Three-path quantum Cheshire cat observed in neutron interferometry

Although our every-day experience rejects it, the quantum Cheshire Cat suggests a potential spatial separation between different properties of a single particle in an interferometer. The first experiment with neutrons confirmed the quantum Cheshire Cat effect by using the path and spin degrees of freedom. The locations of each property are determined qualitatively through reactions to locally applied perturbations. Yet, no consensus on the interpretation has been reached. To clarify the origin of the effect, in the present experiment the energy degree of freedom is used as the third property; the three properties of neutrons appear to be separated in different paths in the interferometer. The analysis of the experiment suggests the strong involvement of the inner product between the state vectors, one evolved from the initial state through the perturbation and the other being the final state. The inner product results in amplitudes from two sub-beams which contribute to the intensity. The cross-term between amplitudes gives rise to the quantum Cheshire Cat.