Correlations, visibilities and Wigner functions in a double-loop neutron interferometer

In a double-loop neutron interferometer two and three beams are superposed behind the first and second loop respectively. The wavefunctions in different arms of the interferometer are discussed using wavepackets. Various correlations can be defined. Both the momentum and the space distributions which are influenced by phase shifters are calculated. Those distributions are marginal distributions of the corresponding Wigner functions. While the momentum distribution can be measured by means of post-selection, the space distribution is directly accessible via the visibility which is expressed by an appropriate correlation function. It is shown that the space distribution behind the first loop can be represented by the visibility which can be determined by measuring neutron intensities behind the second loop.