Physical Review X (Feb 2021)

Demonstration of Quantum Brachistochrones between Distant States of an Atom

  • Manolo R. Lam,
  • Natalie Peter,
  • Thorsten Groh,
  • Wolfgang Alt,
  • Carsten Robens,
  • Dieter Meschede,
  • Antonio Negretti,
  • Simone Montangero,
  • Tommaso Calarco,
  • Andrea Alberti

DOI
https://doi.org/10.1103/PhysRevX.11.011035
Journal volume & issue
Vol. 11, no. 1
p. 011035

Abstract

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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.