324 31 bogoliubov theory 311 7 experimental tests

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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 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 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 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 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 [4]. By absorbing a pho...
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