Signatures of quantum and classical gravity on non-relativistic quantum systems

Understanding the interplay between gravitational phenomena and quantum mechanics is one of the greatest challenges of contemporary physics. Indeed, the theoretical difficulties in merging the theories are exacerbated by the lack of experimental data. Recently, a lot of effort has been devoted to investigating whether, within non-relativistic and weak-field limits, some facets of gravity at the interface with quantum physics could be experimentally tested. This thesis focuses on identifying signatures of gravitational effects on quantum systems in this regime, following two complementary directions. The first half of the thesis explores the effects of a quantized gravitational field when treated as an environment. The established claim in the literature is that gravitational environments induce decoherence in the kinetic-energy basis. It is shown that this result is affected by ambiguities both in the open quantum system (OQS) analysis and in the general relativistic one. The first issue is not specific to gravity but concerns the OQS treatment of Lagrangians that differ by a total derivative. While such Lagrangians are equivalent for closed systems, they can lead to inequivalent reduced dynamics because they can induce different partitions of the Hilbert space between system and environment. From the general relativistic side, the standard result is undermined by an inadequate choice of coordinates, which does not take into account the metric role played by the gravitational field. These issues are resolved by adopting an appropriate Lagrangian and reformulating the analysis in Fermi normal coordinates. This formulation provides an operationally well-defined analysis of gravitational decoherence and it predicts decoherence in the position basis rather than in the kinetic-energy basis. The second half instead explores the possibility that gravity may not be quantized at all, and the consequences that such an assumption necessarily entails. It is customarily assumed that a classical gravitational interaction cannot entangle previously separable quantum masses. This logic is the foundation of tabletop experiments on gravitationally induced entanglement (GIE) as evidence for the quantization of gravity. Such experiments, however, are outside the scope of present day technology, as they require the control of spatial superpositions of mesoscopic masses. Alternative routes, however, can be pursued. We show that a classical gravitational interaction cannot remain deterministic when coupled consistently to quantum matter, but must be random and induce diffusion in the motion of quantum systems. These diffusive effects can be quantitatively bounded from below and probed in non-interferometric experiments, thereby avoiding the main obstacles faced by the entanglement tests. Finally, hybrid classical-quantum theories of gravity are analysed in the context of the GIE proposals. These theories couple classical degrees of freedom of gravity to quantum matter, and they are constructed using the tools of quantum measurement and feedback. We show that such models can generate entanglement between two masses even though gravity is described by classical degrees of freedom, and trace the root of this to some unavoidable non-locality of the models. Nevertheless, a comparison between the entanglement generated in the Tilloy-Diósi model and that generated by the standard Newtonian potential shows that entanglement detection should still quantitatively discriminate quantum gravity from hybrid theories.