Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Researchers hear the sound of quantum drums

12.02.2008
Forty years ago, mathematician Mark Kac asked the theoretical question, "Can one hear the shape of a drum?"

If drums of different shapes always produce their own unique sound spectrum, then it should be possible to identify the shape of a specific drum merely by studying its spectrum, thus "hearing" the drum's shape (a procedure analogous to spectroscopy, the way scientists detect the composition of a faraway star by studying its light spectrum).

But what if two drums of different shapes could emit exactly the same sound? If so, it would be impossible to work backward from the spectrum and uniquely surmise the physical structure of the drum, because there would be more than one correct answer to the question.

It took until the 1990s for mathematicians to prove that, in fact, two drums of different shapes could produce the same sound. In other words, you can't hear the shape of a drum. That outcome, which was physically verified in one instance with vibrations on the surface of soap bubbles, raised theoretical questions about spectroscopy.

"This revolutionized our conception of the fundamental connections between shape and sound, but also had profound implications for spectroscopy in general, because it introduced an ambiguity," according to Stanford physicist Hari Manoharan.

For Manoharan, the next step in studying this conundrum was to take the drum question to another level—a much lower level. He and his students investigated the drum question in the quantum realm, where it could have an effect on real nano-electronic systems.

Using a tunneling scanning microscope and two roomfuls of equipment to move around individual carbon monoxide molecules on a copper surface, they built tiny walls only one-molecule high and shaped them into nine-sided enclosures that could resonate like drums (because of the quantum wave/particle duality of the electrons within the enclosure).

Manoharan calls these enclosures quantum drums. Each drum has only 30 or so electrons inside. They are walled in by roughly100 carbon monoxide molecules.

The result? Just as in the normal world, two nanostructures with different shapes can resonate in the same way, a phenomenon known as isospectrality. Manoharan, along with his graduate student Chris Moon and others, published their result in the Feb 8 edition of the journal Science. To reinforce the point, they created a video, complete with two quantum drums beating with the same sound. (The real "sound" is at ultra-high frequencies in the terahertz range; in the video, the sound has been converted to the range of human hearing.)

The practical value of having two different nanostructures with identical properties may lie in the design of ever-smaller computer chip circuits, Manoharan said. Designers of nano-electronic circuits will have two ways to get the same result. "Now your design palette is twice as big," he said.

While the chip industry attempts to shrink existing circuitry, Manoharan is literally coming from the opposite direction. "My research asks, what if you start at the bottom of the ladder? We assemble structures one atom at a time," he said. The unexplored gap between bottom-up research and the industry's shrink-down effort "is where the excitement is," he said.

The work has a natural connection to the problems of quantum computing, he said.

The research may also have connections to string theory, used by cosmologists attempting to understand the structure of the universe, Manoharan said: "There is somehow embedded into the topology of our universe this bizarre spectral ambiguity." String theories describe complex surfaces that are higher-dimensional analogues of these two-dimensional quantum drums.

The drum research has another finding important to the world of quantum mechanics. While it is impossible to directly observe the quantum phase of the wave functions of the electrons inside the drum structure, Manoharan's team has devised a way to extract that information by taking measurements from two isospectral drums and then mathematically combining the information, a process called quantum transplantation.

"We discovered that this extra degree of freedom in geometry provides us with a method to 'cheat' quantum mechanics and obtain normally obscured quantum-mechanical phase information," Manoharan said.

There are other ways to experimentally determine quantum phase information from atoms or molecules in gases, or from quantum dots and rings, all of them relying on a process called interferometry. The addition of a new method, "geometry over interferometry," will benefit researchers, Manoharan said.

The authors of the Science paper, "Quantum Phase Extraction in Isospectral Electronic Nanostructures," in addition to Manoharan and Moon, are graduate students Laila Mattos, Brian Foster, Gabriel Zeltzer and Wonhee Ko.

Funding for the research came from the National Science Foundation, the U.S. Department of Energy and the Office of Naval Research.

Dan Stober | EurekAlert!
Further information:
http://www.stanford.edu

More articles from Physics and Astronomy:

nachricht Molecule flash mob
19.01.2017 | Technische Universität Wien

nachricht Magnetic moment of a single antiproton determined with greatest precision ever
19.01.2017 | Johannes Gutenberg-Universität Mainz

All articles from Physics and Astronomy >>>

The most recent press releases about innovation >>>

Die letzten 5 Focus-News des innovations-reports im Überblick:

Im Focus: Traffic jam in empty space

New success for Konstanz physicists in studying the quantum vacuum

An important step towards a completely new experimental access to quantum physics has been made at University of Konstanz. The team of scientists headed by...

Im Focus: How gut bacteria can make us ill

HZI researchers decipher infection mechanisms of Yersinia and immune responses of the host

Yersiniae cause severe intestinal infections. Studies using Yersinia pseudotuberculosis as a model organism aim to elucidate the infection mechanisms of these...

Im Focus: Interfacial Superconductivity: Magnetic and superconducting order revealed simultaneously

Researchers from the University of Hamburg in Germany, in collaboration with colleagues from the University of Aarhus in Denmark, have synthesized a new superconducting material by growing a few layers of an antiferromagnetic transition-metal chalcogenide on a bismuth-based topological insulator, both being non-superconducting materials.

While superconductivity and magnetism are generally believed to be mutually exclusive, surprisingly, in this new material, superconducting correlations...

Im Focus: Studying fundamental particles in materials

Laser-driving of semimetals allows creating novel quasiparticle states within condensed matter systems and switching between different states on ultrafast time scales

Studying properties of fundamental particles in condensed matter systems is a promising approach to quantum field theory. Quasiparticles offer the opportunity...

Im Focus: Designing Architecture with Solar Building Envelopes

Among the general public, solar thermal energy is currently associated with dark blue, rectangular collectors on building roofs. Technologies are needed for aesthetically high quality architecture which offer the architect more room for manoeuvre when it comes to low- and plus-energy buildings. With the “ArKol” project, researchers at Fraunhofer ISE together with partners are currently developing two façade collectors for solar thermal energy generation, which permit a high degree of design flexibility: a strip collector for opaque façade sections and a solar thermal blind for transparent sections. The current state of the two developments will be presented at the BAU 2017 trade fair.

As part of the “ArKol – development of architecturally highly integrated façade collectors with heat pipes” project, Fraunhofer ISE together with its partners...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Sustainable Water use in Agriculture in Eastern Europe and Central Asia

19.01.2017 | Event News

12V, 48V, high-voltage – trends in E/E automotive architecture

10.01.2017 | Event News

2nd Conference on Non-Textual Information on 10 and 11 May 2017 in Hannover

09.01.2017 | Event News

 
Latest News

New Study Will Help Find the Best Locations for Thermal Power Stations in Iceland

19.01.2017 | Earth Sciences

Not of Divided Mind

19.01.2017 | Life Sciences

Molecule flash mob

19.01.2017 | Physics and Astronomy

VideoLinks
B2B-VideoLinks
More VideoLinks >>>