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To extract small momentum transfers the im ages were

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Unformatted text preview: th physical momentum −q . This effect was demonstrated experimentally in [2]. Problem 2 Show that wavefunction (3.23) solves equation (3.24) for fp = −vp /up . Problem 3 Consider a sudden change of the scattering length in Bose gas from as1 to as2 . Both interactions are small. Within Bogoliubov theory, describe dynamics of the system. 3.3. PROBLEMS FOR CHAPTER ?? VOLUME 83, NUMBER 15 11 PHYSICAL REVIEW LETTERS 11 OCTOBER 199 which the atomic density was reduced by a factor of 2 and the speed of sound by a factor of 5 from that o the trapped condensate. Thus, Bragg scattering in th expanded sample occurred in the free-particle regime. The momentum transferred to the atomic sample w determined by the average axial position in time-of-flig images. To extract small momentum transfers, the im ages were first fitted (in regions where the Bragg scattere atoms were absent) to a bimodal distribution which co rectly describes the free expansion of a condensate in th FIG. 1. Observation of momentum transfer by Bragg scatThomas-Fermi regime, and of a thermal component [13 tering. (a) Atoms were exposed to...
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