33 8chapter 3 bose einstein condensation of weakly

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Unformatted text preview: q ) (3.29) Ground state |0 is a vacuum of Bogoliubov quasiparticles. Hence state |n in (3.25) should have one Bogoliubov quasiparticle and we obtain S (q, ω ) = n0 (uq − vq )2 δ (ω − Eq ) = n0 q Eq δ (ω − Eq ) (3.30) For small q we find q /Eq ∝ |q |. Results of experimental measurements of both the dispersion of Bogoliubov quasiparticles and the amplitude of the structure factor are shown in fig. 3.3. 8CHAPTER 3. BOSE-EINSTEIN CONDENSATION OF WEAKLY INTERACTING ATOMIC GASES excited state 2 GHz detuning Energy 5 10 14 Hz _ h qc _2 (h q) / 2m 0 100 kHz electronic ground state mc Momentum Figure 3.1: Experimental scheme for probing collective modes in a BEC using off-resonant light scattering. Figure taken from Ref. [4]. Excitations are created by stimulated light scattering using two laser which are both detuned from the atomic resonance. Absorption of one photon and emission of the other provides energy and momentum to create an excitation. 3.2 Gross-Pitaevskii equation In the Bogoliubov analysis we assumed macroscopic condensation of...
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