In this paper, we have investigated theoretically the influence of atomiccollisions on the behaviour of a one-dimensional Bose-Einstein condensateinside a driven optical cavity. We develop the discrete-mode approximation forthe condensate taking into account the interband transitions due to the s-wavescattering interaction. We show that in the Bogoliubov approximation theatom-atom interaction shifts the energies of the excited modes and also playsthe role of an optical parametric amplifier for the Bogoliubov side mode whichcan affect its normal-mode splitting behaviour. On the other hand due to theatomic collisions the resonance frequency of the cavity is shifted which leadsto the decrease of the number of cavity photons and the depletion of theBogoliubov mode. Besides, it reduces the effective atom-photon couplingparameter which consequently leads to the decrease of the entanglement betweenthe Bogoliubov mode and the optical field.
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