Multifold paths of neutrons in the three-beam interferometer detected by tiny energy-kick

A neutron optical experiment is presented to investigate the paths taken by neutrons in a three-beam interferometer. In various beam-paths of the interferometer, the energy of the neutrons is partially shifted so that the faint traces are left along the beam-path. By ascertaining an operational meaning to "the particle's path", which-path information is extracted from these faint traces with minimal-perturbations. Theory is derived by simply following the time evolution of the wave function of the neutrons, which clarifies the observation in the framework of standard quantum mechanics. Which-way information is derived from the intensity, sinusoidally oscillating in time at different frequencies, which is considered to result from the interfering cross terms between stationary main component and the energy-shifted which-way signals. Final results give experimental evidence that the (partial) wave functions of the neutrons in each beam path are superimposed and present in multiple locations in the interferometer.