A perfect crystal neutron loop cavity

Coherent control of neutrons via Bragg diffraction forms the foundation of perfect crystal neutron interferometry, facilitating both fundamental tests of quantum mechanics and applications in quantum information science. In cavity geometries, perfect crystals enable neutron confinement and have been employed in precision measurements of spin-orbit interactions and for neutron electric dipole moment (nEDM) searches. However, in these conventional configurations, neutrons undergo a single pass through the crystal geometry, placing a physical constraint on both crystal and in-flight interaction times and measurement sensitivity. In this work, we introduce a neutron loop cavity that coherently recirculates neutrons through repeated Bragg reflections between perfect silicon crystal blades. This structure is predicted to achieve a neutron survival probability of $\sim64~\%$ for 10,000 Bragg reflections, corresponding to confinement times on the order of seconds. We propose a Schwinger interaction measurement that achieves a $\pi$ spin rotation in 800 Bragg reflections, representing more than a tenfold improvement in sensitivity over recent measurements. Further applications include high-sensitivity nEDM searches targeting the $10^{-27}~$e$\cdot$cm scale, as well as competitive experimental tests of neutron parity violation, the neutron lifetime, and the quantum Zeno effect with neutrons.