Physicists from the University of Bonn, together with scientists from the Massachusetts Institute of Technology (MIT), the Julich Research Center, the universities of Hamburg, Cologne and Padua, have found that speed limits exist for complex quantum operations. The results of the joint work were published in the Physics Magazine of the American Physical Society.
Experts from the University of Bonn explained the principle of the new experiment with a simple example. Let’s say you’re watching a waiter who has to serve a whole tray of champagne on New Year’s Eve just a few minutes before midnight. It rushes from guest to guest at maximum speed. Thanks to the technique worked out over many years of work, he still manages not to spill a drop of the drink.
A little trick helps him in this: while the waiter speeds up his steps, he slightly tilts the tray so that the champagne does not pour out of the glasses. Halfway to the table, he tilts it in the opposite direction and slows down. Only when it comes to a complete stop does it hold it upright again.
Atoms are somewhat like champagne. They can be described as waves of matter that do not behave like a billiard ball, but like a liquid. So anyone who wants to move atoms from one place to another as quickly as possible has to be as skillful as a waiter on New Year’s Eve. “And even then there is a speed limit,” explains Dr. Andrea Alberti, who led the study at the Institute of Applied Physics at the University of Bonn.
In their study, scientists experimentally found out exactly where this limit is. They used a cesium atom as a substitute for champagne and two laser beams perfectly superimposed on each other, but directed against each other. This superposition, which physicists call interference, creates a standing wave of light: like a sequence of “mountains” and “valleys” that initially do not move. “We loaded an atom into one of these valleys and then set in motion a standing wave — that shifted the position of the valley itself,” Alberti explains. “Our goal was to get the atom to the right place in the shortest possible time, without splashing it out of the valley.”
The fact that there is a speed limit in the microcosm was 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 uncertainty of energy. In fact, it depends on how “free” the controlled particle is in relation to its possible energy states: the more energy freedom it has, the faster it is. In the case of atom transfer, for example, the deeper the “valley” in which the cesium atom is trapped, the greater the spread of the energies of quantum states in the valley and, ultimately, the faster it can be transferred. Something similar can be seen in the example of a waiter: if he only fills his glasses halfway, he is less likely to spill champagne when accelerating and decelerating. However, the energy freedom of a particle cannot be increased arbitrarily. “We cannot make our ‘valley’ infinitely deep – it would take too much energy,” emphasizes Alberti.
The speed limit for Mandelstam and Tamm is a fundamental limitation. However, this can be achieved only under certain circumstances, namely, in systems with only two quantum states. “In our case, for example, this happens when the origin and destination are very close to each other,” explains the woman physicist. “Then the material waves of the atom overlap in both places, and the atom can be delivered directly to its destination in one go, that is, without any intermediate stops.”
However, the situation changes when the distance increases to several tens of values of the width of the matter wave, as in the Bonn experiment. Direct teleportation is impossible at these distances. Instead, the particle must go through several intermediate states in order to reach its final destination: the two-level system becomes multi-level. The study shows that a lower speed limit applies to such processes than the two Soviet physicists predicted. The point is that it is determined not only by the uncertainty of energy, but also by the number of intermediate states. Thus, the new work improves the theoretical understanding of complex quantum processes and their limitations.
Physicists’ findings are important not least for quantum computing. The computations that are possible with quantum computers are mainly based on the manipulation of multilevel systems. However, quantum states are very fragile. They last only a short period of time – the time of coherence. The new study reveals the maximum number of operations scientists can perform during the consistency time. This allows it to be used optimally.