By R. Kaiser, C. Westbrook, F. David

ISBN-10: 3540410473

ISBN-13: 9783540410478

Court cases of the NATO complex research Institute convention on Coherent Atomic topic Waves, held July 27 via August 27, 1999. lawsuits comprise all papers in English, however the directories and different lists in either English and French.

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Y. Castin: Bose–Einstein Condensates in Atomic Gases 19 Suppose that the trap is switched oﬀ at t = 0. 49) that is as the sum of kinetic energy, trapping potential energy and interaction energy. At time t = 0+ there is no trapping potential anymore so that the total energy of the gas reduces to Etot (0+ ) = Ekin + Eint . 50) In the limit t → +∞ the gas expands, the density and therefore the interaction energy drop, and all the energy Etot (0+ ) is converted into kinetic energy, which is measured.

19) 2m The problem is then formally reduced to the one of an ideal Bose gas moving in a self-consistent potential. For g > 0 the mean ﬁeld corresponds to repulsive interactions, as 2gρ(r ) expels the atoms from the region of high density, while for g < 0 the mean ﬁeld corresponds to attractive interactions. hHF (1) = 3 Note that for the present calculation the regularization of the pseudo-potential is not necessary. Indeed by considering plane waves as scattering states in ρˆ12 we suppress any problem of divergences in the commutator with V12 , and we can then take V12 as a simple delta distribution.

It is fortunately possible to show for the class of power-law potentials, scaling as 1/rn , that several of our conclusions, obtained in the ﬁnite range case, hold provided that n > 3. g. in the limit of small k’s only the s-wave scattering survives, and fk has a well deﬁned limit for k → 0, allowing one to deﬁne the scattering length. 1 Why not keep the exact interaction potential? For alkali atoms the exact interaction potential has a repulsive hard core, is very deep (as deep as 103 Kelvins times kB for 133 Cs), has a minimum at a distance r12 on the order of 6 ˚ A (for cesium), and contains many bound states corresponding to molecular states of two alkali atoms (see Fig.

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