## Bose-Einstein Condensation in Dilute GasesIn 1925 Einstein predicted that at low temperatures particles in a gas could all reside in the same quantum state. This gaseous state, a Bose-Einstein condensate, was produced in the laboratory for the first time in 1995 and investigating such condensates is one of the most active areas in contemporary physics. The authors of this graduate-level textbook explain this exciting new subject in terms of basic physical principles, without assuming detailed prior knowledge. Chapters cover the statistical physics of trapped gases, atomic properties, cooling and trapping atoms, interatomic interactions, structure of trapped condensates, collective modes, rotating condensates, superfluidity, interference phenomena, and trapped Fermi gases. Problem sets are also included. |

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### Contents

II | 1 |

III | 4 |

IV | 6 |

V | 8 |

VI | 10 |

VII | 13 |

VIII | 14 |

IX | 16 |

LXXXI | 216 |

LXXXII | 218 |

LXXXIII | 219 |

LXXXIV | 225 |

LXXXV | 226 |

LXXXVI | 228 |

LXXXVII | 230 |

LXXXVIII | 236 |

X | 18 |

XI | 21 |

XII | 23 |

XIII | 24 |

XIV | 27 |

XV | 29 |

XVI | 30 |

XVII | 32 |

XIX | 35 |

XX | 36 |

XXI | 37 |

XXII | 38 |

XXIII | 40 |

XXIV | 44 |

XXV | 49 |

XXVI | 55 |

XXVII | 57 |

XXIX | 58 |

XXX | 59 |

XXXI | 60 |

XXXII | 62 |

XXXIII | 64 |

XXXIV | 67 |

XXXV | 71 |

XXXVI | 73 |

XXXVII | 74 |

XXXVIII | 78 |

XXXIX | 81 |

XL | 90 |

XLI | 96 |

XLII | 99 |

XLIII | 100 |

XLIV | 102 |

XLV | 103 |

XLVI | 107 |

XLVII | 111 |

XLVIII | 114 |

XLIX | 120 |

L | 125 |

LI | 131 |

LII | 139 |

LIII | 142 |

LIV | 144 |

LVI | 146 |

LVII | 149 |

LVIII | 151 |

LIX | 154 |

LX | 158 |

LXI | 161 |

163 | |

LXIV | 165 |

LXV | 167 |

LXVI | 171 |

LXVII | 178 |

LXVIII | 179 |

LXIX | 182 |

LXX | 186 |

LXXI | 193 |

LXXII | 195 |

LXXIII | 196 |

LXXIV | 201 |

LXXV | 202 |

LXXVI | 204 |

LXXVII | 205 |

LXXVIII | 207 |

LXXIX | 209 |

LXXX | 214 |

LXXXIX | 237 |

XC | 238 |

XCI | 240 |

XCIII | 245 |

XCIV | 247 |

XCV | 249 |

XCVII | 251 |

XCVIII | 254 |

XCIX | 255 |

C | 257 |

CI | 261 |

CII | 262 |

CIII | 264 |

CIV | 265 |

CV | 267 |

CVII | 268 |

CVIII | 270 |

CIX | 273 |

CX | 280 |

CXI | 281 |

CXII | 287 |

CXIII | 288 |

CXIV | 289 |

CXV | 290 |

CXVII | 292 |

CXVIII | 294 |

CXIX | 298 |

CXX | 301 |

CXXI | 306 |

CXXII | 310 |

CXXIII | 315 |

CXXIV | 318 |

CXXV | 319 |

CXXVI | 320 |

CXXVII | 321 |

CXXVIII | 322 |

CXXIX | 326 |

CXXX | 328 |

CXXXI | 330 |

CXXXII | 333 |

CXXXIII | 335 |

CXXXIV | 336 |

CXXXV | 338 |

CXXXVI | 339 |

CXXXVII | 343 |

CXXXVIII | 348 |

CXXXIX | 350 |

CXL | 354 |

CXLI | 355 |

CXLII | 357 |

359 | |

CXLV | 361 |

CXLVI | 362 |

CXLVII | 366 |

CXLVIII | 370 |

CXLIX | 371 |

CL | 376 |

CLI | 378 |

CLII | 385 |

CLIII | 386 |

CLIV | 388 |

CLV | 391 |

CLVI | 392 |

CLVII | 394 |

397 | |

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### Common terms and phrases

alkali atoms amplitude angular momentum axis Bogoliubov Bose gas Bose-Einstein condensation bosons calculate Chapter chemical potential cloud coefficient collective modes collisions compared components condensate wave function Consequently consider contribution cooling coordinates corresponding denote density depends described dilute dipole distribution function effective interaction electric field electronic spin elementary excitations equal equilibrium evaluated expression factor Fermi fermions Feshbach resonances frequency gases given by Eq Gross-Pitaevskii equation ground-state Hamiltonian harmonic trap Hartree-Fock hydrodynamic hydrogen hyperfine integral interaction energy isotropic kinetic energy laser cooling Lett linear magnetic field magnitude matrix element momenta motion neglected non-interacting non-zero number of particles obtained oscillator particle number phase photons Phys physics PROBLEM processes properties quantum resonance result rotation scattering length single-particle soliton spatial substate superfluid surface symmetry theory thermal excitations thermodynamic Thomas-Fermi approximation tion total energy total number transition temperature uniform vortices wave function wave number wavelength