Applications of quantum random walk and dynamical diffraction for particle and nuclear physics

Even though the Standard Model of particle physics over the years demonstrated a large success in experimental predictions, we are in the constant search for its limitation and extensions. One example of such extension would be the existence of a fifth force. The recent experiment based on neutron interferometry, specifically Pendellösung interferometry, that is usually explained by Dynamical Diffraction (DD) theory of neutron scattering placed the most stringent bound on the strength of a such fifth force. Unfortunately, this DD theory is often hard to use in non-ideal cases where interferometers might have surface roughness or crystal imperfections and impurities. Using the quantum information model of dynamical diffraction, we consider a neutron cavity composed of two perfect crystal silicon blades capable of containing the neutron wavefunction. We show that the internal confinement of the neutrons through Bragg diffraction can be modelled by a quantum random walk. Furthermore, we introduce a toolbox for modelling crystal imperfections such as surface roughness and defects. Good agreement is found between the simulation and the experimental implementation, where leakage beams are present, modelling of which is impractical with the conventional theory of dynamical diffraction. Analysis of the standing neutron waves is presented in regards to the crystal geometry and parameters; and the conditions required for well-defined bounces are derived. The presented results enable new approaches to studying the setups utilizing neutron confinement, such as the experiments to measure neutron magnetic and electric dipole moments.