[en] From the perspective of quantum optics, various lower- and higher-order nonclassical features of correlations have been studied for two physical systems- (i) an optomechanical system composed of a Fabry–Perot cavity with one nonlinearly oscillating mirror and (ii) an optomechanical-like system formed using a Bose–Einstein condensate (BEC) trapped inside an optical cavity. The investigation is performed using a perturbation method that leads to closed form analytic expressions for the time evolution of the relevant bosonic operators. In the first system, it is observed that the radiation pressure coupling leads to the emergence of lower- and higher-order single-mode and two-mode quantum correlations. The effects of the coherent interaction of a nonlinear oscillating mirror with the cavity mode are also studied, and it is observed that the optomechanical system studied here becomes more correlated when the coupling strength is increased. It is also observed that the possibility of observing entanglement depends on the phase of the movable mirror. The Hamiltonian of the trapped BEC system is obtained as a special case of the Hamiltonian of the first system, and the existence of quantum correlations in the trapped BEC system has been established, and variations of those with various physical parameters have been reported with an aim to understand the underlying physical process that leads to and controls the correlations. Finally, the possibility of observing these correlations under the effect of environment has also been performed. Graphical abstract:

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