  Fifty years ago, Hanbury Brown and Twiss (HBT) discovered photon bunching in
light emitted by a chaotic source, highlighting the importance of two-photon
correlations and stimulating the development of modern quantum optics . The
quantum interpretation of bunching relies upon the constructive interference
between amplitudes involving two indistinguishable photons, and its additive
character is intimately linked to the Bose nature of photons. Advances in atom
cooling and detection have led to the observation and full characterisation of
the atomic analogue of the HBT effect with bosonic atoms. By contrast, fermions
should reveal an antibunching effect, i.e., a tendency to avoid each other.
Antibunching of fermions is associated with destructive two-particle
interference and is related to the Pauli principle forbidding more than one
identical fermion to occupy the same quantum state. Here we report an
experimental comparison of the fermion and the boson HBT effects realised in
the same apparatus with two different isotopes of helium, 3He (a fermion) and
4He (a boson). Ordinary attractive or repulsive interactions between atoms are
negligible, and the contrasting bunching and antibunching behaviours can be
fully attributed to the different quantum statistics. Our result shows how
atom-atom correlation measurements can be used not only for revealing details
in the spatial density, or momentum correlations in an atomic ensemble, but
also to directly observe phase effects linked to the quantum statistics in a
many body system. It may thus find applications to study more exotic situations
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