Proposed test for realist theories using Rydberg atoms coupled to a high-Q resonator

From the hypotheses of realism and stationarity, the latter related to the Leggett-Garg assumption of non-invasive measurability, we derive inequalities, involving three autocorrelation functions, to be fulfilled by any two-state stochastic process. We seek to test a broad class of realist theories against quantum mechanics for a system consisting of a Rydberg atom interacting with a single quantized mode in a superconducting resonant cavity. Departures from quantum predictions are enhanced when the temperature is decreased to about 0.5 K and the state of the cavity approximates a Fock state.