Geometric phases as probes of dark sectors

We review recent interferometric schemes designed to probe physics beyond the Standard Model through the detection of 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 fermion systems [A. Capolupo, Phys. Rev. D 84, 116002 (2011); A. Capolupo, S. M. Giampaolo and A. Quaranta, Eur. Phys. J. C 81, 1116 (2021); A. Capolupo, G. Pisacane, A. Quaranta and F. Romeo, Phys. Dark Universe 46, 101688 (2024)].