Nonclassical effects of photon-phonon antibunching in a multifield driven optomechanical cavity

The nonclassical signature of a photon-phonon pair can be tested effectively by violating Cauchy-Schwarz and Bell's inequality, which can arise due to antibunching phenomena in coupled bosonic systems. In this paper, we analyze the measurement criteria imposed on the second-order coherence functions and investigate the quantum correlations leading to the suppression of multi-photon-phonon excitation in a single optomechanical cavity upon driving it with two pumping fields. It is also shown that the Cauchy-Schwarz violation can serve as an ideal precursor to demonstrate stronger tests of locality related to Bell's inequality. We consider weak driving and optomechanical coupling coefficient parameters in the system that enables the unconventional nature of photon (phonon) blockades while operating in the resonance of cavity detuning and mechanical frequency. These findings are valuable for generating sub-Poissonian signals in optimal conditions and have potential applications in hybrid systems for on-demand single photon (phonon) detection.