Quantum World Also Have A Speed Limit

New research from the University of Bonn has shown a speed limit in the quantum world. The study also involved scientists from MIT, the Universities of Hamburg, Cologne and Padua, and the Jülich Research Center.

Let’s see this from an example. When you observe a server who is about to serve an entire tray of champagne glasses, you see he manages to not spill even a single drop, thanks to his technique, learnt over years of work.  

With a little more observation, we find the trick is to tilt the tray slightly so that the champagne doesn’t spill out. Halfway to the table, he tilts it in the opposite direction and slows down and he holds it upright again only when he has stopped.  

We know atoms can be described as waves of matter Thus when one wants to transport atoms from one place to another as quickly as possible must be as skilful as the server.

Dr Andrea Alberti, who led this study at the Institute of Applied Physics of the University of Bonn, said that there was a limit to this speed.  

The study was focused on finding this limit. Caesium atom was used in the research.

Two two laser beams were perfectly superimposed but directed against each other as a tray. The Interference (superimposition) creates a standing wave of light: a sequence of mountains and valleys that initially do not move.

Alberti explained the atom was loaded into one of these valleys and then the standing wave motion was started. This displaced the position of the valley itself. This was done to get the atom to the target location in the shortest possible time without it spilling out of the valley. 

Over 60 years ago, two Soviet physicists, Leonid Mandelstam and Igor Tamm, theoretically proved there was a speed limit in the microcosm. They showed that the maximum speed of a quantum process depends on the energy uncertainty, i.e., how “free” the manipulated particle is regarding its potential energy states: the more energetic freedom it has, the faster it is.

The speed of transportation depended on the depth of the valley. (Depth increase means more spread of the energies of quantum states in the valley). If the server fills the glasses half full, he runs a less risk that the champagne spills over as he speeds up and decelerates. But it isn’t the case of a particle, as it costs too much energy for making the valley infinitely deep.  

The speed limit of Mandelstam and Tamm is a fundamental limit that can be reached under certain circumstances, in systems with only two quantum states.

In the experiment, it happens when the point of origin and destination are very close to each other. As a result, we could do something like teleportation, 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. 

For large distance like the one in the experiment, it is impossible for teleportation. The particle goes through many intermediate states to reach the final destination, turning the two-level system into a multi-level system. The study shows that a lower speed limit applies to such processes than that predicted by the two Soviet physicists: It is determined not only by the energy uncertainty but also by the number of intermediate states.  

The computations that are possible with quantum computers are mostly based on the manipulation of multi-level systems. They last only a short lapse of time, which physicists call coherence time as the quantum states are fragile. The study reveals the maximum number of operations we can perform in the coherence time.

Journal Reference:
Manolo R. Lam, Natalie Peter, Thorsten Groh, Wolfgang Alt, Carsten Robens, Dieter Meschede, Antonio Negretti, Simone Montangero, Tommaso Calarco, Andrea Alberti. Demonstration of Quantum Brachistochrones between Distant States of an Atom. Physical Review X, 2021; 11 (1) DOI: 10.1103/PhysRevX.11.011035