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Various lower- and higher-order nonclassical properties have been studied fortwo physical systems- (i) an optomechanical system composed of a Fabry-Perotcavity with one nonlinearly oscillating mirror and (ii) an optomechanical-likesystem formed using a Bose-Einstein condensate (BEC) trapped inside an opticalcavity. The investigation is performed using a perturbation method that leadsto closed form analytic expressions for the time evolution of the relevantbosonic operators. In the first system, it is observed that the radiationpressure coupling leads to the emergence of lower- and higher-order squeezing,antibunching, entanglement and intermodal squeezing. The effects of thecoherent interaction of a nonlinear oscillating mirror with the cavity mode arestudied, and it is observed that the optomechanical system studied here becomesmore nonclassical (entangled) when the coupling strength is increased. It isalso observed that the possibility of observing entanglement depends on thephase of the movable mirror. The Hamiltonian of the trapped BEC system isobtained as a special case of the Hamiltonian of the first system, and theexistence of various nonclassicality in the trapped BEC system has beenestablished, and variations of those with various physical parameters have beenreported with an aim to understand the underlying physical process that leadsto and controls the nonclassicality.

Lower- and higher-order nonclassicality in a Bose-condensed  optomechanical-like system and a Fabry-Perot cavity with one movable mirror:  squeezing, antibunching and entanglement