Testing energy quantization at the level of 100 kHz by neutron crystal diffraction

For the study of energy quantization in low-frequency potentials and the accompanying quantum effects we analyze a silicon double-crystal arrangement exploiting dynamical diffraction of neutrons to achieve the required extremely high energy resolution. The first crystal prepares a minimum-uncertainty beam that passes a potential region whose influence on the neutron energy is analyzed by the second crystal. With realistic parameters, changes of neutron energy below 0.5 neV can be resolved. This permits a test of quantized energy transfer in periodically time-dependent potentials of a frequency below 100 kHz. We also discuss three specific examples how to observe the quantum phenomena arising from the macroscopic wave packets thereby generated.