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

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