Abstract
We investigate how three-body interactions affect the elementary excitations and dynamic structure factor of a Bose—Einstein condensate trapped in a one-dimensional optical lattice. To this end, we numerically solve the Gross-Pitaevskii equation and then the corresponding Bogoliubov equations. Our results show that three-body interactions can change both the Bogoliubov band structure and the dynamical structure factor dramatically, especially in the case of the two-body interaction being relatively small. Furthermore, when the optical lattice is strong enough, the analytical results, combined with the sum-rule approach, help us to understand that: the effects of three-body interactions on the static structure factor can be significantly amplified by an optical lattice. Our predictions should be observable within the current Bragg spectroscopy experiment.
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