  The paradoxical phenomenon of the quantum Cheshire Cat (qCC) refers to
situations where different properties of a particle appear to be localised in
different paths of an interferometer and therefore spatially separated. This
observation is obtained by implementing a pre- and postselection procedure. The
localisations are determined qualitatively through conspicuous changes induced
by weak interactions. Previous demonstrations of the qCC only used the path and
spin/polarisation degrees of freedom. In addition, the present experiment uses
the neutron's energy as a third property in a three-path interferometer. It is
demonstrated that the three properties of neutrons are found separated in
different paths in the interferometer; a detailed analysis suggests that the
appearance of a property is strongly related to the geometrical relation
between the state vectors of pre- and postselection with weak interactions in
between. If a weak interaction in a path locally generates a state vector with
a component parallel to the reference state in another path, a conspicuous
intensity oscillation is expected and observed. Therefore, the appearance of
the observed intensity oscillations is attributed solely to the cross-terms
between the reference and the newly generated state via weak interactions.
