Forum for Science, Industry and Business

Sponsored by:     3M 
Search our Site:

 

Cool Calculations for Cold Atoms

03.09.2014

New theory of universal three-body encounters

Chemical reactions drive the mechanisms of life as well as a million other natural processes on earth. These reactions occur at a wide spectrum of temperatures, from those prevailing at the chilly polar icecaps to those at work churning near the earth’s core.

At nanokelvin temperatures, by contrast, nothing was supposed to happen. Chemistry was expected to freeze up. Experiments and theoretical work have now show that this is not true. Even at conditions close to absolute zero atoms can interact and manage to form chemical bonds.

Within this science of ultracold chemistry, there is a sub-field that deals with “Efimov states,” named for Russian physicist Vitaly Efimov. In 1970 he predicted that under some conditions all two-particle bound states would be unstable while (paradoxically) some three-particle states could exist. Such states were eventually seen experimentally in 2006, among cesium atoms (see Related JQI Article below).

Two scientists at the Joint Quantum Institute have now formulated a universal theory to describe the properties of these Efimov states, a theory that, for the first time, does not need extra adjustable unknown parameters . This should allow physicists to predict the rates of chemical processes involving three atoms---or even more---using only a knowledge of the interaction forces at work.

The JQI authors, Yujun Wang and Paul Julienne, publish their results in the journal Nature Physics (see Reference Publication below).

PICO-ELECTRON VOLTS

Efimov states are fragile. They depend for their existence on quantum effects and on the subtle interplay of two phenomena: Feshbach resonance and van der Waal forces. Quantum effects are necessarily at work at ultracold temperatures in the nano-kelvin regime. Here atoms should be viewed not as hard balls, typically a few tenths of nanometers across, but as wave packets, blobs extending over hundreds of nm.

It is common, when talking about colliding particles, to see them as cars speeding toward each other, perhaps meeting head on or glancing off at a relative angle. It is more unusual to visualize the collision if the “particles” are so large as to overlap each other at relatively great distances. More strange still if three such particles are involved in an interaction whose result will be a loosely-bound confederation.

In the study of Efimov states, the primary force at work among the atoms is the van der Waals force, named for Dutch physicist Johannes Diderik van der Waals. This long-range force among atoms or molecules arises from the temporary appearance of electric dipole moments in the particles.

Even for a neutral atom, a momentary imbalance of charge---more of the atomic electrons’ negative charge might appear to the left, say, leaving a positive preponderance on the right---will constitute an electric dipole, which in turn can attract an atom with a complementary dipole orientation. This induced-dipole force varies at the inverse sixth power of the distance between the two particles.

Another way of controlling inter-particle collisions at ultracold temperatures is to turn on an external magnetic field. For certain ranges of field strength, two particles can be coaxed to form semi-stable objects called Feshbach resonances, named for US physicist Herman Feshbach. Feshbach resonances are commonly used in cold-physics to control interactions, and this is especially true in the study of Efimov states.

Often Feshbach resonances are described in terms of a parameter, a, called the scattering length, denoting the effective distance over which the interaction takes place If a is positive and large (much larger than the nominal range of the force between the atoms), weak binding of atoms can happen. If a is negative, a slight attraction of two atoms can occur but not binding. If, however, a is large and three atoms are present, then the Efimov state can appear. Indeed an infinite number of such states can occur.

In general since it allows interactions over large distances, the Feshbach effect is more important than the van der Waals force. But the JQI research has shown how the van der Waals force can be decisive in forming Efimov states, especially when the scattering length is short. Many scientists had believed that making consistent predictions of triplet-forming interactions would be difficult to make. Instead, the Wang-Julienne model successfully incorporates this short-distance regime.

Thus there should be a series of Efimov states, with various binding energies. But unlike atoms, where the quantum energy levels (denoting how much energy is needed to liberate the electron from its atomic binding) are in the electron volt (eV) range, Efimof states are typified by quantum energies of billionths of an eV or less.

THE NEW JQI THEORY

Wang and Julienne build their theory of 3-body van der Waals physics around the Schrödinger equation, the equation introduced by Erwin Schrödinger in the 1920s to treat particles as waves. Only here it is three particles---viewed as three sets of waves, or rather as a complex of waves representing the three particles---carefully studied in pairwise fashion to simulate an effective composite force field in which the three particles operate.

The result is a theoretical tool that can predict the important Efimov properties, namely the energies of the Efimov states, the widths of those states (essentially the fuzziness of our knowledge of the precise energy value), and the rates at which the three-particle states will form inside a gas of ultracold atoms.

“Our theory works for a full range of scattering lengths,” said Yujun Wang describing the JQI work, “whereas the previous theories could only apply to large scattering lengths. We don't need adjustable parameters. The only inputs in our theory are the known two-body Feshbach parameters and our calculations using the Schrodinger equation. So our theory does not rely on any of the unknown three-body inputs that have been used in previous theories to fit the experimental data. In these two aspects our theory is more comprehensive and powerful. We can make quantitative predictions without relying on the unknowns, so that our results can be directly compared to experiments.”


Figure 1. Three panels illustrate the condition of Efimov states (3-atom stable states). The upper, bell-shaped surface represents the probability density for each of the three geometries, while the gray surface represents the strength of the van der Waals force for that geometry. Left panel: the three interacting atoms lie in an equilateral triangle formation. Middle panel: two of the atoms are rather closer together than to the third atom. Right panel: the geometry of the middle panel but with the atoms lying farther apart from each other. The dimples in the probability density surface reflect the more complicated interaction when two of the atoms are close together.Credit JQI/Yujun

Research Contact
Paul Julienne
Yujun Wang
Media Contact
Phillip F. Schewe|
(301) 403-0989

Phillip F. Schewe | Eurek Alert!

More articles from Physics and Astronomy:

nachricht Prediction: More gas-giants will be found orbiting Sun-like stars
22.02.2017 | Carnegie Institution for Science

nachricht NASA's fermi finds possible dark matter ties in andromeda galaxy
22.02.2017 | NASA/Goddard Space Flight Center

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: Breakthrough with a chain of gold atoms

In the field of nanoscience, an international team of physicists with participants from Konstanz has achieved a breakthrough in understanding heat transport

In the field of nanoscience, an international team of physicists with participants from Konstanz has achieved a breakthrough in understanding heat transport

Im Focus: DNA repair: a new letter in the cell alphabet

Results reveal how discoveries may be hidden in scientific “blind spots”

Cells need to repair damaged DNA in our genes to prevent the development of cancer and other diseases. Our cells therefore activate and send “repair-proteins”...

Im Focus: Dresdner scientists print tomorrow’s world

The Fraunhofer IWS Dresden and Technische Universität Dresden inaugurated their jointly operated Center for Additive Manufacturing Dresden (AMCD) with a festive ceremony on February 7, 2017. Scientists from various disciplines perform research on materials, additive manufacturing processes and innovative technologies, which build up components in a layer by layer process. This technology opens up new horizons for component design and combinations of functions. For example during fabrication, electrical conductors and sensors are already able to be additively manufactured into components. They provide information about stress conditions of a product during operation.

The 3D-printing technology, or additive manufacturing as it is often called, has long made the step out of scientific research laboratories into industrial...

Im Focus: Mimicking nature's cellular architectures via 3-D printing

Research offers new level of control over the structure of 3-D printed materials

Nature does amazing things with limited design materials. Grass, for example, can support its own weight, resist strong wind loads, and recover after being...

Im Focus: Three Magnetic States for Each Hole

Nanometer-scale magnetic perforated grids could create new possibilities for computing. Together with international colleagues, scientists from the Helmholtz Zentrum Dresden-Rossendorf (HZDR) have shown how a cobalt grid can be reliably programmed at room temperature. In addition they discovered that for every hole ("antidot") three magnetic states can be configured. The results have been published in the journal "Scientific Reports".

Physicist Dr. Rantej Bali from the HZDR, together with scientists from Singapore and Australia, designed a special grid structure in a thin layer of cobalt in...

All Focus news of the innovation-report >>>

Anzeige

Anzeige

Event News

Booth and panel discussion – The Lindau Nobel Laureate Meetings at the AAAS 2017 Annual Meeting

13.02.2017 | Event News

Complex Loading versus Hidden Reserves

10.02.2017 | Event News

International Conference on Crystal Growth in Freiburg

09.02.2017 | Event News

 
Latest News

Microhotplates for a smart gas sensor

22.02.2017 | Power and Electrical Engineering

Scientists unlock ability to generate new sensory hair cells

22.02.2017 | Life Sciences

Prediction: More gas-giants will be found orbiting Sun-like stars

22.02.2017 | Physics and Astronomy

VideoLinks
B2B-VideoLinks
More VideoLinks >>>