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 freeparticle regime.
The momentum transferred to the atomic sample w
determined by the average axial position in timeofﬂig
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 scatThomasFermi regime, and of a thermal component [13
tering. (a) Atoms were exposed to...
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 Fall '10
 EugeneDemler
 Physics, BoseEinstein condensation, Bogoliubov Theory, Bogoliubov quasiparticles

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