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
satisfy equations
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 densitydensity response function is
called the dynamic structure factor
 nρ† 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
1
ρ† = √
q
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 nonzero.
Two photon oﬀresonant light scattering shown in ﬁgure 3.1 can be used to
measure the dynamic structure factor of the BEC [4]. By absorbing a pho...
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This document was uploaded on 02/27/2014 for the course PHYS 284 at Harvard.
 Fall '10
 EugeneDemler
 Physics

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