Creating nearly Heisenberg-limited matter-waves exploiting tunable interactions

The wave nature of matter implies wavepackets with minimal combined uncertainty in position and momentum, a limit which can hardly be reached for clouds of large atom numbers of interacting particles. Here, we report on a high-flux source of ultra-cold atoms realizing near-Heisenberg-limited expansion rates upon release from the trap. Depending on the value of the scattering length, we model our system either with a scaling approach based on the Thomas-Fermi approximation, or with a variational approach based on a Gaussian atomic density approximation, observing the transition between the weak and strong interaction regimes. Finally, we discuss applications of our methods to test foundational principles of quantum mechanics such as the superposition principle or their extension to other atomic species.