Possibility of observing energy decoherence due to quantum gravity

It has recently been proposed that quantum gravity might lead to the decoherence of superpositions in energy, corresponding to a discretization of time at the Planck scale. The proposal seems amenable to experimental verification with methods from quantum optics and atomic physics. However, we argue that the predicted decoherence is unobservable in such experiments if it acts globally on the whole experimental setup. This is related to the unobservability of the global phase in interference. We then show how local energy decoherence, which acts separately on system and phase reference, could be detected with remarkable sensitivity and over a wide range of length scales by long-distance Ramsey interferometry with metastable atomic states. The sensitivity of the experiments can be further enhanced using multiatom entanglement