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. 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 where the target state cannot be reached through a local transformation. 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 upon a fundamental limit of quantum state dynamics and are expected to find relevant applications in quantum sensing and quantum computing.

}, Author = {Lam, M. R. AND Peter, N. AND Groh, T. AND Alt, W. AND Robens, C. AND Meschede, D. AND Negretti, A. AND Montangero, S. AND Calarco, T. AND Alberti, A.}, Journal = {Phys. Rev. X (Featured in Physics)}, Pages = {011035}, Title = {{Demonstration of quantum brachistochrones between distant states of an atom}}, Volume = {11}, Year = {2021} }