# Synopsis: Chaos at the nanoscale

#### Nonlinear dynamics and chaos in two coupled nanomechanical resonators

R. B. Karabalin, M. C. Cross, and M. L. Roukes

Published April 13, 2009

The miniaturization of electromechanical devices to nanometer scales is an ongoing endeavor that could lead to exceptionally sensitive sensors and other applications. A challenge in this effort is the large-scale integration of these devices, which will require understanding the effects of interactions between them.

In an article appearing in Physical Review B, Rassul Karabalin, Michael Cross, and Michael Roukes at the California Institute of Technology, demonstrate and study complex nonlinear behavior in a nanoelectromechanical system consisting of two mechanically coupled beams, each 6$\mu$m long. The beams are clamped on both ends and can be driven independently with a high degree of control while their displacements are detected using laser interferometry.

The beams exhibit both a linear response and more complex chaotic dynamics that can be described by coupled nonlinear equations of motion. An interesting finding is that the range of amplitudes over which one oscillating beam has a linear response can be extended by appropriately driving the second one, which increases each device’s range of practical usefulness. In addition, Karabalin et al. observe a particular kind of coupling between modes that may be useful for carrying out quantum measurements using nanomechanical systems. – Alex Klironomos