First evidence of chaos in the quantum world

Experiments reveal long-sought "fingerprinting" chaotic behavior in a quantum system

Snapshot of the cesium spin state after 40 cycles © Poul Jessen
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For the first time, researchers have demonstrated the "fingerprints" of classical chaos in the quantum world as well. The experiment with cesium atoms, now described in "Nature", represents the long sought proof for the existence of this phenomenon in both classical and quantum physics.

In the world we experience on a daily basis, chaos sometimes seems to be the rule rather than the exception. In fact, chaotic systems play a decisive and influential role, for example, in weather and climate, but also in neural networks or on the stock market. These systems are so complex that tiny triggers such as the famous "wingbeat of a butterfly" can have unpredictable effects. So far, all this has only been true in the world of classical physics. Whether there is such a classic chaos in the realm of the smallest particles, quantum physics, was previously unknown.

The problem: The quantum world is dominated by uncertainties: An atom can behave here both as a wave and as a particle. However, this requires that its position and speed can not be determined simultaneously without changing them. And that's the problem: if the starting point of a quantum particle is not known, it is also not possible to determine whether it reacts to disturbances according to the conditions of classic chaos.

Spin of a cesium atom as a test system

Now, scientists around Poul Jessen, a professor of quantum physics at the University of Arizona, have done a series of experiments that show that classical chaos "spills over" into the quantum world. As a basis, they used a quantum system that was supposed to imitate the textbook example of chaos, the so-called "kicked-top" or magnetic pendulum. The scientists manipulated the spin of individual laser-cooled cesium atoms.

"Think of it as a microscopic magnetic pendulum rotating at a constant speed around its axis, " explains Jessen. Instead of the magnets, which normally disturb the pendulum and induce chaotic movements, the researchers changed the spin axis of the atom in a series of magnetic "kicks" and "spins" by laser light. At the end of each manipulation cycle, they quantified the quantum state of atom spin using a kind of tomographic technique. In principle, they received individual shots and stop-motion films showing how the spinning atom behaved. display

Commuting between stability and chaos

And, surprisingly, the spin of the atom apparently followed the same boundaries between stability and chaos that characterize the macroscopic experiment: it was dynamically stable in the same regions and dynamically unpredictable in others. The quantum system remained unrestricted in the stable phases, but confined in the chaotic. For researchers, this is the first clear "fingerprint" of classical chaos in the realm of quantum mechanics.

A limitation in quantum physics is a state in which two spatially separated particles are influenced by the state of each other via a kind of "ghostly long-range effect", as Albert Einstein called it. For example, if you change the polarization of a photon in such a pair of distorted particles, those of the other will also flip over.

(University of Arizona, 09.10.2009 - NPO)