We have studied two-body correlations of atoms in an expanding cloud above and below the Bose-Einstein condensation threshold. The observed correlation function for a thermal cloud shows a bunching behavior, whereas the correlation is flat for a coherent sample. These quantum correlations are the atomic analog of the Hanbury Brown Twiss effect. We observed the effect in three dimensions and studied its dependence on cloud size.

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, 3 He (a fermion) and 4 He (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 7,8 or momentum correlations 9 in an atomic ensemble, but also to directly observe phase 2 effects linked to the quantum statistics in a many body system. It may thus find applications to study more exotic situations 10 .Two-particle correlation analysis is an increasingly important method for studying complex quantum phases of ultracold atoms 7,8,9,10,11,12,13 . It goes back to the discovery by Hanbury Brown and Twiss 1 , that photons emitted by a chaotic (incoherent) light source tend to be bunched: the joint detection probability is enhanced, compared to that of statistically independent particles, when the two detectors are close together.Although the effect is easily understood in the context of classical wave optics 14 , it took some time to find a clear quantum interpretation 3,15 . The explanation relies upon interference between the quantum amplitude for two particles, emitted from two source points S 1 and S 2 , to be detected at two detection points D 1 and D 2 (see fig. 1). For bosons, the two amplitudes D S D S must be added, which yields a factor of 2 excess in the joint detection probability, if the two amplitudes have the same phase. The sum over all pairs (S 1 ,S 2 ) of source points washes out the interference, unless the distance between the detectors is small enough that the phase difference between the amplitudes is less than one radian, or equivalently if the two detectors are separated by a distance less than the coherence length. Study of the joint detection rates vs. detector separation along the i-direction then reveals a bump whose width l i is the coherence length along that axis 1,5,16,17,18,19 . For a source size s i along i (standard half width at e -1/2 of a Gaussian density profile), one has a half width at 1/e of l i = ht / 2πms i , where m is the mass of the particle, t the time of flight from the source to the detector, and h Planck's constant. This formula is the analogue of the formula l i = Lλ / 2πs i for photons if one identifies λ = h / mv with the de Broglie wavelength for particles travelling at velocity v = L / t from the source to the detector.For indistinguishable fermions, the two-body wave function is antisymmetric, and the two amplitudes must be subtracted, yielding a null probability for joint detection in the same coherence volume. In the language of particles, it means th...