Abstract: | How fast can a quantum system evolve between two states? This question is not only important for its basic nature, but it also has far-reaching implications on future quantum technologies. There are two well-known limits on the maximum evolution rate, named after their discoverers—Mandelstam–Tamm and Margolus–Levitin. Despite their fundamental character, only the Mandelstam–Tamm limit has been so far investigated and exclusively in effective two-level systems.
In this colloquium, I will report on a recent experimental study [1] where we put both limits to the test in a multi-level system. The experiment consists in following with high temporal resolution the quantum dynamics of a matter wave sliding down an optical potential. Our measurements reveal a crossover between the two quantum speed limits, depending on the energy distribution of the quantum state. We find a striking difference between a two-level and a multi-level system—excitations of a multi-level system do not saturate the speed limit but, unexpectedly, produce a small, universal deviation from it.
In the second part of this colloquium, I will address a related question, what is the fastest route—the quantum brachistochrone—to transport an atom between distant states. We demonstrate [2] coherent transport of an atomic matter wave over a distance of 15 times its size in the shortest possible time. Owing to the large separation between the two sites, the two limits above fail to capture the relevant time scale. In contrast, we show that quantum optimal control provides solutions to the quantum brachistochrone problem.
Our results, establishing quantum speed limits beyond the simple two-level system, are important to understand the ultimate performance of quantum computing devices and related advanced quantum technologies. |
