Observation of an Efimov spectrum in an atomic system

Abstract

In 1970 V. Efimov predicted a puzzling quantummechanical effect that is still of great interest today. He found that three particles subjected to a resonant pairwise interaction can join into an infinite number of loosely bound states even though each particle pair cannot bind. Interestingly, the properties of these aggregates, such as the peculiar geometric scaling of their energy spectrum, are universal, i.e. independent of the microscopic details of their components. Despite an extensive search in many different physical systems, including atoms, molecules and nuclei, the characteristic spectrum of Efimov trimer states still eludes observation. Here we report on the discovery of two bound trimer states of potassium atoms very close to the Efimov scenario, which we reveal by studying three-particle collisions in an ultracold gas. Our observation provides the first evidence of an Efimov spectrum and allows a direct test of its scaling behaviour, shedding new light onto the physics of few-body systems.From nuclei, atoms and molecules up to galaxies, our complex world is made up of many kinds of aggregates whose properties depend on the details of the interactions between their components. This scenario is expected to drastically change as one moves to the world of few neutral quantum particles. The physics of these systems is typically dominated by two-body interactions, which in the limit of vanishing collision energies can be described by a single parameter, namely the s-wave scattering length, independently from the nature of the particles and of the microscopic shape of their interaction 1,2 . If the two-body scattering length becomes resonantly large, the binding of few such particles into larger aggregates is predicted to become universal, in the sense that its properties depend only on the scattering length and few other global parameters 3 .These expectations have been so far verified only for twobody bound states 2 , and even the seemingly simple case of three particles is still under investigation. In this frame, a landmark theoretical result was obtained in 1970 by Efimov 4,5 . He extended previous studies 6 to show that three identical bosons with large two-body scattering length a, even without two-body bound states, can form weakly bound trimer states with size greatly exceeding the characteristic range r 0 of the two-body potential. The binding properties of such states follow a universal behaviour, regardless of the microscopic peculiarities of their components and of their interaction. Efimov indeed identified an effective three-particle interaction potential of the form -(s 0 2 +1/4)/R 2 , where R is the overall size of the three-body system and s 0 1.00624 is a universal parameter 4 . This simple potential is known to support an infinite number of bound states whose energy spectrum exhibits a peculiar geometric scaling where two consecutive states are linked by the relation E n =E n-1 exp(-2/s 0 ). This perfect scaling is predicted to apply only for the special case of a system with infinite...

Universality of Brunnian (N-body Borromean) four- and five-body systems

“…Recently, three experiments evidenced two four-body bound states connected to an Efimov trimer [14][15][16], in accordance with the theoretical predictions of Ref. [12].…”

Semiclassical analysis of the Efimov energy spectrum in the unitary limit

“…A signature of the Efimov spectrum is its geometric scaling, with the ratio of the adjacent energy levels being constant. This was predicted by Efimov [1] and has been verified by recent experiments [4].…”

Three-body parameter for Efimov states inLi6

“…The scattering length has a pole at resonance, corresponding to a two-body bound state exactly at threshold. Signatures of Efimov states were first observed in an ultracold gas of cesium atoms [7] and have since been found in many other systems, including other bosonic gases [8][9][10][11][12][13], three-component fermionic spin mixtures [14][15][16][17], and mixtures of atomic species [18][19][20][21]. Moreover, extensions of the Efimov scenario to universal states of larger clusters [22][23][24] have been demonstrated in experiments [9,25,26], highlighting the general nature of universal few-body physics.…”