This licentiate thesis in theoretical physics focuses on the existence of quantum features in physical systems such as axion dark matter and gravity. Our focus is mostly on effects which appear at low energies, a regime in which our models can be confronted with current experiments or within the foreseeable future. In our first project, we focus on squeezing of axion dark matter, a quantum mechanical effect which accompanies the standard mean field description of axions. We have showed that within a reasonable set of assumptions, the quantum state of axions is highly squeezed. This theoretical finding suggests that the mean field description of axion dark matter is incomplete, since the latter conceals many interesting and possibly experimentally relevant phenomena, and paves the way for axion dark matter studies beyond the mean field approximation. Moreover, in this thesis, some ongoing work on axion dark matter decoherence is presented. Our goal is to test whether axion dark matter squeezing is robust against decoherence. Preliminary results indicate that squeezing is not diminished in presence of environmental interactions. Our results stem from an interdisciplinary approach at the intersection between cosmology, quantum optics, quantum open systems and cold atoms. Our second work focuses on quantum features of gravity. An almost century old question is how gravity can be reconciled with the laws of quantum mechanics. This question remains still open and part of the reason is the lack of experimental evidence. However, in recent years, the rapid progress of experimental techniques allows for quantum control and manipulation of larger and larger quantum systems. These new experimental routes have sparkled an interest in testing such fundamental questions with tabletop experiments. One particularly interesting proposal aims to test whether gravity can mediate entanglement between two spatially superposed mesoscopic masses. This proposal, in order to deduce the existence of quantized gravitational mediators, relies on a quantum-information-theoretic argument, the so-called LOCC (Local Operations and Classical Communication). In our work, we critically assess this proposal, its underlying assumptions and what teaches about quantum gravity. We conclude that the LOCC argument is not useful and by invoking it, one cannot unambiguously infer the existence of quantum mediators unless the principle oflocality is elevated to a fundamental principle of nature. We support our claim by explicitly showing that well known relativistic field theories, apart from local formulations can also admit non-local ones. Therefore, the entanglement generating quantum channel can be either local or non-local.

The hunt for Dark Matter plays a truly critical role in contemporary physics. At both the largest and smallest scales, deep questions are being raised about the fundamental nature of the universe - questions that confirmation and then characterisation of particle dark matter will provide many answers to. This thesis presents some of the world's most sensitive searches to date for certain types of axion dark matter, axion-like particles, and two-neutrino double electron capture. These have been conducted using the Large Underground Xenon (LUX) experiment. Evidence for dark matter and physics beyond the Standard Model of particle physics is described in Chapter 1, while Chapter 2 gives an overview of proposed candidates for particle dark matter. The various experimental approaches being used to detect particle dark matter are presented in Chapter 3. Direct detection with time projection chambers plays a major role in this thesis, with particular interest in the LUX detector, that is described in its components and operations. Chapter 4 presents LUX direct searches for weakly interacting massive particles. Although I have contributed to these analyses, they are included for completeness only, as they are not part of my central work. The LUX collaboration's searches for axion dark matter and axion-like particle have delivered world-leading results on the axion-electron coupling constant. These results, that I personally led and which have been published in Physics Review Letters, are presented in Chapter 5, along with sensitivity studies, also led by me, made for the future LUX-ZEPLIN experiment. Finally, a search for two-neutrino double electron capture of 124Xe, that I performed using LUX data to extract a limit on the half life of the process, is presented in Chapter 6. Although being allowed by the Standard Model, two-neutrino double electron capture shares the matrix element calculation framework with the neutrinoless channel of the same process, becoming of great interest in the scope of neutrino physics. Conclusions follow and close the thesis.