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27 e q eit 2q fermis golden then gives the rate with

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Unformatted text preview: ton from one laser beam an atom goes into an excited state (but only virtually since there is strong frequency detuning) and then gets de-excited by a photon from the other beam. By treating optical fields as classical, one can obtain effective Hamiltonian describing interaction of atoms with the laser fields V0 † −iωt (3.27) (ρ e + ρ† q eiωt ) − 2q Fermi’s golden then gives the rate with which excitations are created in the system (this is linear response theory and applies only for exciting a relatively small number of atoms) Veff = W = V02 S (q, ω ) (3.28) What is being measured in experiments is the number of atoms excited into a state with finite momentum as a function of wavevector and frequency differences of the two laser beams (see figs 3.1 and 3.2). To apply formulas (3.25), (3.27) to the BEC we write ρ† in equation (3.26) q using creation and annihilation operators of the Bogoliubov quasiparticles. The 1 /2 leading term in N0 1 ρ† = √ (b0 b† + b† b−q ) = q q 0 V N0 V 1/2 † (uq − vq )(αq − α...
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