We identify two qualitatively different mechanisms that control three-body recombination in a spinpolarized gas near zero temperature. A universal curve describes the recombination rate versus the two-body scattering length a. It grows as a 4 for large jaj, with different mechanisms for a , 0 and a . 0. Our calculations document a previously established mechanism that causes K 3 to grow rapidly as the two-body scattering length a increases toward 1`, and a new tunneling mechanism that produces an even stronger enhancement of K 3 as a ! 2`. The expectations based on these two mechanisms can be modified by quantum mechanical interference or resonance effects.

We present the first theoretical treatment that accounts in detail for a recent observation of overlapping Bose-Einstein condensates of two different 87 Rb hyperfine states [C. J. Myatt et al., Phys. Rev. Lett. 78, 586 (1997)]. Despite the complicated geometry, we have completed a threedimensional Hartree-Fock calculation for the coupled condensates. The calculation explains a number of its key properties: (i) The manner in which one condensate partially wraps around the other, (ii) the mean separation between the two condensates including the effects of gravity and of their mutual interaction, and (iii) the surprisingly long lifetime of the trap. [S0031-9007(97)03154-2]

In recent years extensive theoretical and experimental studies of universal few-body physics have led to advances in our understanding of universal Efimov physics. Whereas theory had been the driving force behind our understanding of Efimov physics for decades, recent experiments have contributed an unexpected discovery. Specifically, measurements have found that the so-called threebody parameter determining several properties of the system is universal, even though fundamental assumptions in the theory of the Efimov effect suggest that it should be a variable property that depends on the precise details of the short-range two-and three-body interactions. The present Letter resolves this apparent contradiction by elucidating previously unanticipated implications of the two-body interactions. Our study shows that the three-body parameter universality emerges because a universal effective barrier in the three-body potentials prevents the three particles from simultaneously getting close together. Our results also show limitations on this universality, as it is more likely to occur for neutral atoms and less likely to extend to light nuclei. PACS numbers: 31.15.ac,31.15.xj, In the early 70's, Vitaly Efimov predicted a strikingly counterintuitive quantum phenomenon [1], today known as Efimov effect: in three-body systems for which the two-body s-wave scattering length a is much larger than the characteristic range r 0 of the two-body interaction, an infinite number of three-body bound states can be formed even when the short-range two-body interactions are too weak to bind a two-body state (a < 0). The Efimov effect, once considered a mysterious and esoteric effect, is today a reality that many experiments in ultracold quantum gases have successfully observed and continued to explore [2][3][4][5][6][7][8][9][10][11][12][13][14]. One of the most fundamental assumptions underlying our theoretical understanding of this peculiar effect is that the weakly bound three-body energy spectrum, and other low-energy three-body scattering observables, should depend on a three-body parameter that encapsulates all details of the interactions at short distances [15]. For this reason, the three-body parameter has been viewed as nonuniversal since its value for any specific system would depend on the precise details of the underlying two-and three-body interactions [16][17][18].In nuclear physics, this picture seems be consistent, i.e., three-body weakly bound state properties seem to be sensitive to the nature of the two-and three-body short-range interactions [17]. More recently, however, Berninger et al. [3] have directly explored this issue for alkali atoms whose scattering lengths are magnetically tuned near different . Even though the short-range physics can be expected to vary from one resonance to another, Efimov resonances were found for values of the magnetic field at which a=a − 3b =−9.1(2)r vdW , where r vdW is the van der Waals length [20, 21]. Therefore, in each of these cases, the three-body parameter was approximatel...

The adiabatic hyperspherical method is used to investigate the spectrum of the helium trimer and to explore effects on the spectrum of varying the helium masses as well as the interaction strength. When a realistic helium dimer potential is adopted, only two isotopic combinations are observed to have three-body bound states: 4 He 3 and 4 He 2 3 He. By artificially adjusting the dimer potential, we also determine the range of interaction strengths for which halo states can result. The existence of Efimov states for both physical and unphysical systems is also examined.