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. 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.
Highlights
How fast can a quantum process be? Previous efforts to answer this question have resulted in fundamental insights into quantum state dynamics [1,2,3,4,5,6,7] and shed light on the ultimate physical limits to the rate of information processing [8,9,10]
A precise formulation of such a speed limit was first derived by Mandelstam and Tamm [1] considering the transformation of a quantum state jψiniti into an orthogonal one jψtargeti
We see that inequality (1) fails to give a meaningful bound on the shortest transport duration τQB if we examine its scaling with respect to the transport distance d: While the minimum time τQB is naturally expected to increase with d, remarkably, the time τMT exhibits rather the opposite behavior, as it decreases with d (Appendix M)
Summary
How fast can a quantum process be? Previous efforts to answer this question have resulted in fundamental insights into quantum state dynamics [1,2,3,4,5,6,7] and shed light on the ultimate physical limits to the rate of information processing [8,9,10]. A precise formulation of such a speed limit was first derived by Mandelstam and Tamm [1] considering the transformation of a quantum state jψiniti into an orthogonal one jψtargeti. They discovered that the duration τQB of the fastest process—the quantum brachistochrone— is bound by the inverse of the energy uncertainty [18], τQB. The MandelstamTamm bound shows that the duration of a quantum process cannot vanish, unless infinitely large energy resources can be controlled. Demonstration of the Mandelstam-Tamm bound in Eq (1) was given in effective two-level systems using ultracold atoms [34,35] and superconducting transmon circuits [36]
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