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 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.
- Received 1 October 2020
- Revised 9 November 2020
- Accepted 21 January 2021
DOI:https://doi.org/10.1103/PhysRevX.11.011035
Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.
Published by the American Physical Society
Physics Subject Headings (PhySH)
Focus
FocusAn Atom Pushed to Its Speed Limit
Published 19 February 2021
Researchers have transported an atom between two locations in the shortest possible time, an achievement that has implications for quantum technologies.
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Popular Summary
Knowing how fast a quantum process can be reveals the ultimate limits to information processing. This concept of a minimum time or path to complete some process has deep roots in physics: In 1696, Bernoulli posed his now-famous brachistochrone problem, which essentially asked what the profile of a wire should be to allow a bead to slide from one point to a lower point in the least amount of time. The analog solution to the brachistochrone problem for two-level quantum systems—the fastest path connecting two of these quantum states—has been long known. These solutions, however, are generally not applicable to larger quantum systems. Here, we experimentally demonstrate a shortest-duration quantum process that fundamentally cannot be reduced to two-level dynamics.
Specifically, we carry out fast coherent transport of an atomic wave packet over a distance 15 times its size. Our measurements of the transport fidelity sharply resolve the transition from a quantum-controllable to a quantum-noncontrollable process as the time is shortened, thus revealing the existence of a minimum duration—a quantum speed limit. Based on a geometric approach to quantum state dynamics, we provide a close lower bound on the minimum process duration beyond the two-level-system paradigm.
These results shed light upon a fundamental speed limit of quantum state dynamics. Identifying quantum processes of the shortest duration is important in quantum sensing and quantum computing.
