Evidence for Universal Four-Body States Tied to an Efimov Trimer

arXiv:0903.1276v2 [cond-mat.other] 9 Apr 2009 Evidence for universal four-body states tied to an Efimov trimer F. Ferlaino,1 S. Knoop,1 M. Berninger,1 W. Harm,1 J. P. D’Incao,2,3 H.-C. N¨agerl,1 and R. Grimm1,2 1Institut f¨ur Experimentalphysik and Zentrum f¨ur Quantenphysik, Universit¨at Innsbruck, 6020 Innsbruck, Austria 2Institut f¨ur Quantenoptik und Quanteninformation, ¨Osterreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria 3JILA, University of Colorado and NIST, Boulder, Colorado 80309-0440, USA (Dated: October 26, 2018) We report on the measurement of four-body recombination rate coefficients in an atomic gas. Our results obtained with an ultracold sample of cesium atoms at negative scattering lengths show a resonant enhancement of losses and provide strong evidence for the existence of a pair of four-body states, which is strictly connected to Efimov trimers via universal relations. Our findings confirm recent theoretical predictions and demonstrate the enrichment of the Efimov scenario when a fourth particle is added to the generic three-body problem. PACS numbers: 03.75.-b, 34.50.Cx, 67.85.-d, 21.45.-v Few-body physics produces bizarre and counterintuitive phenomena, with the Efimov effect representing the major paradigm of the field [1]. Early in the 1970s, Efimov found a solution to the quantum three-body problem, predicting the existence of an infinite series of universal weakly bound three- body states. Surprisingly, these Efimov trimers can even exist under conditions where a weakly bound dimer state is absent [2, 3, 4]. An essential prerequisite for the Efimov effect is a large two-body scattering length a, far exceeding the char- acteristic range of the interaction potential. Ultracold atomic systems with tunable interactions [5] have opened up unprece- dented possibilities to explore such few-body quantum sys- tems under well controllable experimental conditions. In par- ticular, a can be made much larger than the van der Waals length rvdW [6], the range of the interatomic interaction. In the last few years, signatures of Efimov states have been observed in ultracold atomic and molecular gases of cesium atoms [7, 8], and recently in three-component Fermi gases of 6Li [9, 10], in a Bose gas of 39K atoms [11], and in mixtures of 41K and 87Rb atoms [12]. In all these experiments, Efimov states manifest themselves as resonantly enhanced losses, ei- ther in atomic three-body recombination or in atom-dimer re- laxation processes. The recent observations highlight the uni- versal character of Efimov states, and they also point to a rich playground for future experiments. As a next step in complexity, a system of four identical bosons with resonant two-body interaction challenges our un- derstanding of few-body physics. The extension of univer- sality to four-body systems has been attracting increasing in- terest both in theory [14, 15, 16, 17, 18, 19] and experi- ment [13]. A particular question under debate is the pos- sible relation between universal three- and four-body states [14, 15, 16, 17, 19]. In this context, Hammer and Platter predicted the four-body system to support universal tetramer states in close connection with Efimov trimers [17]. Recently, von Stecher, D’Incao, and Greene presented key predictions for universal four-body states [19]. For each Efi- mov trimer, they demonstrate the existence of a pair of uni- versal tetramer states according to the conjecture of Ref. [17]. Such tetramer states are tied to the corresponding trimer through simple universal relations that do not invoke any four- A + A + A + A D + A + A D + D T + A Tetra1 Tetra2 FIG. 1: (color online) Extended Efimov scenario describing a univer- sal 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 (Tetra1 and Tetra2) associated with each Efimov trimer (T). For illustrative purposes, we have artificially re- duced the universal Efimov scaling factor from 22.7 to about 2. The shaded regions indicate the scattering continuum associated with the relevant dissociation threshold. The four-body threshold is at zero energy and refers to four free atoms (A+A+A+A). In the a > 0 re- gion, the dimer-atom-atom threshold (D+A+A) and the dimer-dimer threshold (D+D) are also depicted. The weakly bound dimer, only existing for a ≫rvdW > 0, has universal halo character and its bind- ing energy is given by ¯h2/(ma2) [2, 13]. The open arrow marks the intersection of the first Efimov trimer (T) with the atomic threshold, while the filled arrows indicate the corresponding locations of the two universal tetramer states. body parameter [14, 16, 19]. The authors of Ref. [19] suggest resonantly enhanced four-body recombination in an atomic gas as a probe for such universal tetramer states. They also find hints on the existence of one of the predicted four-body resonances by reinterpreting our earlier recombination mea- surements

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