Demonstration of Quantum Brachistochrones between Distant States of an Atom

Abstract

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 twolevel 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.