Hanbury Brown and Twiss Bunching of Phonons and of the Quantum Depletion in an Interacting Bose Gas

We report the realization of a Hanbury Brown and Twiss (HBT)-like experiment with a gas of interacting bosons at low temperatures. The low-temperature regime is reached in a three-dimensional optical lattice arid atom-atom correlations are extracted from the detection of individual metastable helium atoms after a long free fall. We observe, in the noncondensed fraction of the gas, a HBT bunching whose properties strongly deviate from the HBT signals expected for noninteracting bosons. In addition, we show that the measured correlations reflect the peculiar quantum statistics of atoms belonging to the quantum depletion and of the Bogoliubov phonons, i.e., of collective excitations of the many-body quantum state. Our results demonstrate that atom-atom correlations provide information about the quantum state of interacting particles, extending the interest of HBT-like experiments beyond the case of noninteracting particles.