Hints of universal behavior seen in exotic three-atom states

September 23, 2011
This graph shows the existence of Efimov triplet states as a function of the scattering length, a, and the binding energy. Outside the green area the three atoms exist singly or as a pair plus a lone atom. Inside the green area a series of three-atom states can exist. Credit: Picture courtesy of the University of Innsbruck

A novel type of inter-particle binding predicted in 1970 and observed for the first time in 2006, is forming the basis for an intriguing kind of ultracold quantum chemistry. Chilled to nano-kelvin temperatures, cesium atoms -- three at a time -- come together to form a bound state hundreds or even thousands of times larger than individual atoms. Unlike the case of ordinary atoms, wherein electrons are bound to a nucleus in a spectrum of energy levels on the order of an electron volt (that is, it would typically take an eV of energy to free the electron), the cesium triplets feature energy levels that are measured in trillionths of an electron volt (peV). Stranger still, a new experiment observing four such cesium states reports that the states' sizes are roughly the same. This has taken theorists by complete surprise.

In the seventeenth century derived the classical force laws used to calculate the force between two objects. Calculating the behavior of three-body groupings such as the Moon/Earth/Sun system was much harder; indeed Newton never succeeded. Nowadays such problems can be studied with , but only are possible, and not exact, analytical solutions.

In 1970, however, Russian physicist Vitaly Efimov predicted that under some special conditions, three bodies, such as atoms at ultralow temperatures, could be made to enter into stable states whose behavior could be calculated with remarkable ease. Then in 2006 exactly such states were actually observed by scientists at the University of Innsbruck. Now, these researchers have extended their work and demonstrated that the "three-body parameter," used to describe how the three participating bodies interact, varies in a consistent way regardless of the atomic species used.

Paul Julienne, a scientist at the Joint Quantum Institute (JQI), operated by the University of Maryland and the National Institute of Standards and Technology (NIST), contributed theoretical help to the Innsbruck scientists conducting the experiment, a team led by Rudolf Grimm. "None of the experts in three-body physics had expected this kind of universal behavior to show up in these 3-atom systems," Julienne said. "This behavior came as a big surprise." And the universality, in turn, might suggest the existence of some new kind of ultracold chemistry at work.

Efimov's 1970 work met with much skepticism, especially since his prediction specified that three particles could form stable partnerships even though none of the two-particle matchups were stable. That is, 3 particles could accomplish what 2 particles could not. This novel arrangement has been compared to the "Borromean Rings," a set of three rings used on heraldic symbol for the Borromeo family during the Italian Renaissance. The three rings hold together unless any one of the rings is removed.

Efimov's prediction applies not just to atoms but to any 3 particles. For example, helium-6, a semi-stable nucleus consisting of 2 protons and 4 neutrons, can be made by from a helium-4 nucleus and 2 extra neutrons. The 2 neutrons cannot form a stable composite; neither can He-4 plus 1 extra neutron. But the three-body He4-n-n system is stable, at least for a while.

Such Borromean nuclei have been known for some time, but atoms have turned out to be more useful in pursuing the novel interactions called for in Efimov's theory. That's because atoms can be chilled to nano-kelvin temperatures in traps and made to interact with great precision. As atoms cool down, they get larger---at least in a quantum sense: as waves, their equivalent wavelength can be many times larger than their nominal particle size (a hydrogen atom is about 0.1 nm across). Furthermore, by applying an external magnetic field, subtle interactions among neutral atoms can be achieved.

Such interactions, called Feshbach resonances, were used to bring together, three at a time, in Efimov states. These atoms were part of a vapor held at temperatures of tens of nano-K. In 2006 the Innsbruck team reported seeing one such troika of atoms. Now, in the 16 September 2011 issue of Physical Review Letters, the Innsbruck-JQI-Durham researchers are reporting the observation of three more state of 3 atoms bound together.

These trimers are quantum objects; they have no classical counterpart. The weak binding of the super-cold Cs atoms is described in terms of a parameter, a, called the scattering length. 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, negative, and three atoms are present, then the Efimov state can appear. Indeed an infinite number of such states can occur. The Efimov state has an energy spectrum, as if it were a chemical element all by itself, with each binding energy level scaling with the value of a. This kind of universal behavior was expected.

The effective size of these Efimov-triplets is referred to as the three-body parameter. In the case of the four cesium states seen so far, the value is just about the same, about 50 nm, or about 500 times the size of a hydrogen atom. This, combined with the three-body-parameter values observed in experiments for lithium and possibly for other elements being studied right now, suggests that while adjusting for the size of the respective all the species are behaving in the same way. This kind of universality was totally unexpected.

"It is really amazing how the new research field developed since we found the first traces of Efimov states, "said Grimm. "Now things have become reality, things we did not even dream about five years ago."

Explore further: Rice physicists find reappearing quantum trios

More information: "Universality of the Three-Body Parameter for Efimov States in Ultracold Cesium," by M. Berninger, A. Zenesini,1 B. Huang, W. Harm, H.-C. Na¨gerl, F. Ferlaino, R. Grimm, P. S. Julienne, and J. M. Hutson, 16 September 2001 Physical Review Letters.

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not rated yet Sep 23, 2011
Sounds similar to a BoseEinstein condensate.
3.2 / 5 (9) Sep 23, 2011
Sounds similar to a BoseEinstein condensate.
And it actually is, just the particles involved there aren't bosons but so-called anyons, i.e. the mixed state of bosons and fermions of fractional effective charge. Such anyons cannot stay at place like bosons, but they still cannot move freely and collide mutually like the fermions. It's the consequence of the Heissenberg's uncertainty principle: if you restrict the motion of fermions into thin layer an uncertainty in particle momentum will emerge. There is an animation illustrating, how the Efimov triplets are formed:

not rated yet Sep 23, 2011
Interesting graphic Callipo, thx.

" The size of each three particle Efimov state is much larger than the force-range between the individual particle pairs. This means that the state is purely quantum mechanical. "

..... Can two groups of atoms in an Efimov state be entangled ?
1 / 5 (2) Sep 23, 2011
man this is totally effed up. , i meant effimoved up :)
1 / 5 (2) Sep 23, 2011
As atoms cool down, they get larger---at least in a quantum sense: as waves, their equivalent wavelength can be many times larger than their nominal particle size (a hydrogen atom is about 0.1 nm across).

This is a wonderful description. Simply imagining this description stimulates imagination - imagining such a mechanism to describe water's anomaly:
In an expanding volume the density increases following a steady drop in temperature at constant pressure.
2.6 / 5 (5) Sep 24, 2011
Calippo's graphic shows three limit cycle oscillators that are each one third out of phase with respect to the other two. This is consistent with the coupled oscillator work done by Art Winfree (and Kuramoto, Strogatz, Mirollo and others) that arose in an entirely different context. Winfree's work specifies that systems of limit cycle oscillators will couple or self-organize, but when they do, there are only certain allowable patterns. For a three oscillator system, Winfree specified that one-third out of phase was an allowable pattern. His field was biomathematics, but the math is not dependent upon the original context of Winfree's work. Winfree's theory, dating back to the 1960's, may explain both the pattern and, more importantly, the mechanism for this self-organization.
not rated yet Sep 24, 2011
The new thing with Efimov physics is the Borromean ring structure of the states and that these states arise when the scattering length is negative. Both aspects do not have classical counterparts, thus non-intuitive and, at first, purely theoretical. Having a negative scattering length is like having a negative radius, it doesn't make sense physically. Also, saying that particles don't interact after you "pluck" one particle out of the system, doesn't make sense physically. I hope that gives a little perspective on this problem.
2 / 5 (4) Sep 25, 2011
A negative scattering length means that there is no bound state (between two particles). The emphasis here should be on the ginormous (not a physics term) scattering length. Great length (500 times the size of a hydrogen atom) and lack of (two particle) bound states means that there is only one relevant "force"--namely, the mingled oscillations of three particles.

That is why Art Winfree's theory of coupled oscillators should be considered. It is universal, and it focuses exclusively on oscillations. A good description may be found in Scientific American, December 1993, a copy of which may be found on the website of Prof. Steven Strogatz at Cornell. See particularly the diagram showing three oscillators, each one-third out of phase. Again, Winfree's work predates Efimov by a few years, and the two worked in different fields (mathematics as applied to biology, for Winfree). The Efimov state may not have a classical counterpart in physics, but it does elsewhere.
not rated yet Sep 25, 2011
A picoelectronvolt photon has a frequency in the audio range, 241 Hz, ie it is longer wavelength even than radio waves.
not rated yet Sep 25, 2011
A picoelectronvolt photon has a frequency in the audio range, 241 Hz, ie it is longer wavelength even than radio waves.

Does that mean that the EM could directly interact with the eardrum or that the air would harmonize to that frequency?
1 / 5 (2) Sep 25, 2011
Both aspects do not have classical counterparts, thus non-intuitive and, at first, purely theoretical
I send the classical interpretation in my first post above. At these low temperatures the behavior of atoms is quite classical because of low energy levels (compare the behavior of electrons inside of so-called Rydberg atoms). The wavefunction of Efimov states really appears like three-leaf clover.


Negative scattering length correspond anti-Stokes dispersion, which is quite common phenomena.
not rated yet Sep 26, 2011
This article is the answer to:

"Why can't physicists have threesomes?"
1 / 5 (3) Oct 03, 2011
Winfree's theory of coupled oscillators may well explain the "surprise" discussed in the foregoing article. The surprise is that "the three body parameter ... varies in a consistent way regardless of the atomic species used." Further below in the article "...while adjusting for the size of the specific atoms, all the species are behaving in the same way. This kind of universality was completely unexpected."

As noted in my prior comments, Art Winfree described how "limit cycle oscillators" (Winfre's term) will couple or coordinate their oscillations in specific patterns. Per Winfree, a three body system will coordinate oscillations in several ways, one of which is one third out of phase--that's the Efimov pattern in this article.

A quantum of energy is a type of limit cycle oscillation, in my view. So Winfree's theory is a promising theoretical approach, predating Efimov, that "predicts" this universality. Further inquiry into Winfree's theory is likely to be fruitful.

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