Evidence for universal four-body states tied to an Efimov trimer

Institut für Experimentalphysik,
University of Innsbruck, and
Austrian Academy of Sciences,
Innsbruck, Austria

Efimov physics is taking off


Already in the 1970’s, the Russian theorist Vitaly Efimov found a stunning solution to the quantum three-body problem, predicting one of the most counterintuitive quantum phenomena in few-body physics. A system of three particles can bind together in ultra-weakly bound trimer states, even when none of the two-particle subsystems can form dimers. Amazingly, there is an infinite series of such trimer states, which  accumulate at the atomic threshold .

Efimov's original work has been motivated by understanding nuclear matter but its predictions go well beyond system-specific behavior: The Efimov effect is universal! Nuclear, molecular, and ultracold atomic matter are all expected to exhibit Efimov states, despite the vastly different energy scales involved. It took more than 35 years until first evidence of the mysterious “Efimov” three-body states was found in ultracold samples of optically trapped Cs atoms by our group in Innsbruck. After the long time since Efimov´s predistion, the field is now taking off at an amazing speed, and an increasing number of ultracold atomic and molecular systems reveal traces of Efimov states.

From three to four: a quantum leap in few-body physics


How does universality extend to four bodies? Do universal four-body states exist and how do they relate to the Efimov effect?   These are the questions that challenge our understanding! The addition of just a further single particle into the usual three-body Efimov scenario leads to a dramatic increase in complexity both in theory and experiment.

Recently, two theory groups (Hammer and Platter [1]; von Stecher, D’Incao, and Greene [2]) made a major step in studying the four-body problem. In particular, they predicted the existence of pairs of universal four-body states being closely tied to Efimov trimers. The tetramer  pairs emerge as a natural consequence of the presence of  Efimov trimer states. 


Fig.1: Extended Efimov scenario describing a universal system of four identical bosons;

Energies are plotted as a function of the inverse scattering length. The red solid lines
illustrate the pairs of universal tetramer states associated with each Efimov trimer.
In the four-body pictures, the Efimov trimers give rises to an infinite sequence of
trimer-atom thresholds (green dashed lines)


In experiments, four-body phenomena are an unexplored terrain. Doubts about the possibility to observe four-body phenomena in atomic systems can be raised because of the competition with the usually much stronger three-body processes that could mask four-body processes.


Our experiment now shows that these highly complex processes can be observed and studied in ultracold atomic samples.  We confirm the central theoretical predictions. Our results on recombination in an ultracold gas of cesium atoms show a pair of resonances caused by four-body processes as fingerprints of the predicted pair of four-body states tied to an Efimov trimer.

Fig.2: Loss rate coefficient for four-body recombination as a
function of the scattering length a. The resonant increase observed
at around -410 a is induced by one of the predicted universal
tetramer state intersecting the atomic threshold (see inset).





Evidence for universal four-body states tied to an Efimov trimer

F. Ferlaino, S. Knoop, M. Berninger, W. Harm, J. P. D´Incao,  H.-C. Nägerl, R. Grimm

Phys. Rev. Lett. 102, 140401 (2009)

pre-print: arXiv:09031276


[1]  Universal properties of the four-body system with large scattering length

      H. Hammer and L. Platter, Eur. Phys. J. A 32, 113 (2007)



[2]  Four-body legacy of the Efimov effect

      J. von Stecher, J. P. D’Incao, and C. H. Greene 



Related Articles


  [3]  Viewpoint in Physics: Ultracold experiment strikes universal physics--again

               Brett D. Esry

               Physics 2, 26 (2009)





This work has been carried out in the LevT experiment.

from left to right:


Michael Mark


Martin Berninger


Hanns-Christoph Nägerl


 Francesca Ferlaino

 (Lise-Meitner Fellow)


Rudi Grimm


Steven Knoop

(Marie Curie Fellow)  





Walter Harm 


Jose Paulo D´Incao


Further links

German version

Press release (in German)

Pictures to download

The Innsbruck Few-Body Story




The experiment is supported by the Austrian Science Fund (FWF) within No. SFB 15 (project part 16). F. F. is supported within the Lise Meitner program of the FWF.


last change: 07-04-2009 by FF