Lower Speed Limit Also Applies to Complex Quantum Processes

Even in the realm of the tiniest particles with their own unique rules, things cannot continue extremely fast. Now, physicists from the University of Bonn have demonstrated the extent of the speed limit for complicated quantum operations.

Researchers from the Massachusetts Institute of Technology (MIT), the universities of Hamburg, Cologne and Padua, and the Jülich Research Center also participated in the new study. The outcomes are significant for realizing quantum computers, among many other things.

The study results have been published in the leading Physical Review X journal and covered by the Physics Magazine of the American Physical Society.

For example, one can imagine a waiter who, on New Year’s Eve, is required to serve a tray full of champagne glasses only a few minutes before midnight.

The waiter rushes from one guest to another at an extreme pace. Due to his method, perfected over several years of work, he somehow makes sure that even a single drop of the valuable liquid is not spilled on the floor.

A small trick helps the waiter to achieve this: While he speeds up his steps, he slightly tilts the tray so that the champagne does not fall from the glasses. But halfway to the table, he tilts the tray in the reverse direction and slows down his speed, and then holds the tray upright again only when he comes to a complete stop.

In some ways, atoms are analogous to champagne. They can be defined as waves of matter, which act more like a liquid and not like a billiard ball. Therefore, anyone who wishes to transport atoms from one location to another as rapidly as possible should be as dexterous as the waiter on New Year’s Eve.

“And even then, there is a speed limit that this transport cannot exceed,” explained Dr Andrea Alberti, who headed the new study at the Institute of Applied Physics of the University of Bonn.

Cesium Atom as a Champagne Substitute

In their analysis, the investigators experimentally studied where exactly this limitation lies. They utilized a cesium atom as a champagne substitute as well as a couple of laser beams that were perfectly superimposed but directed against one another as a tray.

This kind of superposition, known as interference by physicists, produces a standing wave of light—a series of valleys and mountains that are initially immobile.

We loaded the atom into one of these valleys, and then set the standing wave in motion—this displaced the position of the valley itself. Our goal was to get the atom to the target location in the shortest possible time without it spilling out of the valley, so to speak.

Dr Andrea Alberti, Study Lead, Institute of Applied Physics, University of Bonn

There is a speed limit in the microcosm and this fact was already hypothetically shown by two Soviet physicists, Leonid Mandelstam and Igor Tamm, over six decades ago.

The duo demonstrated that the highest speed of a quantum process relies on the energy uncertainty, that is, how 'free' the exploited particle is with regard to its potential energy states—if the particle has more energetic freedom, it will be relatively faster.

With regard to the transport of an atom, for instance, if the valley in which the cesium atom is confined turns out to be deeper, then the energies of the quantum states in the valley will spread more, and the atom will be ultimately transported faster.

An analogous phenomenon can be observed in the example of the waiter: If he happens to fill the glasses just half full (to the annoyance of the guests), he faces less risk of spilling the champagne over as he decelerates and accelerates. But the energetic freedom of a particle cannot be increased randomly.

“We can’t make our valley infinitely deep—it would cost us too much energy,” emphasized Alberti.

Beam Me Up, Scotty!

The speed limit of both Mandelstam and Tamm is an underlying limit. But one can only reach it under specific situations, such as in systems that have just a couple of quantum states.

In our case, for example, this happens when the point of origin and destination are very close to each other. Then the matter waves of the atom at both locations overlap, and the atom could be transported directly to its destination in one go, that is, without any stops in between—almost like the teleportation in the Starship Enterprise of Star Trek.

Dr Andrea Alberti, Study Lead, Institute of Applied Physics, University of Bonn

But the scenario is different when the distance increases to many dozens of matter-wave widths as in the case of the Bonn experiment. However, direct teleportation is not possible for such distances.

Rather, the particle should undergo many intermediate states to reach its last destination—that is, the two-level system turns out to be a multi-level system.

The new study demonstrates that a lower speed limit is relevant to these processes than that estimated by the two Soviet physicists: It is established both by the energy uncertainty and the number of intermediate states. In this manner, the study enhances the theoretical interpretation of intricate quantum processes and their limitations.

The discoveries made by the physicists are significant not just for quantum computing. The computations that are viable with quantum computers are largely based on the exploitation of multi-level systems.

But quantum states are highly delicate and last only a brief lapse of time, which physicists refer to as coherence time. Hence, it is vital to pack as many computational operations as possible into this time.

Our study reveals the maximum number of operations we can perform in the coherence time. This makes it possible to make optimal use of it.

Dr Andrea Alberti, Study Lead, Institute of Applied Physics, University of Bonn

Funding

The research work was financially supported by the German Research Foundation (DFG) as part of the Collaborative Research Center SFB/TR 185 OSCAR. Financially support was also provided by the Reinhard Frank Foundation in association with the German Technion Society, and by the German Academic Exchange Service.

Journal Reference:

Lam, M. R., et al. (2021). Demonstration of Quantum Brachistochrones between Distant States of an Atom; Physical Review X. doi.org/10.1103/PhysRevX.11.011035.