Quantum interferometric probe of neutron--hidden neutron oscillations

The nature of dark matter remains an outstanding problem in particle physics and cosmology. Hidden-sector extensions of the Standard Model predict a neutral partner of the neutron, whose weak mixing with ordinary neutrons induces oscillations between visible and dark baryonic states. We show that macroscopic quantum interferometry provides a direct and experimentally accessible probe of this phenomenon. In particular, a Mach--Zehnder interferometer with very cold neutrons converts neutron--hidden neutron oscillations into measurable phase-dependent intensity modulations. By combining controlled phase shifts with tunable magnetic fields and material potentials, the setup enables a resonant exploration of the hidden-sector parameter space. We find that existing cold-neutron facilities can probe mixing amplitudes down to $\epsilon_{nn'} \sim 10^{-14}\,\mathrm{eV}$ for mass splittings $\delta m \sim 10^{-9}\,\mathrm{eV}$, accessing a previously unexplored region of parameter space relevant to baryonic dark matter scenarios. These results establish neutron interferometry as a precision laboratory tool for testing hidden-sector physics.