At the level of atoms, our definition of chaos has run into a problem.
Chaos is usually defined by a system’s movement: Set a pendulum swinging, track exactly where it goes, and its motion will reveal whether it is chaotic. Atoms, however, are governed by the uncertainty principle, which means that their location cannot be known precisely. What’s more, the laws of quantum mechanics say that hypersensitivity to initial conditions, which is considered the primary characteristic of a chaotic system, is physically impossible for atoms—at least in the way it’s understood at the classical level.
This presents a serious quandary because quantum mechanics is considered the most basic set of universal laws. Chaos must have some connection with the quantum level, but how it manifests itself, or how to quantify it, has thus far eluded physicists. Work published recently in Nature helps shed light on this problem as researchers working with cooled atoms searched for what they call signatures of chaos.
If such hypersensitivity to initial conditions cannot happen in a quantum system, other red flags of classical chaos might still be detectable. This could indicate that chaos in some form could exist at the level of atoms, or, at the very least, would imply a connection between quantum events and classical chaos. “Though you will never be able to find hypersensitivity to initial conditions in the quantum system, you are able to tell if the outward signs produced by classical chaotic systems are the same in quantum systems,” says Poul Jessen of Arizona State University, the lead researcher on the Nature paper.
In order to see these signatures, physicists have taken the conditions that cause chaotic behavior in human-scale systems and applied them on the atomic level. Jessen and his collaborators recently succeeded in making a quantum “kicked top” out of cesium atoms for the first time.
Kicked tops are an excellent example of chaotic systems when it comes to classic physics. You start an object twirling—say, a gyroscope—and then give it a series of kicks and twists as it spins. The initial condition that decides whether a gyroscope moves stably or chaotically is the direction of its axis when it starts spinning.
In order to visualize the gyroscope’s behaviour, the different values of its angular momentum are plotted on the surface of a globe. Some initial orientations of its axis cause the momentum to swerve in a “chaotic sea,” covering most of the surface of the globe. But other orientations cause the spin to settle into stable, regular motion in one of three main “islands” in the sea.
In their experiment, researchers substituted atoms for gyroscopes and looked at how angular momenta affected the atoms’ quantum states. What they found was intriguing: Some spins of the quantum top locked the atoms into a stable set of islands, while other values let the atoms’ quantum states wander erratically.
The number and location of the islands, when plotted, corresponded eerily to the classical model. So while the atoms’ behavior could not technically be called chaotic because they cannot show hypersensitivity, they mimicked the evolution of the classical, chaotic system almost exactly. Other measurements indicated that the system might have some sensitivity to disturbances, another interesting link to chaotic behaviour.
These observations alone provided good evidence that something related to chaos was happening. But the most fascinating result was that one of the strangest properties of atoms, entanglement, shot up in areas corresponding to the chaotic sea. When two quantum-scale objects, like atoms or nuclei, are entangled, performing an action on one instantaneously affects the other even if vast distances separate the entangled objects. Einstein famously called entanglement “spooky action at a distance,” and it forms the basis of modern attempts to built quantum computers.
Could entanglement be a signature of chaos?
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