How long does a tuning fork ring? 'Quantum-mechanics' solve a very classical problem

Mar 08, 2011
Researchers at the University of Vienna and the Technische Universitaet Muenchen have solved a long-standing problem in the design of mechanical resonators: the numerical prediction of the design-limited damping. The electron microscopic picture shows one of their micro resonators with which they proved the performance of their calculations. Credit: Garrett Cole, University Vienna

Austrian and German researchers at the University of Vienna and Technische Universitaet Muenchen have solved a long-standing problem in the design of mechanical resonators: the numerical prediction of the design-limited damping. They report their achievement, which has a broad impact on diverse fields, in the forthcoming issue of Nature Communications. The article describes both a numerical method to calculate the mechanical damping as well as a stringent test of its performance on a set of mechanical microstructures.

From the wooden bars in a xylophone or the head of a drum, to the strings and sound box of a guitar or violin, musical instruments are the most familiar examples of mechanical resonators. The actual of these instruments create that we hear as sound. The purity of the emitted tone is intimately related to the decay of the vibration amplitude, that is, the mechanical losses of the system. A figure of merit for mechanical losses is the quality factor, simply called "Q", which describes the number of oscillations before the amplitude has decayed to a minute fraction of its starting value. The larger Q, the purer the tone and the longer the system will vibrate before the sound damps out.

In addition to the aesthetic examples found in a concert hall, mechanical resonators have become increasingly important for a wide variety of advanced technological applications, with such diverse uses as filtering elements in wireless communications systems, timing oscillators for commercial electronics, and cutting-edge research tools which include advanced and emerging quantum electro- and optomechanical devices. Rather than producing pleasing acoustics, these applications rely on very "pure" vibrations for isolating a desired signal or for monitoring minute frequency shifts in order to probe external stimuli.

For many of these applications it is necessary to minimize the mechanical loss. However, it had previously remained a challenge to make numerical predictions of the attainable Q for even relatively straightforward geometries. Researchers from Vienna and Munich have now overcome this hurdle by developing a finite-element-based numerical solver that is capable of predicting the design-limited damping of almost arbitrary mechanical resonators. "We calculate how elementary mechanical excitations, or phonons, radiate from the into the supports of the device", says Garrett Cole, Senior Researcher in the Aspelmeyer group at the University of Vienna. "This represents a significant breakthrough in the design of such devices."

The idea goes back to a previous work by Ignacio Wilson-Rae, physicist at the Technische Universitaet Muenchen. In collaboration with the Vienna group the team managed to come up with a numerical solution to compute this radiation in a simple manner that works on any standard PC. The predictive power of the numerical Q-solver removes the guesswork that is currently involved (e.g., trial and error prototype fabrication) in the design of resonant mechanical structures. The researchers point out that their "Q-solver" is scale independent and thus can be applied to a wide range of scenarios, from nanoscale devices all the way up to macroscopic systems.

Explore further: Scientists find way to maintain quantum entanglement in amplified signals

More information: Phonon-tunnelling dissipation in mechanical resonators, Garrett D. Cole, Ignacio Wilson-Rae, Katharina Werbach, Michael R. Vanner, Markus Aspelmeyer, Nature Communications, 8 March, 2011, DOI: DoI: 10.1038/ncomms1212

Provided by Technische Universitaet Muenchen

4.2 /5 (5 votes)

Related Stories

Recommended for you

Exotic state of matter propels quantum computing theory

Jul 23, 2014

So far it exists mainly in theory, but if invented, the large-scale quantum computer would change computing forever. Rather than the classical data-encoding method using binary digits, a quantum computer would process information ...

Quantum leap in lasers brightens future for quantum computing

Jul 22, 2014

Dartmouth scientists and their colleagues have devised a breakthrough laser that uses a single artificial atom to generate and emit particles of light. The laser may play a crucial role in the development of quantum computers, ...

Boosting the force of empty space

Jul 22, 2014

Vacuum fluctuations may be among the most counter-intuitive phenomena of quantum physics. Theorists from the Weizmann Institute (Rehovot, Israel) and the Vienna University of Technology propose a way to amplify ...

User comments : 1

Adjust slider to filter visible comments by rank

Display comments: newest first

deepsand
1.7 / 5 (6) Mar 09, 2011
Title reads "'Quantum-mechanics' solve a very classical problem."

Nowhere in the article is such stated.