Hanbury Brown and Twiss correlations across the Bose-Einstein condensation threshold

Hanbury Brown and Twiss correlations-correlations in far-field intensity fluctuations-yield fundamental information on the quantum statistics of light sources, as demonstrated after the discovery of photon bunching(1-3). 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(4-8). Here we use two-point density correlations to study how coherence is gradually established when crossing the Bose-Einstein condensation 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, and for all probed temperatures. The qualitative features of our observations are captured by ideal Bose gas theory(9), whereas the quantitative differences illustrate the role of particle interactions.