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: New research signals big future for quantum radar

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

New filter could advance terahertz data transmission

22 hours ago

University of Utah engineers have discovered a new approach for designing filters capable of separating different frequencies in the terahertz spectrum, the next generation of communications bandwidth that ...

The super-resolution revolution

23 hours ago

Cambridge scientists are part of a resolution revolution. Building powerful instruments that shatter the physical limits of optical microscopy, they are beginning to watch molecular processes as they happen, ...

Precision gas sensor could fit on a chip

Feb 27, 2015

Using their expertise in silicon optics, Cornell engineers have miniaturized a light source in the elusive mid-infrared (mid-IR) spectrum, effectively squeezing the capabilities of a large, tabletop laser onto a 1-millimeter ...

A new X-ray microscope for nanoscale imaging

Feb 27, 2015

Delivering the capability to image nanostructures and chemical reactions down to nanometer resolution requires a new class of x-ray microscope that can perform precision microscopy experiments using ultra-bright ...

New research signals big future for quantum radar

Feb 26, 2015

A prototype quantum radar that has the potential to detect objects which are invisible to conventional systems has been developed by an international research team led by a quantum information scientist at the University ...

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.

Please sign in to add a comment. Registration is free, and takes less than a minute. Read more

Click here to reset your password.
Sign in to get notified via email when new comments are made.