A speed limit also applies in the quantum world

Even in the world of the smallest particles with their own special rules, things cannot go infinitely fast. Physicists at the University of Bonn have now shown what the speed limit is for complex quantum operations. The study also involved scientists from MIT, the universities of Hamburg, Cologne and Padua and the Jülich Research Center. Among other things, the results are important for the realization of quantum computers. They are published in the prestigious magazine Physical overview X, and covered by the Physics Magazine of the American Physical Society.

Suppose you observe a waiter (the exclusion is already history) who has to serve a whole dish of champagne glasses on New Year’s Eve just a few minutes before midnight. He rushes fast from gas to gas. Thanks to his technique, perfected by many years of work, he still manages not to spill even a single drop of the precious liquid.

A little trick helps him do this: As the waiter speeds up his steps, he tilts the tray a little so the champagne doesn’t spill out of the glasses. Halfway to the table he tilts it in the opposite direction and slows down. Only when he has come to a complete stop does he keep it upright again.

Atoms are similar in some respects to champagne. It can be described as matter waves that do not act like a billiard ball, but more like a liquid. Anyone who wants to transport atoms from one place to another as quickly as possible must therefore be as skilled as the waiter on New Year’s Eve. “And even then, there is a speed limit that this transportation cannot exceed,” explains Dr. Andrea Alberti, who led this study at the Institute of Applied Physics at the University of Bonn.

Cesium atom as a champagne substitute

In their study, the researchers experimentally investigated exactly where this limit lies. They used a cesium atom as a champagne substitute and two laser beams that were placed perfectly on top of each other but as a tray facing each other. This superposition, called physicist interference, creates a standing wave of light: a series of mountains and valleys that initially do not move. “We loaded the atom into one of these valleys, and then set the standing wave in motion – it displaced the position of the valley itself,” says Alberti. “Our goal was to bring the atom to the target site in the shortest possible time without spilling it out of the valley, so to speak.”

The fact that there is a speed limit in the microcosm was theoretically demonstrated more than 60 years ago by two Soviet physicists, Leonid Mandelstam and Igor Tamm. They showed that the maximum velocity of a quantum process depends on the energy uncertainty, ie how “free” the manipulated particle is with respect to the possible energy states: the more energetic freedom it has, the faster it is. In the case of the transport of an atom, the deeper the valley in which the cesium atom is trapped, the more the energies of the quantum states in the valley disperse, and the faster the atom can be transported. Something similar can be seen in the waiter’s example: if he fills the glasses only half full (to the annoyance of the guests), he runs less risk of the champagne overflowing if he accelerates and slows down. However, the energetic freedom of a particle cannot be increased arbitrarily. “We can not make our valley infinitely deep – it will cost us too much energy,” Alberti emphasizes.

Radiate me, Scotty!

The speed limit of Mandelstam and Tamm is a fundamental limitation. However, one can only achieve this under certain conditions, namely in systems with only two quantum states. “In our case, it happens, for example, when the point of origin and destination are very close to each other,” the physicist explains. “Then the atomic waves of the atom overlap in both places, and the atom can be transported directly to its destination, that is, without intervals – almost like the teleportation in Star Trek’s Starship Enterprise.”

However, the situation is different as the distance grows to several tens of matter wavelengths as in the Bonn experiment. For these distances, direct teleportation is impossible. Instead, the particle must pass through several intermediate states to reach its final destination: the two-level system becomes a multi-level system. The study shows that a lower velocity limit applies to such processes than predicted by the two Soviet physicists: It is determined not only by the energy uncertainty, but also by the number of intermediate states. In this way, the work improves the theoretical understanding of complex quantum processes and their limitations.

The findings of the physicists are not only important for quantum computing. The calculations that are possible with quantum computers are mostly based on the manipulation of multilevel systems. However, quantum conditions are very fragile. It only lasts a short time, which physicists call coherence time. It is therefore important to pack as many computer operations as possible during this time. “Our study reveals the maximum number of operations we can perform in the coherence time,” Alberti explains. “It makes it possible to make the most of it.”