Quantum mechanics sets fundamental limits on how fast quantum states can be transformed in time. Two well-known quantum speed limits are the Mandelstam–Tamm (MT) and the Margolus–Levitin (ML) bounds, which relate the maximum speed of evolution to the system's energy uncertainty and mean energy, respectively. Here, we test concurrently both limits in a multi-level system by following the motion of a single atom in an optical trap using fast matter wave interferometry. Our data reveal two different regimes: one where the MT limit constrains the evolution at all times, and a second where a crossover to the ML limit is manifested at longer times. We take a geometric approach to quantify the deviation from the speed limit, measuring how much the matter wave's quantum evolution deviates from the geodesic path in the Hilbert space of the multi-level system. Our results, establishing quantum speed limits beyond the simple two-level system, are important to understand the ultimate performance of quantum computing devices and related advanced quantum technologies.

}, Author = {Ness, G. AND Lam, M. R. AND Alt, W. AND Meschede, D. AND Sagi, Y. AND Alberti, A.}, Journal = {arXiv:2104.05638 [quant-ph]}, Pages = {}, Title = {{Observing quantum-speed-limit crossover with matter wave interferometry}}, Volume = {}, Year = {2021} }