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We theoretically investigate quantum entanglement and coherence in a hybrid Laguerre-Gaussian rotating cavity optomechanical system with two-level atoms, where cavity and mechanical modes are coupled through the exchange of orbital angular momentum. Our study shows that the injection of atoms with a suitable choice of the physical parameters can significantly improve the degree of optomechanical entanglement in all aspects. In the study of quantum coherence research, we show more comprehensively the negative and positive effects of atoms on the coherence. The result obtained is that only when the atom is significantly offresonant to driving field, the coupling strength in between the atoms and light field increases and the quantum coherence can be enhanced, otherwise it will reduce quantum coherence. In addition, the atomic decay suppresses quantum coherence phenomenon.

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The quantum optomechanical system serves as an interface for coupling between photons, excitons, and mechanical oscillations. We use the quantum Langevin approach to study a hybrid optomechanical system that contains a single undoped semiconductor quantum well in a cavity, where one of its mirrors is a thin dielectric membrane having quadratic response to the cavity fields. A decorrelation method is employed to solve for a large number of coupled equations. Transient mean numbers of cavity photons, moving membranes, and excitons that provide dynamical behavior are computed. We obtain the two-boson second-order correlation functions for the cavity field and the membrane oscillator, and their cross correlations that provide nonclassical quantum statistical properties and useful insights into the quadratic optomechanical system.

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