  Various lower- and higher-order nonclassical properties 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 squeezing,
antibunching, entanglement and intermodal squeezing. The effects of the
coherent interaction of a nonlinear oscillating mirror with the cavity mode are
studied, and it is observed that the optomechanical system studied here becomes
more nonclassical (entangled) 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 various nonclassicality 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 nonclassicality.
