  We report an experimental realization of the quantum paradox of the
separation of a single photon from one of its properties (the so-called
"quantum Cheshire cat"). We use a modified Sagnac interferometer with displaced
paths to produce appropriately pre- and postselected states of heralded single
photons. Weak measurements of photon presence and circular polarization are
performed in each arm of the interferometer by introducing weak absorbers and
small polarization rotations and analyzing changes in the postselected signal.
The absorber is found to have an appreciable effect only in one arm of the
interferometer, while the polarization rotation significantly affects the
signal only when performed in the other arm. We carry out both sequential and
simultaneous weak measurements and find good agreement between measured and
predicted weak values. In the language of Aharonov et al. and in the sense of
the ensemble averages described by weak values, the experiment establishes the
separation of a particle from one its properties during the passage through the
interferometer.
