Neutron spin echo techniques have the capability to construct and manipulate entangled quantum neutron beams, which were used to answer fundamental questions of quantum mechanics and can serve as potential probes for material research. Modern spin-echo devices, such as Magnetic Wollaston Prisms(MWP) and resonance radiofrequency(RF) neutron flippers, can produce and control quantum neutron states with high fidelity, thanks to their magnetic fields with well-defined shapes and boundaries. Mathematical descriptions of the mechanism of these devices are introduced in this thesis based purely on quantum mechanics and solvable ideal models. Specifically a quantum wave packet description of such neutron beams is established to express Bell states entangling spatial paths and spin or Greenberger-Horne-Zeilinger(GHZ) states having paths, spin, and total energies entangled together. Meanwhile, we proposed novel RF flipper designs inheriting the same idea from MWP using the Meissner effect of superconductors to shape the magnetic fields. The magnetic field simulation program MagNet was used to design and optimize the magnetic components in these RF flippers and guide the construction of these devices. Existing spin echo devices including MWPs and RF flippers are turned into quantum interferometers in experiments that investigate hidden variable theories and quantum contextuality. Given the Bell and GHZ states prepared by these devices, we tested both Clauser-Horne-Shimony-Holt(CHSH) version quantum contextuality inequalities and Mermin contextuality inequalities. The final results of violations of classically predicted limits strengthened the theoretical foundation of quantum mechanics but more importantly, proved the creation of mode entangled neutron beams using spin echo devices. The wave packet model along with the experimental results, enlightened a route to interesting material research fields, where the new RF flippers ready to be tested should make a difference.