Chaos in a cold cloud of trapped ions.

Chaos in a cold cloud of trapped ions

In isolation, a cloud of magnesium ions, each carrying a positive charge, would push itself apart. But at sufficiently low temperatures and trapped in an electromagnetic field, such ions can settle into an orderly array -- a fragile, crystal-like structure in which the ions are many times farther apart than atoms in a crystal. Small changes in the strength or geometry of the confining, electromagnetic field or in the wavelength or intensify of the laser beams responsible for cooling the ions to less than a degree above absolute zero (SN: 7/23/88, p.52) readily shift the array back into disordered state.

Now researchers have turned up theoretical and experimental evidence suggesting that this phase transition from an ordered to a disordered state may be an example of a transition to chaos. In other words, the complicated motion of the ions in the disordered state, rather than being truly random and unpredictable, is deterministic. Describable by a set of equations, this type of motion is so sensitive to minute variations in local conditions that even neighboring particles follow rapidly diverging paths.

In the July 18 PHYSICAL REVIEW LETTERS, Richard G. Brewer of the IBM Almaden Research Center in San Jose, Calif., and his co-worekrs report the results of experiments on a pair of cooled, trapped barium ions and computer simulations of the equations governing their motion. By detecting the faint light given off by the ions, the researchers can actually see when the ions are essentially fixed in place and when they are moving chaotically. They can shift their two-ion system into a chaotic state simply by changing the radio-frequency voltage that defines the electromagnetic trap.

The results demonstrate the delicate interplay of the repulsive electrical forces between the ions, the confining electromagnetic field and the effects of the cooling laser beams, which leads to chaos. "I think this is a new way of studying chaos," Brewer says. "The complexity and the richness of phenomena that occur in chaos is so overwhelming that one could spend quite a bit of time both on the computer and in the laboratory trying to verify predictions. Here, we have one of the simplest systems possible: two particles in a potential well."

In the July 28 NATURE, Herbert Walther and his colleagues at the Max-Planck-Institut fur Quantenoptik in Garching, West Germany, report similar transitions among groups of from two to 100 magnesium ions. Their results show that the ordering of ions into a crystal-like structure takes place under somewhat different conditions from their breaking apart into a disordered cloud, an effect also seen in the IBM experiments. That observation is analogous to a situation in which a crystalline material melts and freezes at different temperatures.

David J. Wineland and his colleagues at the National Bureau of Standards in Boulder, Colo., have experimented with as many as 15,000 laser-cooled beryllium ions in a magnetic trap, as reported in the May 16 PHYSICAL REVIEW LETTERS. They, too, have seen transitions between disordered clouds of ions and more orderly structures. In this case, however, the ions appear to organize themselves into a number of concentric, spherical shells. The ions move about readily within or on a shell -- a liquid-like phase -- but rarely diffuse from one shell to another.

"The study of simple phase-transition dynamics in clouds of trapped ions will allow non-equilibrium statistical mechanics to be investigated directly with relatively few particles," Peter Knight and Richard Thompson of the Imperial College of Science and Technology in London comment in the July 28 NATURE. "Indeed, the changing nature of the transition as the number of particles increases offers new insights for correlated statistical systems."