BOSE-EINSTEIN CONDENSATION IN DILUTE GASES
CONTENTS INTRODUCTION BOSE–EINSTEIN CONDENSATION IN ATOMIC CLOUDS SUPER?UID 4HE OTHER CONDENSATES OVERVIEW PROBLEMS REFERENCES THE NON-INTERACTING BOSE GAS THE BOSE DISTRIBUTION 2 1 1 DENSITY OF STATES TRANSITION TEMPERATURE AND CONDENSATE FRACTION 2 2 1 CONDENSATE FRACTION DENSITY PRO?LE AND VELOCITY DISTRIBUTION 2 3 1 THE SEMI-CLASSICAL DISTRIBUTION THERMODYNAMIC QUANTITIES 2 4 1 CONDENSED PHASE 2 4 2 NORMAL PHASE 2 4 3 SPECI?C HEAT CLOSE TO TC E?ECT OF ?NITE PARTICLE NUMBER LOWER-DIMENSIONAL SYSTEMS ATOMIC PROPERTIES ATOMIC STRUCTURE THE ZEEMAN E?ECT RESPONSE TO AN ELECTRIC ?ELD ENERGY SCALES TRAPPING AND COOLING OF ATOMS MAGNETIC TRAPS 4 1 1 THE QUADRUPOLE TRAP 4 1 2 THE TOP TRAP 4 1 3 MAGNETIC BOTTLES AND THE IO?E–PRITCHARD TRAP IN?UENCE OF LASER LIGHT ON AN ATOM 4 2 1 FORCES ON AN ATOM IN A LASER ?ELD 4 2 2 OPTICAL TRAPS LASER COOLING: THE DOPPLER PROCESS THE MAGNETO-OPTICAL TRAP SISYPHUS COOLING EVAPORATIVE COOLING SPIN-POLARIZED HYDROGEN INTERACTIONS BETWEEN ATOMS INTERATOMIC POTENTIALS AND THE VAN DER WAALS INTERACTION BASIC SCATTERING THEORY 5 2 1 E?ECTIVE INTERACTIONS AND THE SCATTERING LENGTH SCATTERING LENGTH FOR A MODEL POTENTIAL SCATTERING BETWEEN DI?ERENT INTERNAL STATES 5 4 1 INELASTIC PROCESSES 5 4 2 ELASTIC SCATTERING AND FESHBACH RESONANCES DETERMINATION OF SCATTERING LENGTHS 5 5 1 SCATTERING LENGTHS FOR ALKALI ATOMS AND HYDROGEN THEORY OF THE CONDENSED STATE THE GROSS–PITAEVSKII EQUATION THE GROUND STATE FOR TRAPPED BOSONS 6 2 1 A VARIATIONAL CALCULATION 6 2 2 THE THOMAS–FERMI APPROXIMATION SURFACE STRUCTURE OF CLOUDS HEALING OF THE CONDENSATE WAVE FUNCTION DYNAMICS OF THE CONDENSATE GENERAL FORMULATION 7 1 1 THE HYDRODYNAMIC EQUATIONS ELEMENTARY EXCITATIONS COLLECTIVE MODES IN TRAPS 7 3 1 TRAPS WITH SPHERICAL SYMMETRY 7 3 2 ANISOTROPIC TRAPS 7 3 3 COLLECTIVE COORDINATES AND THE VARIATIONAL METHOD SURFACE MODES FREE EXPANSION OF THE CONDENSATE SOLITONS MICROSCOPIC THEORY OF THE BOSE GAS EXCITATIONS IN A UNIFORM GAS 8 1 1 THE BOGOLIUBOV TRANSFORMATION 8 1 2 ELEMENTARY EXCITATIONS EXCITATIONS IN A TRAPPED GAS 8 2 1 WEAK COUPLING NON-ZERO TEMPERATURE 8 3 1 THE HARTREE–FOCK APPROXIMATION 8 3 2 THE POPOV APPROXIMATION 8 3 3 EXCITATIONS IN NON-UNIFORM GASES 8 3 4 THE SEMI-CLASSICAL APPROXIMATION COLLISIONAL SHIFTS OF SPECTRAL LINES ROTATING CONDENSATES POTENTIAL ?OW AND QUANTIZED CIRCULATION STRUCTURE OF A SINGLE VORTEX 9 2 1 A VORTEX IN A UNIFORM MEDIUM 9 2 2 A VORTEX IN A TRAPPED CLOUD 9 2 3 O?-AXIS VORTICES EQUILIBRIUM OF ROTATING CONDENSATES 9 3 1 TRAPS WITH AN AXIS OF SYMMETRY 9 3 2 ROTATING TRAPS VORTEX MOTION 9 4 1 FORCE ON A VORTEX LINE THE WEAKLY-INTERACTING BOSE GAS UNDER ROTATION SUPER?UIDITY 10 1 THE LANDAU CRITERION 10 2 THE TWO-COMPONENT PICTURE 10 2 1 MOMENTUM CARRIED BY EXCITATIONS 10 2 2 NORMAL ?UID DENSITY 10 3 DYNAMICAL PROCESSES 10 4 FIRST AND SECOND SOUND 10 5 INTERACTIONS BETWEEN EXCITATIONS 10 5 1 LANDAU DAMPING TRAPPED CLOUDS AT NON-ZERO TEMPERATURE 11 1 EQUILIBRIUM PROPERTIES 11 1 1 ENERGY SCALES 11 1 2 TRANSITION TEMPERATURE 11 1 3 THERMODYNAMIC PROPERTIES 11 2 COLLECTIVE MODES 11 2 1 HYDRODYNAMIC MODES ABOVE TC 11 3 COLLISIONAL RELAXATION ABOVE TC 11 3 1 RELAXATION OF TEMPERATURE ANISOTROPIES 11 3 2 DAMPING OF OSCILLATIONS MIXTURES AND SPINOR CONDENSATES 12 1 MIXTURES 12 1 1 EQUILIBRIUM PROPERTIES 12 1 2 COLLECTIVE MODES 12 2 SPINOR CONDENSATES 12 2 1 MEAN-?ELD DESCRIPTION 12 2 2 BEYOND THE MEAN-?ELD APPROXIMATION INTERFERENCE AND CORRELATIONS 13 1 INTERFERENCE OF TWO CONDENSATES 13 1 1 PHASE-LOCKED SOURCES 13 1 2 CLOUDS WITH DE?NITE PARTICLE NUMBER 13 2 DENSITY CORRELATIONS IN BOSE GASES 13 3 COHERENT MATTER WAVE OPTICS 13 4 THE ATOM LASER 13 5 THE CRITERION FOR BOSE–EINSTEIN CONDENSATION 13 5 1 FRAGMENTED CONDENSATES FERMIONS 14 1 EQUILIBRIUM PROPERTIES 14 2 E?ECTS OF INTERACTIONS 14 3 SUPER?UIDITY 14 3 1 TRANSITION TEMPERATURE 14 3 2 INDUCED INTERACTIONS 14 3 3 THE CONDENSED PHASE 14 4 BOSON–FERMION MIXTURES 14 4 1 INDUCED INTERACTIONS IN MIXTURES 14 5 COLLECTIVE MODES OF FERMI SUPER?UIDS