Demonstration of Quantum Brachistochrones between Distant States of an Atom

Transforming an initial quantum state into a target state through the fastest possible route - a quantum brachistochrone - is a fundamental challenge for many technologies based on quantum mechanics. In two-level systems, the quantum brachistochrone solutions are long known. These solutions, however, are not applicable to larger systems, especially when the target state cannot be reached through a local transformation. Here, we demonstrate fast coherent transport of an atomic wave packet over a distance of 15 times its size - a paradigmatic case of quantum processes going beyond the two-level system. Our measurements of the transport fidelity reveal the existence of a minimum duration - a quantum speed limit - for the coherent splitting and recombination of matter waves. We obtain physical insight into this limit by relying on a geometric interpretation of quantum state dynamics. These results shed light on a fundamental limit of quantum state dynamics and are expected to find relevant applications in quantum sensing and quantum computing.