FAYETTEVILLE, Ark. - A University of Arkansas physicist has discovered a "quantum fractal" pattern - with unforeseen mathematical capabilities - that results when you "squeeze" the spatial uncertainty of a quantum wave. This space-time interference pattern repeats itself at discrete intervals, creating a sub-atomic quantum counter that could potentially be used in quantum computers. Researchers speculate that these quantum computers some day might be able to quickly perform calculations thousands of times faster than classical computers.

These quantum devices that William G. Harter, professor of physics, found also automatically calculate all prime factors of any integer for which they are "wired."

Harterreports his findings in an upcoming issue of Physical Review A and will also make a presentation of the work at the International Symposium on Molecular Physics, June 11-16, at Ohio State University.

"The wave has a code for every rational number in its repertoire," Harter said.

The key to Harter’s quantum counter comes from forcing quantum systems such as light to choose between their wave-like and particle-like behavior, by squeezing the spatial uncertainty to make the system as much like a particle as possible. This causes a tiny explosion, a kind of nanoscopic "big bang," due to the Heisenberg uncertainty relation.

Using computer graphics, Harter simulated the "tiny pop," as he sometimes calls it, and examined the quantum debris and fragments produced by the reverberating wave. What emerged was a pattern reminiscent of chaos and fractal structure seen in well-known classical mechanical theories of the past 20 years.

Careful examination showed how this "quantum chaos" differed from classical chaos; instead of being like a street riot, it was more like an intricate ballet performance full of symmetry.

The wave-like behavior of the particle in such a system creates the sloshing or periodic fluctuations called "quantum revivals," with different wave patterns taking turns leaping up together.

"Each revival is unique and can be read like numbers on a digital clock," Harter said. "Where the wave is not provides important quantum clues." Harter has shown that the wave patterns do a form of group theory, a type of mathematics related to number theory and algebra.

These "quantum revivals" could be used in series or in parallel, and Harter speculates that they could be used, for instance, to make binary to decimal conversions and for other mathematical tasks.

Harter also said that this behavior is possible in a number of physical systems ranging from polarized photons in optical fibers to electrons in quantum dots or even spinning molecules.

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