  We propose a novel neutron interferometry setup to explore the potential
existence of mirror neutrons, a candidate for dark matter. Our work
demonstrates that if mirror neutrons exist, neutrons will acquire an observable
geometric phase due to mixing with these mirror counterparts. This geometric
phase, detectable through our interferometric setup, could serve as a direct
probe for the presence of mirror matter particles. Additionally, this
investigation could shed light on unresolved issues in particle physics, such
as the neutron lifetime puzzle. We discuss the setup's versatility and
limitations, showing its capability to explore a wide range of parameters in
neutron interferometry and potentially uncover new physics.
