The study from the University of Bonn determines the minimum time for complex quantum operations.
Even in the world of smaller particles with their own special rules, things cannot go on indefinitely 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 with, the universities of Hamburg, Cologne and Padua and the Jülich Research Center. The results are important for the realization of quantum computers, among others. They are published in the prestigious journal Physical Review X, and are covered by the Journal of Physics of the American Physical Society.
Suppose you are watching a waiter (jam is already history) who on New Year’s Eve has to serve a whole tray of champagne glasses just minutes before midnight. He rushes from guest to guest at maximum speed. Thanks to his technique, perfect for many years of work, he nevertheless manages not to spill even a drop of precious liquid.
A little trick helps him to do this: As the waiter speeds up his steps, he tilts the tray slightly so that the champagne does not spill out of the glasses. Halfway to the table, he tilts it in the opposite direction and slows down. Only when he has stopped completely does he keep him back on his feet.
Atoms are in some ways similar to champagne. They can be described as waves of matter, which do not behave like a billiard ball, but more like a liquid. Anyone who wants to transport atoms from one place to another as soon as possible should be as skilled as the waiter on New Year’s Eve. “And even then, there is a speed limit that this transport cannot cross,” explains Dr. Andrea Alberti, who led this study at the Institute of Applied Physics of the University of Bonn.
Cesium atom as a substitute for champagne
In their study, researchers experimentally investigated exactly where this boundary lies. They used a cesium atom as a substitute for champagne and two laser beams perfectly superimposed but directed against each other like a tray. This superposition, called interference by physicists, creates a standing wave of light: a sequence of mountains and valleys that do not initially move. “We loaded the atom into one of these valleys and then put the wave on its feet – that shifted the position of the valley itself,” says Albert. “Our goal was to get the atom to the target site in the shortest time possible without spilling out of the valley, so to speak.”
The fact that there is a speed limit in the microcosm was already theoretically demonstrated by two Soviet physicists, Leonid Mandelstam and Igor Tamm more than 60 years ago. They showed that the maximum velocity of a quantum process depends on energy uncertainty, i.e., how “free” the manipulated particle is in relation to its potential energy states: the more energetic freedom it has, the faster it is . In the case of transporting an atom, for example, the deeper the valley into which the cesium atom is trapped, the more the energies of the quantum states in the valley propagate, and ultimately the faster the atom can be transported. Something similar can be seen in the waiter’s example: If he only fills the glasses half full (to the annoyance of the guests), he runs less risk of the champagne spilling as 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 would cost us a lot of energy,” Alberti points out.
Beam me, Scotty!
The speed limit of Mandelstam and Tamm is a basic limit. However, one can achieve it only in certain circumstances, namely in systems with only two quantum states. “In our case, for example, this happens when the point of origin and the destination are very close to each other,” explains the physicist. “Then the waves of atomic matter in both places overlap, and the atom can be transported directly to its destination with one motion, that is, without any stop in between – almost like teleporting to the Starship Enterprise of Star Trek.”
However, the situation is different when the distance increases to several tens of wavelengths of matter as in Bonn’s experiment. For these distances, direct teleportation is impossible. Instead, the particle must go through several intermediate states to reach its final destination: The two-tier system becomes a multi-tier system. The study shows that a lower speed limit applies to such processes than that predicted by two Soviet physicists: It is determined not only by 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 constraints.
The findings of physicists are important, not so much for quantum computing. The calculations that are possible with quantum computers are mainly based on the manipulation of multi-level systems. However, quantum states are very fragile. They last only a short waste of time, which physicists call coherence time. It is therefore important to pack as many computing operations as possible at this time. “Our study reveals the maximum number of operations we can perform at the time of coherence,” explains Albert. “It enables its optimal use.”
Reference: “Demonstration of the Brachistochrones Quantum between Distant States of an Atom” by Manolo R. Lam, Natalie Peter, Thorsten Groh, Wolfgang Alt, Carsten Robens, Dieter Meschede, Antonio Negretti, Simone Montangero, Tommaso Calarco and Andrea Alberti, 19 February 2021, Physical Review X.
DOI: 10.1103 / PhysRevX.11.011035
The study was funded by the German Research Foundation (DFG) as part of the SFB / TR 185 OSCAR Research Cooperation Center. Funding was also provided by the Reinhard Frank Foundation in collaboration with the German Technical Society and the German Academic Exchange Service.