A speed limit also applies to the quantum world

Even in the world of the smallest particles with their own special rules, things cannot happen 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, from the universities of Hamburg, Cologne and Padua, and from the Jülich Research Center. The results are important for the realization of quantum computers, among other things. They are published in the prestigious magazine. Physical Review X, and covered by the Physics Magazine of the American Physical Society.

Suppose you watch a waiter (the block is history) who on New Year’s Eve has to serve an entire tray of glasses of champagne just minutes before midnight. He runs from guest to guest at high speed. Thanks to his technique, perfected over many years of work, however, he manages not to spill 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 that the champagne doesn’t run out of the glasses. Halfway to the table, he tilts it in the opposite direction and slows down. Only when he stops completely does he hold him again.

Atoms are, in some ways, similar to champagne. They can be described as waves of matter, which behave not 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 yet, there is a speed limit that this transport cannot exceed”, explains Dr. Andrea Alberti, who conducted this study at the Institute of Applied Physics at the University of Bonn.

Cesium atom as a substitute for champagne

In their study, the researchers investigated experimentally exactly where that limit is. They used a cesium atom as a substitute for champagne and two laser beams perfectly overlapping, but directed against each other like a tray. This overlap, called interference by physicists, creates a standing wave of light: a sequence of mountains and valleys that initially do not move. “We charge the atom in one of these valleys and then put the stationary wave in motion – this has shifted the position of the valley itself,” says Alberti. “Our goal was to get the atom to its destination in the shortest possible time, without it spreading out of the valley, so to speak.”

The fact that there is a speed limit in the microcosm has already been theoretically demonstrated by two Soviet physicists, Leonid Mandelstam and Igor Tamm, more than 60 years ago. They showed that the maximum speed of a quantum process depends on the energy uncertainty, that is, how “free” the manipulated particle is in relation to its possible energy states: the more energy freedom it has, the faster it is. In the case of the transport of an atom, for example, the deeper the valley in which the cesium atom is trapped, the more scattered are the energies of the quantum states in the valley and, ultimately, the faster the atom can be transported. Something similar can be seen in the waiter’s example: If he only refills the glasses in half (much to the guests’ dismay), he is less at risk of the champagne spilling as he speeds up and slows down. However, the energy freedom of a particle cannot be increased arbitrarily. “We cannot make our valley infinitely deep – that would cost us a lot of energy”, emphasizes Alberti.

Radiate me, Scotty!

The speed limit of Mandelstam and Tamm is a fundamental limit. However, it can only be achieved in certain circumstances, namely in systems with only two quantum states. “In our case, for example, this happens when the point of origin and destination are very close to each other”, explains the physicist. “So the atom’s matter waves at both locations overlap, and the atom could be transported directly to its destination at once, that is, without any stops in between – almost like teleportation on the Star Trek Enterprise spacecraft. . “

However, the situation is different when the distance increases to several dozen wavelengths of matter, 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 speed limit lower than that predicted by the two Soviet physicists applies to such processes: 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 restrictions.

Physicists’ findings are important not only for quantum computing. The possible calculations with quantum computers are mainly based on the manipulation of multi-level systems. Quantum states are very fragile, however. They only last a short time, which physicists call coherence time. Therefore, it is important to package as many computational operations as possible at this time. “Our study reveals the maximum number of operations that we can carry out in the coherence time”, explains Alberti. “This makes it possible to make optimal use of it.”