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Unformatted text preview: 3) where C is normalization constant. To ﬁnd coeﬃcients fp one simply notes that
state (3.23) should be a vaccum of Bogoliubov quasiparticles. Hence it should
αp |ΨBog = (up bp + vp b† p )|ΨBog = 0
for all momenta p. The last condition requires fp = −vp /up . (3.24) 3.1. BOGOLIUBOV THEORY 3.1.1 7 Experimental tests of the Bogoliubov theory Information about collective modes of many body systems is contained in the
response functions. Imaginary part of the density-density response function is
called the dynamic structure factor
| n|ρ† |0 |2 δ (ω − (En − E0 ))
q S (q, ω ) = (3.25) n Here |0 denotes the ground state, summation over n goes over all excited states
|n , density operator at wavevctor q is given by
ρ† = √
V b† +q bk
k (3.26) k Note that the diﬀerence in momenta of states |0 and |n must be q for the
matrix element in (3.25) to be non-zero.
Two photon oﬀ-resonant light scattering shown in ﬁgure 3.1 can be used to
measure the dynamic structure factor of the BEC . By absorbing a pho...
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- Fall '10