Lab Mimics Jupiter's Trojan Asteroids Inside a Single Atom

Rice University graduate student Shuzhen Ye used an ultraviolet laser to create a Rydberg atom in order to study the orbital mechanics of electrons. (Credit: Jeff Fitlow/Rice University)

ScienceDaily  — Rice University physicists have gone to extremes to prove that Isaac Newton's classical laws of motion can apply in the atomic world: They've built an accurate model of part of the solar system inside a single atom of potassium.

In a new paper published this week in Physical Review Letters, Rice's team and collaborators at the Oak Ridge National Laboratory and the Vienna University of Technology showed they could cause an electron in an atom to orbit the nucleus in precisely the same way that Jupiter's Trojan asteroids orbit the sun.

The findings uphold a prediction made in 1920 by famed Danish physicist Niels Bohr about the relationship between the then-new science of quantum mechanics and Newton's tried-and-true laws of motion.

"Bohr predicted that quantum mechanical descriptions of the physical world would, for systems of sufficient size, match the classical descriptions provided by Newtonian mechanics," said lead researcher Barry Dunning, Rice's Sam and Helen Worden Professor of Physics and chair of the Department of Physics and Astronomy. "Bohr also described the conditions under which this correspondence could be observed. In particular, he said it should be seen in atoms with very high principal quantum numbers, which are exactly what we study in our laboratory."

Bohr was a pioneer of quantum physics. His 1913 atomic model, which is still widely invoked today, postulated a small nucleus surrounded by electrons moving in well-defined orbits and shells. The word "quantum" in quantum mechanics derives from the fact that these orbits can have only certain well-defined energies. Jumps between these orbits lead to absorption or emission of specific amounts of energy termed quanta. As an electron gains energy, its quantum number increases, and it jumps to higher orbits that circle ever farther from the nucleus.

In the new experiments, Rice graduate students Brendan Wyker and Shuzhen Ye began by using an ultraviolet laser to create a Rydberg atom. Rydberg atoms contain a highly excited electron with a very large quantum number. In the Rice experiments, potassium atoms with quantum numbers between 300 and 600 were studied.

"In such excited states, the potassium atoms become hundreds of thousands of times larger than normal and approach the size of a period at the end of a sentence," Dunning said. "Thus, they are good candidates to test Bohr's prediction."

He said comparing the classical and quantum descriptions of the electron orbits is complicated, in part because electrons exist as both particles and waves. To "locate" an electron, physicists calculate the likelihood of finding the electron at different locations at a given time. These predictions are combined to create a "wave function" that describes all the places where the electron might be found. Normally, an electron's wave function looks like a diffuse cloud that surrounds the atomic nucleus, because the electron might be found on any side of the nucleus at a given time.

Dunning and co-workers previously used a tailored sequence of electric field pulses to collapse the wave function of an electron in a Rydberg atom; this limited where it might be found to a localized, comma-shaped area called a "wave packet." This localized wave packet orbited the nucleus of the atom much like a planet orbits the sun. But the effect lasted only for a brief period.

"We wanted to see if we could develop a way to use radio frequency waves to capture this localized electron and make it orbit the nucleus indefinitely without spreading out," Ye said.

They succeeded by applying a radio frequency field that rotated around the nucleus itself. This field ensnared the localized electron and forced it to rotate in lockstep around the nucleus.

A further electric field pulse was used to measure the final result by taking a snapshot of the wave packet and destroying the delicate Rydberg atom in the process. After the experiment had been run tens of thousands of times, all the snapshots were combined to show that Bohr's prediction was correct: The classical and quantum descriptions of the orbiting electron wave packets matched. In fact, the classical description of the wave packet trapped by the rotating field parallels the classical physics that explains the behavior of Jupiter's Trojan asteroids.

Jupiter's 4,000-plus Trojan asteroids -- so called because each is named for a hero of the Trojan wars -- have the same orbit as Jupiter and are contained in comma-shaped clouds that look remarkably similar to the localized wave packets created in the Rice experiments. And just as the wave packet in the atom is trapped by the combined electric field from the nucleus and the rotating wave, the Trojans are trapped by the combined gravitational field of the sun and orbiting Jupiter.

The researchers are now working on their next experiment: They're attempting to localize two electrons and have them orbit the nucleus like two planets in different orbits.

"The level of control that we're able to achieve in these atoms would have been unthinkable just a few years ago and has potential applications in, for example, quantum computing and in controlling chemical reactions using ultrafast lasers," Dunning said.

The research was funded by the National Science Foundation, the Robert A. Welch Foundation, the Austrian Science Fund and the Department of Energy. Paper co-authors include S. Yoshida of the Vienna University of Technology; C.O. Reinhold of Oak Ridge National Laboratory and the University of Tennessee; and J. Burgdörfer of Vienna University of Technology and the University of Tennessee.

Story Source:

The above story is reprinted from materials provided by Rice University.

Note: Materials may be edited for content and length. For further information, please contact the source cited above.

---

Journal Reference:

1. B. Wyker, S. Ye, F. Dunning, S. Yoshida, C. Reinhold, J. Burgdörfer. Creating and Transporting Trojan Wave Packets. Physical Review Letters, 2012; 108 (4) DOI:10.1103/PhysRevLett.108.043001

Faster computer graphics: Digitally mimicking photographic blur caused by moving objects

ScienceDaily (June 13, 2011) — Photographs of moving objects are almost always a little blurry -- or a lot blurry, if the objects are moving rapidly enough. To make their work look as much like conventional film as possible, game and movie animators try to reproduce this blur. But counterintuitively, producing blurry images is actually more computationally complex than producing perfectly sharp ones.

In August, at this year's Siggraph conference -- the premier computer-graphics conference -- researchers from the Computer Graphics Group at MIT's Computer Science and Artificial Intelligence Laboratory will present a pair of papers that describe new techniques for computing blur much more efficiently. The result could be more convincing video games and frames of digital video that take minutes rather than hours to render.

The image sensor in a digital camera, and even the film in a conventional camera, can be thought of as a grid of color detectors, each detector corresponding to one pixel in the final image. If the objects being photographed are stationary, then during a single exposure, each detector registers the color of just one point on an object's surface. But if the objects are moving, light from different points on an object, and even from different objects, will strike a single detector. The detector effectively averages the colors of all the points, and the result is blur.

Digitally rendering a frame of video is a computationally intensive process with several discrete stages. First, the computer has to determine how the objects in the scene are moving. Second, it has to calculate how rays of light from an imagined light source would reflect off the objects. Finally, it determines which rays of light would actually reach an imagined lens. If the objects in the video are moving slowly enough, the computer has to go through that process only once per frame. If the objects are moving rapidly, however, it may have to go through it dozens or even hundreds of times.

Colorfast

Given how difficult blurring is to calculate, you might think that animators would simply ignore it. But that leads to surprisingly unconvincing video. "The motion doesn't look fluid at all," says Jaakko Lehtinen, who worked on both projects as a postdoc in the Computer Graphics Group and is now a senior research scientist with graphics-chip manufacturer Nvidia.

To get a sense of what motion without blur looks like, Lehtinen says, consider the type of clay animation familiar from old movies or Christmas specials such as "Rudolph the Red-Nosed Reindeer." "This doesn't have motion blur, because the scene is actually stationary when you take the picture," Lehtinen says. "It just looks choppy. The motion doesn't look natural."

The MIT researchers took two different approaches to simplifying the computation of blur, corresponding to two different stages in the graphics-rendering pipeline. Graduate student Jonathan Ragan-Kelley is the lead author on one of the Siggraph papers, joined by associate professor Frédo Durand, who leads the Computer Graphics Group; Lehtinen; graduate student Jiawen Chen; and Michael Doggett of Lund University in Sweden. In that paper, the researchers make the simplifying assumption that the way in which light reflects off a moving object doesn't change over the course of a single frame. For each pixel in the final image, their algorithm still averages the colors of multiple points on objects' surfaces, but it calculates those colors only once. The researchers found a way to represent the relationship between the color calculations and the shapes of the associated objects as entries in a table. For each pixel in the final image, the algorithm simply looks up the corresponding values in the table. That drastically simplifies the calculation but has little effect on the final image.

Adopting the researchers' proposal would require modifying the architecture of graphics chips. "You can imagine really just going ahead and building what they suggest," says Henry Moreton, a distinguished engineer at Nvidia. "But I think that the greater value of the paper is that it points at strategies for solving these problems more elegantly, more efficiently, and more practically. Whether they manifest themselves in exactly the fashion that the paper presents is probably not that likely. But what they did is they pointed to a new way of attacking the problem."

Turning the tables

The second of the Computer Graphics Group's Siggraph papers, led by Lehtinen and also featuring Durand, Chen and two of Lehtinen's Nvidia colleagues, reduces the computational burden of determining which rays of light would reach an imagined lens. To produce convincing motion blur, digital animators might ordinarily consider the contributions that more than 100 discrete points on the surfaces of moving objects make to the color value of a single pixel. Lehtinen and his colleagues' algorithm instead looks at a smaller number of points -- maybe 16 or so -- and makes an educated guess about the color values of the points in between. The result: A frame of digital video that would ordinarily take about an hour to render might instead take about 10 minutes.

In fact, both techniques apply not only to motion blur but also to the type of blur that occurs in, say, the background of an image when the camera is focused on an object in the foreground. That, too, is something that animators seek to reproduce. "Where the director and the cinematographer choose to focus the lens, it directs your attention when you're looking at the picture in subtle ways," Lehtinen says. If an animated film has no such lapses in focus, "there's just something wrong with it," Lehtinen says. "It doesn't look like a movie." Indeed, Lehtinen says, even though the paper has yet to be presented, several major special-effects companies have already contacted the researchers about the work.

Story Source:

The above story is reprinted (with editorial adaptations by ScienceDaily staff) from materials provided by Massachusetts Institute of Technology. The original article was written by Larry Hardesty, MIT News Office.

Note: If no author is given, the source is cited instead.

Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.

View the original article here

Faster computer graphics: Digitally mimicking photographic blur caused by moving objects

ScienceDaily (June 13, 2011) — Photographs of moving objects are almost always a little blurry -- or a lot blurry, if the objects are moving rapidly enough. To make their work look as much like conventional film as possible, game and movie animators try to reproduce this blur. But counterintuitively, producing blurry images is actually more computationally complex than producing perfectly sharp ones.

In August, at this year's Siggraph conference -- the premier computer-graphics conference -- researchers from the Computer Graphics Group at MIT's Computer Science and Artificial Intelligence Laboratory will present a pair of papers that describe new techniques for computing blur much more efficiently. The result could be more convincing video games and frames of digital video that take minutes rather than hours to render.

The image sensor in a digital camera, and even the film in a conventional camera, can be thought of as a grid of color detectors, each detector corresponding to one pixel in the final image. If the objects being photographed are stationary, then during a single exposure, each detector registers the color of just one point on an object's surface. But if the objects are moving, light from different points on an object, and even from different objects, will strike a single detector. The detector effectively averages the colors of all the points, and the result is blur.

Digitally rendering a frame of video is a computationally intensive process with several discrete stages. First, the computer has to determine how the objects in the scene are moving. Second, it has to calculate how rays of light from an imagined light source would reflect off the objects. Finally, it determines which rays of light would actually reach an imagined lens. If the objects in the video are moving slowly enough, the computer has to go through that process only once per frame. If the objects are moving rapidly, however, it may have to go through it dozens or even hundreds of times.

Colorfast

Given how difficult blurring is to calculate, you might think that animators would simply ignore it. But that leads to surprisingly unconvincing video. "The motion doesn't look fluid at all," says Jaakko Lehtinen, who worked on both projects as a postdoc in the Computer Graphics Group and is now a senior research scientist with graphics-chip manufacturer Nvidia.

To get a sense of what motion without blur looks like, Lehtinen says, consider the type of clay animation familiar from old movies or Christmas specials such as "Rudolph the Red-Nosed Reindeer." "This doesn't have motion blur, because the scene is actually stationary when you take the picture," Lehtinen says. "It just looks choppy. The motion doesn't look natural."

The MIT researchers took two different approaches to simplifying the computation of blur, corresponding to two different stages in the graphics-rendering pipeline. Graduate student Jonathan Ragan-Kelley is the lead author on one of the Siggraph papers, joined by associate professor Frédo Durand, who leads the Computer Graphics Group; Lehtinen; graduate student Jiawen Chen; and Michael Doggett of Lund University in Sweden. In that paper, the researchers make the simplifying assumption that the way in which light reflects off a moving object doesn't change over the course of a single frame. For each pixel in the final image, their algorithm still averages the colors of multiple points on objects' surfaces, but it calculates those colors only once. The researchers found a way to represent the relationship between the color calculations and the shapes of the associated objects as entries in a table. For each pixel in the final image, the algorithm simply looks up the corresponding values in the table. That drastically simplifies the calculation but has little effect on the final image.

Adopting the researchers' proposal would require modifying the architecture of graphics chips. "You can imagine really just going ahead and building what they suggest," says Henry Moreton, a distinguished engineer at Nvidia. "But I think that the greater value of the paper is that it points at strategies for solving these problems more elegantly, more efficiently, and more practically. Whether they manifest themselves in exactly the fashion that the paper presents is probably not that likely. But what they did is they pointed to a new way of attacking the problem."

Turning the tables

The second of the Computer Graphics Group's Siggraph papers, led by Lehtinen and also featuring Durand, Chen and two of Lehtinen's Nvidia colleagues, reduces the computational burden of determining which rays of light would reach an imagined lens. To produce convincing motion blur, digital animators might ordinarily consider the contributions that more than 100 discrete points on the surfaces of moving objects make to the color value of a single pixel. Lehtinen and his colleagues' algorithm instead looks at a smaller number of points -- maybe 16 or so -- and makes an educated guess about the color values of the points in between. The result: A frame of digital video that would ordinarily take about an hour to render might instead take about 10 minutes.

In fact, both techniques apply not only to motion blur but also to the type of blur that occurs in, say, the background of an image when the camera is focused on an object in the foreground. That, too, is something that animators seek to reproduce. "Where the director and the cinematographer choose to focus the lens, it directs your attention when you're looking at the picture in subtle ways," Lehtinen says. If an animated film has no such lapses in focus, "there's just something wrong with it," Lehtinen says. "It doesn't look like a movie." Indeed, Lehtinen says, even though the paper has yet to be presented, several major special-effects companies have already contacted the researchers about the work.

Story Source:

The above story is reprinted (with editorial adaptations by ScienceDaily staff) from materials provided by Massachusetts Institute of Technology. The original article was written by Larry Hardesty, MIT News Office.

Note: If no author is given, the source is cited instead.

Disclaimer: Views expressed in this article do not necessarily reflect those of ScienceDaily or its staff.

View the original article here