Synopsis: Doing sums with swirls

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Doing Arithmetic With Nonlinear Acoustic Vortices

Régis Marchiano and Jean-Louis Thomas

Published August 4, 2008

Calculating minds have employed a wide variety of objects to carry out computations, from stones and fingers, to electrons, strands of DNA, and recently quantum states and spintronics. Essentially anything that can represent numbers can be used to do arithmetic, but it helps if the object is robust—that is, the numbers shouldn’t change in the presence of noise or environmental contact (which is what makes quantum computing so difficult). Even better would be a system that goes beyond binary (two-level) logic computations to multilevel logic that might carry more information.

In Physical Review Letters, Régis Marchiano and Jean-Louis Thomas of the Université Pierre et Marie Curie report on their efforts to use vortices as computational elements. Vortices can be screw dislocations in a material, acoustic waves, or swirls in a liquid, but they always possess a topological “charge” related to the phase or winding number (similar to the number of times you would revolve around the axis while climbing a spiral staircase). Such vortices exist in acoustic or optical systems in both linear and nonlinear media, so there are many opportunities for creating and controlling them.

The researchers created vortices in water tanks with arrays of piezoelectric transducers and measured the pressure fields at the end of the tank using a tiny hydrophone. By creating vortices with different acoustic frequencies, and allowing these vortices to mix, they found that the resulting “output” vortex represented the sums and differences of the original topological charges. The vortices are not only resistant to changes in topological charge caused by perturbations but the charge can occur in integer multiples of 2π, rather than only two conventional binary values of 0 and 1. Although a useful computational device is unlikely to emerge from this work soon, it suggests a different way to add and subtract. – David Voss

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