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In this paper, we investigate theoretically a system consisting of a onedimensional Bose-Einstein condensate trapped inside the optical lattice of anoptical cavity. In the weak-interaction regime and under the Bogoliubovapproximation, the wave function of the Bose-Einstein condensate can bedescribed by a classical field (condensate mode) having some quantumfluctuations (the Bogoliubov mode) about the mean value. Such a system behavesas a so-called atomic parametric amplifier, similar to an optical parametricamplifier, where the condensate and the Bogoliubov modes play respectively, theroles of the pump field and the signal mode in the degenerate parametricamplifier and the s-wave scattering frequency of atom-atom interaction playsthe role of the nonlinear gain parameter. We show that using the nonlineareffect of atomic collisions, how one can manipulate and control the state ofthe Bogoliubov mode and produce squeezed states.

Squeezed-state generation via nonlinear atom-atom interaction in the atomic field of a Bose-Einstein condensate interacting with an optical cavity