The 'butterfly effect' has now been seen at the quantum level. Credit: Millard H. Sharp / Science Photo Library

A hidden partnership between two of the hottest topics in physics — quantum entanglement and chaos theory — may have been uncovered by a series of ingenious experiments with caesium atoms. The relationship could provide clues about where the quantum realm ends and the classical world begins.

Chaos theory describes how the slightest change in the starting conditions of a system can have dramatic effects on how it develops. It's usually explained using the 'butterfly effect', in which the atmospheric changes caused by the beating of a butterfly's wings in one location could eventually lead to the production of a tornado in another. Chaos is usually thought to be a large-scale phenomenon, associated with classical physics and absent from the microscopic quantum realm.

But now Poul Jessen, at the University of Arizona in Tucson, and his colleagues have found the fingerprints of chaos in a quantum system. Their discovery links chaos to entanglement — the purely quantum property in which multiple particles can become inextricably intertwined, so that making changes to one instantly affects its partners.

"They've brought together two sexy concepts in physics that are usually thought to operate in completely different regimes," says optical physicist Nir Davidson at the Weizmann Institute of Science in Rehovot, Israel. "That is surprising and interesting."

Quantum kick

Jessen's team searched for signs of chaos within a set of cooled caesium atoms, using them as the quantum equivalent of an everyday object that displays chaotic behaviour — a child's spinning top. Just as the axis of the spinning top changes direction and can wobble wildly if it is nudged, each caesium atom can be characterized by an internal quantum property known as spin — the direction of which will change if it is 'kicked' by applying pulses of a magnetic field. The goal was to see if kicking this 'quantum top' caused the spin to change direction chaotically.

They've brought together two sexy concepts in physics that are usually thought to operate in completely different regimes. Nir Davidson , Weizmann Institute of Science

According to the team's calculations, if the quantum top behaved like a classical top, then kicking it should produce two possible outcomes depending on the initial direction of its spin. If the top's initial spin direction lay in one of three subsets of possible directions — dubbed islands of stability — each successive kick would knock the spin in a regular way, sending it around a stable orbit within that island. If, however, the initial spin direction lay outside these islands, in the 'chaotic sea', the spin should jump around rapidly and unpredictably.

When they did the experiment, they found almost exactly that behaviour — if the quantum top started out in an island of stability, its spin changed in a regular way, but if not, chaos ruled and its spin direction changed quickly and erratically. "It looks like the quantum system knows about classical boundaries and respects them," says Jessen.

Physicist Fritz Haake of Duisburg-Essen University, Germany, was one of the first to propose that chaotic signatures might show up in a quantum top, and admires the experimental achievement. "It has taken both ingenuity and advances in technology to demonstrate quantum chaos this way," he says.

Tangled up

Having seen chaotic behaviour, Jessen's team then explored its possible ties to entanglement. Caesium atoms contain electrons that orbit a nucleus, and it is possible for the direction of an electron's spin to become entangled with that of the nucleus's spin. The team began their experiment with a set of atoms that did not display this kind of entanglement and then checked whether kicking the atoms would provoke the electron and nuclear spins to entangle.

"We found that atoms starting out in one of the islands of stability remained unentangled, but for those that started out in the chaotic sea, the electron and nuclear spins rapidly became entangled," says Jessen. "This suggests that chaos may have some fundamental connection to entanglement." The work is published in this week's Nature1.

The finding has implications for building quantum computers that, in principle, work by closely controlling the entanglement of atomic spins. "This underscores how hypersensitive quantum systems are to slight perturbations," says Jessen. "You really have to worry about how easily errors can be generated — which, of course, those trying to build [such systems] have already seen."

The result also touches on a fundamental question in physics: where does the exotic quantum realm end and the familiar classical world begin? The study supports long-standing ideas that there is no single sharp boundary between the quantum and classical worlds, says quantum physicist Wojciech Zurek of the Los Alamos National Laboratory in New Mexico. "The obvious thing to do now is to look at which classical features emerge first and which quantum features last longest," he says.

Jessen and his team hope to investigate how larger quantum systems blend into the classical regime. "It's a challenge," says Jessen. "But we're taking our first baby steps in that direction."