This thesis in theoretical physics explores fundamental aspects of gravity and quantum mechanics, focusing on how quantum effects arise in gravitational and cosmological contexts. Specifically, we investigate how novel quantum effects in axion dark matter models—a promising dark matter candidate with numerous ongoing experimental detection efforts—manifest and critically examine the implications of gravity-induced entanglement proposals as potential experimental tests of quantum gravity. Additionally, we propose new approaches to testing fundamental principles of gravity, particularly in identifying and constraining possible discrepancies between how gravitational fields are sourced and probed, both in the classical and quantum domains. By drawing on insights from quantum optics and cosmology while leveraging recent experimental advancements, this thesis challenges existing paradigms and proposes new methods for exploring the interplay between gravity and quantum mechanics.

In Paper I, we focus on squeezing of axion dark matter, a quantum effect that accompanies the standard description of axions. The commonly used mean-field treatment obscures potential quantum signatures in the system. We show that under standard assumptions, the quantum state of axions is highly squeezed. This suggests that the mean-field description of axion dark matter is incomplete, paving the way for studies beyond this approximation. Moreover, this thesis explores the decoherence of axion dark matter, assessing whether squeezing remains robust in the presence of decoherence—an essential step toward experimental probing such an effect. We demonstrate that squeezing persists under generic environmental interactions, indicating that quantum effects may be expected for dark matter. Our results stem from an interdisciplinary approach bridging cosmology, quantum optics, quantum open systems, and cold atoms.

In Paper II, we explore the quantum aspects of gravity. For nearly a century, reconciling gravity with quantum mechanics has been a challenge, hindered by the lack of experimental evidence. Recent advances in quantum control of large systems have renewed interest in testing this through tabletop experiments. An influential proposal aims to test whether gravity mediates entanglement between two spatially superposed mesoscopic masses, using a quantum-information-theoretic argument based on LOCC (Local Operations and Classical Communication) to infer quantized gravitational mediators. However, there has been a heated debate about what conclusions can be drawn from such an experiment. We critically assess this proposal, its assumptions, and its implications for quantum gravity. We conclude that the LOCC argument is insufficient to unambiguously infer quantum mediators unless locality is elevated to a fundamental principle of nature. We support this claim by showing that well-known relativistic field theories, beyond their local formulations, admit equally viable non-local ones. Thus, the entanglement-generating quantum channel can be local or non-local, even within relativity. We also highlight that cosmic microwave background observations already provide evidence for the quantization of the Newtonian potential. Nevertheless, the experiment probes a new, untested regime—how quantum delocalized source masses gravitate.

Paper III builds on the conclusions of Paper II, specifically examining how delocalized masses source gravity. We investigate whether it is sensible, within established theories, to distinguish between sourcing and probing gravity. To explore this, we first analyze classical Newtonian gravity, revisiting studies on violations of active and passive gravitational mass. We introduce novel parameters capturing a broader range of possible violations, including quantum mechanical ones. Using existing experimental setups, such as Cavendish and free-fall experiments, we propose new methods to constrain these parameters. Our constraints could match or surpass those from prior experiments. This work opens a new avenue for testing the fundamental principle of the equality of active and passive gravitational masses—an area that has received little attention. Additionally, we extend beyond classical tests, proposing novel quantum experiments. This stems from the intriguing possibility that, while no distinction exists between active and passive gravitational mass in classical physics, such violations could emerge, through mass-energy equivalence, in the deep quantum gravity domain.