Crucial tests of macrorealist and semi-classical gravity models with freely falling mesoscopic nanospheres

Recently, several proposals have been made to test the quantum superposition principle in the mesoscopic regime. Most of these tests consist of a careful measurement of the loss of interference due to decoherence. Here we consider, instead, the spread in position of a freely falling nanosphere. We study in depth the dependence of this spread on self-gravity in the presence of decoherence (exotic and non-exotic). We show that the influence of self-gravity is robust in the presence of weak decoherence, and quantify this robustness by introducing a new parameter, the critical decoherence, aimed at estimating the critical value above which self-gravity is overwhelmed by decoherence. We also emphasise the crucial role played by the spread of the initial wave packet for the sensitivity of free-fall experiments to decoherence.