Creating nearly Heisenberg-limited matter-waves exploiting tunable interactions

Heisenberg's uncertainty principle suggests the existence of matter waves with minimal combined uncertainty in position and momentum. This limit is challenging to obtain with large ensembles of interacting particles. Here we report on a high-flux source of ultra-cold atoms with free expansion rates near the Heisenberg limit directly upon release from the trap. Our results are achieved through dynamic tuning of the atomic scattering length across two orders of magnitude interaction strength via magnetic Feshbach resonances. We model the interaction energy of the ensembles with a scaling approach based on the Thomas-Fermi approximation in the strong interaction regime and a variational approach based on a Gaussian atomic density approximation in the weak interaction regime, observing the transition between both experimentally. Paired with matter-wave lensing techniques, our method is expected to produce quantum degenerate atoms with interaction energies in the femtokelvin range, paving the way for precision tests of quantum mechanics on unexplored energy scales.