  Hanbury Brown and Twiss (HBT) correlations, i.e. correlations in far-field
intensity fluctuations, yield fundamental information on the quantum statistics
of light sources, as highlighted after the discovery of photon bunching.
Drawing on the analogy between photons and atoms, similar measurements have
been performed for matter-wave sources, probing density fluctuations of
expanding ultracold Bose gases. Here we use two-point density correlations to
study how coherence is gradually established when crossing the Bose-Einstein
condensation (BEC) threshold. Our experiments reveal a persistent multimode
character of the emerging matter-wave as seen in the non-trivial spatial shape
of the correlation functions for all probed source geometries from nearly
isotropic to quasi-one-dimensional (quasi-1D), and for all probed temperatures.
The qualitative features of our observations are captured by ideal Bose gas
theory, the quantitative differences illustrate the role of particle
interactions.
