Quantum speed limits crossover probed by matter wave interferometry

Quantum speed limits dictate the rate of quantum state evolution and thus restrict the maximal performance of any quantum technology. The two most celebrated limits are formulated in terms of the state's energy uncertainty (Mandelstam-Tam bound) and average energy (Margolus-Levitin bound). We perform matter wave interferometry experiments and track the motion of a single atom in a spin-dependent lattice. This setup constitutes an open multi-level quantum system in which we test the speed limits. Our results show that only the combination of the two limits provides the relevant bound. Specifically, we find that at short evolution times, the Mandelstam-Tam limit is always the tighter bound. A crossover to the Margolus-Levitin limit may occur at longer times, depending on the ratio between the first two energy moments. Our work elucidates the role of each quantum speed limit and establishes matter wave interferometry as a powerful tool to study fast quantum state dynamics.