We propose here a scheme based on the measurement of quadrature phase coherence that is aimed at testing the Clauser-Horne-Shimony-Holt Bell inequality in an optomechanical setting. Our setup is constituted by two optical cavities dispersively coupled to a common mechanical resonator. We show that it is possible to generate Einstein-Podolsky-Rosen--like correlations between the quadratures of the output fields of the two cavities and, depending on the system parameters, to observe the violation of the Clauser-Horne-Shimony-Holt inequality.
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Manninen et al. (2018) studied this question.
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