Evidence for Efimov quantum states in an
ultracold gas of Cs atoms

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

In our ultracold Cs (cesium) gases, we have found evidence for the existence of Efimov quantum states [1]. Despite considerable experimental efforts, the detection of these states has remained an elusive goal for over 35 years. Our results are published on March 16th 2006 in Nature.

In 1970, theoretical physicist V. Efimov proposed the existence of very weakly bound three-body quantum states. His original work appeared in Russian language in 'Soviet Journal of Nuclear Physics' [2], the english translation was published one year later [3].

V. Efimov in 1977. Currently, he is a member of the University of Washington nuclear theory group.

Efimov quantum states are a solution to the notoriously diffucult quantum mechanical three-body problem. Efimov predicted that three particles would enter into a bound state (called a trimer) if for each pair the corresponding two-body state (the dimer) could be made to disappear. Surprisingly, his findings are independent of the precise nature of the two-body interaction, and Efimov trimer states are thus generic entities that should be observable in various domains of few-body quantum physics. In this universality lies the great interest that has kept the search for Efimov states going for over 35 years.

These trimer states have no classical analogue, because the binding mechanism is purely quantum mechanical. In order to characterize Efimov trimers, one has to fully rely on the description in terms of their quantum mechanical wavefunctions. These wavefunctions belong to the class of quantum halo states, which feature the greatest probability of finding its constituents at mutual distances which are classically forbidden. A brief descripition of Efimov's scenario is found here.

Efimov trimer states appear in the limit where the two-body interaction is too weak to support a two-body bound state (also called dimer state). This remarkable and counter-intuitive property is symbolised by three entangled rings which would fall apart if any one ring is removed. Due to a close resemblance with the symbol of the Borromeo family of northern italy, these states are also termed Borromean states.

An artist's impression of Borromean states: Remove any one ring and the other two will fall apart. The right picture displays the Borromeo family symbol. (Pictures taken from here & here).

Efimov also explored the effect of his trimers on collisions among three particles and particle-dimer scattering [4]. In our experiments we work with gases from Cs atoms which we cool down to a few billionths of a degree Kelvin above the absolute zero. At these extremely low energies the quantum character of matter dominates the behavior of the gas. Also, we can tune the interaction strength simply by varying the magnetic field strength using a Feshbach resonance [5]. This makes our systems ideal candidates for the search for Efimov quantum states. The fingerprint of Efimov trimers in our system appears as resonant enhancement and suppression of three-body collisions as a function of the two-atom interaction strength.



[1] Evidence for Efimov quantum states in an ultracold gas of caesium atoms
T. Kraemer, M. Mark, P. Waldburger, J. G. Danzl, C. Chin, B. Engeser, A. D. Lange, K. Pilch, A. Jaakkola, H.-C. Nägerl and R. Grimm
Nature 440, 315-318 (16 March 2006), doi:10.1038/nature04626

[2] Weakly bound states of three resonantly-interacting particles
V. N. Efimov
(original, russian) download PDF

[3] Weakly bound states of three resonantly-interacting particles
V. N. Efimov
(english translation ) download PDF

[4] Low-energy properties of three resonantly interacting particles
V. Efimov
Sov. J. Nuc. Phys. 29, 546 (1979)

[5] Observation of Feshbach resonances in a Bose–Einstein condensate
Nature 392, 151 - 154 (12 March 1998), doi:10.1038/32354


Related Articles

[6] News and Views: Quantum physics: A ménage à trois laid bare
Brett D. Esry and Chris H. Greene
Nature 440, 289-290 (16 March 2006), doi:10.1038/440289b

[7] Editor's Summary: Three Into One Does Go

[8] Geheimnisvolle Quantenzustände erstmals beobachtet

[9] Atoms in new state of matter behave like Three Musketeers: all for one, one for all
University of Chicago News Office


The Teams

The experiments have been conducted in the group of Prof. Rudi Grimm at the Institut für Experimentalphysik, University of Innsbruck, as a joined effort of the LevT- and GOST-project.

LevT project homepage

GOST project

Additional picture material can be found here



We are supported by the Austrian Science Fund (Fonds zur Förderung der wissenschaftlichen Forschung, FWF) in the frame of the Spezialforschungsbereich F15 "Control and Measurement of Coherent Quantum Systems" and by the European Union in the frame of the Cold Molecules TMR Network.



last change: 06-03-20 by JH