2 BEC Depletion;226
1.7.4.3;10.3 Phonon Pair Creation;228
1.7.4.3.1;10.3.1 Time Refraction;228
1.7.4.3.2;10.3.2 Dynamical Casimir Effect;232
1.7.4.4;10.4 Acoustic Black Holes;234
1.7.4.4.1;10.4.1 Hawking Radiation;235
1.7.4.4.2;10.4.2 Effective Metric in a Condensate;236
1.7.4.4.3;10.4.3 Acoustic Hawking (Unruh) Radiation;237
1.7.4.5;References;239
1.7.5;Chapter 11: Superfluidity;241
1.7.5.1;11.1 Phonon Kinetics;241
1.7.5.2;11.2 Phonon Fluid Equations;244
1.7.5.3;11.3 Slow Perturbations in the Superfluid;246
1.7.5.4;11.4 Superfluid Currents;248
1.7.5.5;11.5 Phonon Landau Damping;250
1.7.5.6;11.6 Roton Excitation;251
1.7.5.6.1;11.6.1 Wave Kinetic Equation with Dipolar Interactions;252
1.7.5.6.2;11.6.2 Dispersion Relation;253
1.7.5.6.3;11.6.3 Roton Instability;254
1.7.5.7;References;256
1.7.6;Chapter 12: Rotating BECs;257
1.7.6.1;12.1 Quantum Vortices;257
1.7.6.2;12.2 Vortex Nucleation;260
1.7.6.3;12.3 Tkachenko Modes;261
1.7.6.4;12.4 Rossby Waves;262
1.7.6.5;12.5 Rossby-Tkatchenko Modes;268
1.7.6.6;12.6 Coupling with Photon OAM States;270
1.7.6.7;References;272
1.7.7;Chapter 13: Quantum Coherence;273
1.7.7.1;13.1 Atom Interferometry;273
1.7.7.2;13.2 Time Interferometry;275
1.7.7.3;13.3 Decoherence Processes;278
1.7.7.4;13.4 Gravitational Decoherence;281
1.7.7.5;13.5 Josephson Tunneling of a Condensate;285
1.7.7.6;References;290
1.8;Part III The Physics of Ultracold Plasmas;291
1.8.1;Chapter 14: Ultra-cold Plasmas;292
1.8.1.1;14.1 Different Plasma Regimes;293
1.8.1.2;14.2 Basic Plasma Properties;295
1.8.1.3;14.3 Ionization Processes;298
1.8.1.4;14.4 Single Particle Motion;300
1.8.1.5;14.5 Adiabatic Invariants;304
1.8.1.6;14.6 Plasma Equations;308
1.8.1.6.1;14.6.1 Klimontovitch Equation;309
1.8.1.6.2;14.6.2 Vlasov Equation;311
1.8.1.6.3;14.6.3 Kinetic Equations with Collisions;313
1.8.1.7;14.7 Fluid Equations;314
1.8.1.8;References;317
1.8.2;Chapter 15: Physics of Rydberg Plasmas;319
1.8.2.1;15.1 Plasma Expansion in the Collisional Regime;320
1.8.2.1.1;15.1.1 Free Diffusion;320
1.8.2.1.2;15.1.2 Ambipolar Diffusion Regime;322
1.8.2.1.3;15.1.3 Recombination in Volume;323
1.8.2.2;15.2 Collisionless Plasma Expansion;324
1.8.2.3;15.3 Strongly Coupled Ions;327
1.8.2.3.1;15.3.1 Ion-Neutral Coupling;327
1.8.2.3.2;15.3.2 Ion-Ion Coupling;330
1.8.2.3.3;15.3.3 Phase Transitions;331
1.8.2.4;15.4 Disorder Induced Heating;335
1.8.2.5;15.5 Quasi-equilibrium States;337
1.8.2.6;15.6 Rydberg Atoms;340
1.8.2.6.1;15.6.1 Basic Properties;340
1.8.2.6.2;15.6.2 Rydberg Blockade;343
1.8.2.7;15.7 Three-Body Recombination;348
1.8.2.8;References;350
1.8.3;Chapter 16: Waves in Rydberg Plasmas;352
1.8.3.1;16.1 Isotropic Plasmas;353
1.8.3.2;16.2 Polaritons and Slow Light;356
1.8.3.3;16.3 Ponderomotive Force;362
1.8.3.4;16.4 Electron Drift Instability;364
1.8.3.5;16.5 Drift Waves at Plasma Gradients;366
1.8.3.6;16.6 Waves in Magnetized Cold Plasmas;368
1.8.3.6.1;16.6.1 General Dispersion Relation;368
1.8.3.6.2;16.6.2 Parallel Propagation;371
1.8.3.6.3;16.6.3 Perpendicular Propagation;373
1.8.3.7;16.7 Waves in Expanding Plasmas;374
1.8.3.8;16.8 Waves in Strongly Coupled Plasmas;377
1.8.3.9;References;379
1.8.4;Chapter 17: Kinetic Theory of Waves;380
1.8.4.1;17.1 Kinetic Dispersion Relation;381
1.8.4.2;17.2 Electron Plasma Waves;384
1.8.4.3;17.3 Ion Acoustic Waves;386
1.8.4.4;17.4 Waves in Quantum Plasmas;387
1.8.4.5;17.5 Sound Waves in a Turbulent Plasma;391
1.8.4.5.1;17.5.1 Plasmon Kinetic Equation;391
1.8.4.5.2;17.5.2 Ion Oscillations;393
1.8.4.6;References;394
1.8.5;Chapter 18: Conclusions;396
1.9;Appendix;398
1.9.1;A.1 Atomic Structure;398
1.9.2;A.2 Quantum Theory of Radiative Transitions;402
1.10;Index;407