Featured Research

from universities, journals, and other organizations

Hearing The Sound Of Quantum Drums

Date:
February 9, 2008
Source:
Stanford University
Summary:
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. The drum research is important to the world of quantum mechanics.

Quantum shape shifting. Molecular nanostructures of different shape (top and bottom surfaces), linked topologically (beam) to share the same spectrum, enable the measurement of quantum mechanical phase. Background: color-encoded quantum state transplantation matrix.
Credit: Manoharan lab, Stanford University

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

Related Articles


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.

Here the sound of the quantum drums at: http://www.stanford.edu/group/mota/qin/Movie%20S1%20-%20Isospectrality.mov

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.


Story Source:

The above story is based on materials provided by Stanford University. Note: Materials may be edited for content and length.


Cite This Page:

Stanford University. "Hearing The Sound Of Quantum Drums." ScienceDaily. ScienceDaily, 9 February 2008. <www.sciencedaily.com/releases/2008/02/080208080532.htm>.
Stanford University. (2008, February 9). Hearing The Sound Of Quantum Drums. ScienceDaily. Retrieved October 24, 2014 from www.sciencedaily.com/releases/2008/02/080208080532.htm
Stanford University. "Hearing The Sound Of Quantum Drums." ScienceDaily. www.sciencedaily.com/releases/2008/02/080208080532.htm (accessed October 24, 2014).

Share This



More Computers & Math News

Friday, October 24, 2014

Featured Research

from universities, journals, and other organizations


Featured Videos

from AP, Reuters, AFP, and other news services

Microsoft Riding High On Strong Surface, Cloud Performance

Microsoft Riding High On Strong Surface, Cloud Performance

Newsy (Oct. 24, 2014) — Microsoft's Q3 earnings showed its tablets and cloud services are really hitting their stride. Video provided by Newsy
Powered by NewsLook.com
The Best Apps to Organize Your Life

The Best Apps to Organize Your Life

Buzz60 (Oct. 23, 2014) — Need help organizing your bills, schedules and other things? Ko Im (@konakafe) has the best apps to help you stay on top of it all! Video provided by Buzz60
Powered by NewsLook.com
Nike And Apple Team Up To Create Wearable ... Something

Nike And Apple Team Up To Create Wearable ... Something

Newsy (Oct. 23, 2014) — For those looking for wearable tech that's significantly less nerdy than Google Glass, Nike CEO Mark Parker says don't worry, It's on the way. Video provided by Newsy
Powered by NewsLook.com
Chameleon Camouflage to Give Tanks Cloaking Capabilities

Chameleon Camouflage to Give Tanks Cloaking Capabilities

Reuters - Innovations Video Online (Oct. 22, 2014) — Inspired by the way a chameleon changes its colour to disguise itself; scientists in Poland want to replace traditional camouflage paint with thousands of electrochromic plates that will continuously change colour to blend with its surroundings. The first PL-01 concept tank prototype will be tested within a few years, with scientists predicting that a similar technology could even be woven into the fabric of a soldiers' clothing making them virtually invisible to the naked eye. Matthew Stock reports. Video provided by Reuters
Powered by NewsLook.com

Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
 
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:  

Breaking News:

Strange & Offbeat Stories

 

Space & Time

Matter & Energy

Computers & Math

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:  

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile iPhone Android Web
Follow Facebook Twitter Google+
Subscribe RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins