Temporal Bell-type inequalities for two-level Rydberg atoms coupled to a high-Q resonator

Following the strategy of showing specific quantum effects by means of the violation of a classical inequality, a pair of Bell-type inequalities is derived on the basis of certain additional assumptions, whose plausibility is discussed in detail. Such inequalities are violated by the quantum mechanical predictions for the interaction of a two-level Rydberg atom with a single mode sustained by a high-Q resonator. The experimental conditions required in order to show the existence of forbidden values, according to a hidden variables formalism, in a real experiment are analyzed for various initial field statistics. In particular, the revival dynamics expected for the interaction with a coherent field leads to classically forbidden values, which would indicate a purely quantum effect.