From Dark Matter Searches to the Nature of Gravity: Quantum Sensors in Fundamental Physics

Modern theoretical physics is shaped by a tension between elegant paradigms and deep unresolved puzzles, which makes advancing our understanding of nature especially challenging. Progress demands new information capable of guiding us beyond existing frameworks. This thesis explores the precision frontier in the search for new physics; more specifically, the role of quantum sensors and tabletop precision experiments as probes of two intertwined directions beyond the standard paradigms: model-independent signatures of dark matter, and the effective microscopic structure of gravity. In Part I, we develop dark matter signatures in matter-wave interferometers, atom gradiometers, and gravitational wave detectors. We characterize phase shift and decoherence in matter-wave interferometers induced by dark matter scattering. The low energy-threshold allows reach into the sub-GeV light mass regime where low momentum-transfer scatterings are below traditional detection thresholds. We also study the decoherence background in space-based interferometers caused by astrophysical backgrounds. Aside from particle dark matter, we study classical signals from dark matter through pure gravitational interactions. We construct a simplified computational framework for signatures of linearized gravity perturbations in atom gradiometers, and apply it to model signatures of dark matter from ultralight bosonic fields to ultraheavy clumps. We also analyze similar scenarios where ultraheavy dark matter clumps induce deterministic or stochastic signals in present and proposed gravitational wave detectors, and use the result to draw constraints on fifth-force interaction strengths. In Part II, we turn to signatures of physics beyond general relativity. We study the vacuum fluctuation background predicted by the "pixellon" phenomenological model of quantized spacetime, and show that next-generation gravitational wave detectors would have access to its predicted noise spectrum. We then construct a Lorentz-invariant field-theoretic model of entropic gravity in which the Newtonian coupling is set by the energy density of a thermal scalar bath. We study the linear response of a test mass system in the presence of such an entropic force, including the dissipation and thermal fluctuations of the force that satisfy the fluctuation--dissipation relation, and identify a thermal phase lag whose distinctive frequency dependence may make it an observable signature in low-frequency precision experiments. We also analyze the entanglement generation condition for such an entropic force model. Uniting the two parts, we see that many detectors have dual purposes for gravitationally interacting dark matter and signatures of gravity. The formalisms for modeling these two classes of new physics in precision sensors share substantial common structure. We emphasize that these quantum sensors cover a unique ground in both dark matter searches and in constraining models of low-energy gravity.