Geometric Phases as Probes of Dark Sectors and Fundamental Symmetries

We review recent interferometric schemes designed to probe physics beyond the Standard Model through the detection of geometric phases. Within the kinematic approach to non-cyclic geometric phases, we discuss how interactions with hidden-sector degrees of freedom, such as axion-like particles and mirror-matter candidates, can induce potentially observable phase shifts in ordinary fermionic systems. We further show how the same geometric framework can be extended to particle mixing systems and fundamental symmetries, providing a phase-based signature of the Charge–Parity–Time (CPT) violation. These results illustrate how geometric phases can encode information that is not always directly accessible through standard transition probabilities, making quantum interferometry a complementary tool for testing dark-sector interactions, fundamental properties of elementary particles, acceleration-induced quantum-field effects, and phase-based thermometry. We also critically assess the experimental requirements and limitations of the proposed schemes.