Generation of continuous variable quantum correlation via an optomechanical nanobeam crystal composed of dielectric material layers

In this paper, we explore the generation of continuous-variable quantum correlations in an optomechanical nanobeam crystal, which consists of two dielectric mirrors designed as Bragg reflectors. These mirrors are constructed from alternating layers, with varying refractive indices, and their transmissive and reflective properties are analyzed using the transfer matrix method. The system is driven by a laser field tuned to the blue-detuned sideband, enabling coupling between the cavity and mechanical modes through radiation pressure. We explore various forms of quantum correlations, including entanglement, quantum steering, and quantum discord. Logarithmic negativity is employed to quantify entanglement, while quantum steering is assessed to evaluate the steerability between subsystems. Quantum discord is employed to measure non-classical correlations that extend beyond entanglement. Our findings emphasize that the strength of quantum correlation is affected by several factors, including laser power, single-photon coupling strength, and the refractive index of the mirror layers. Notably, all forms of correlations diminished with increasing temperature. These results underline the potential of the proposed system for advancing continuous-variable quantum information processing, offering versatile platforms for studying and harnessing quantum correlations in practical applications.