Origin of the Three-Body Parameter Universality in Efimov Physics

Abstract

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...

Three-body parameter for Efimov states inLi6

“…Efimov states may be considered to be supported by an effective adiabatic potential that is a function of the hyperradius R. For a zero-range two-body potential with large scattering length a, this potential is attractive and proportional to R −2 for R |a| [44] and supports an infinite number of bound states as a → ±∞. For potential curves with long-range van der Waals tails, however, Wang et al [29] have shown that the effective adiabatic potential reaches a minimum and then rises to a wall or barrier near R = 2r vdW . The positions of the minimum and wall depend to some extent on the details of the two-body potential and the number of bound states it supports but become nearly universal as the number of two-body bound states increases.…”

“…However, in atomic systems it has been found experimentally [13,27] that the 3BP is nearly constant when expressed in terms of the van der Waals length r vdW [6], which quantifies the dispersion interaction between two neutral atoms. We refer to this feature of Efimov physics as van der Waals universality of the 3BP, and it has been the subject of a number of theoretical investigations [28][29][30][31][32][33].…”

Efimov-driven phase transitions of the unitary Bose gas

“…This is assured through a parameter, the three-body hard core R 0 , that bounds from below the energies of the Efimov states. In cold-atom systems, this parameter is on the order of the van der Waals length l vdW [17][18][19] . Experimental coldatom systems are metastable, and particles disappear from the trap into deeply-bound states via the notorious three-body losses.…”

Comparing and contrasting nuclei and cold atomic gases

“…Some recent theoretical works have addressed the corrections coming from the finite range of inter-atomic potentials in the coordinate-space formalism (Thøgersen et al 2008b, Thøgersen, Fedorov, Jensen, Esry & Wang 2009, Wang, D'Incao & Esry 2011, Sørensen et al 2011) and using momentum-space effective field theory (Massignan & Stoof 2008, Platter et al 2009, Ji et al 2010, Naidon et al 2012. In particular, the study of (Massignan & Stoof 2008) provide results that are close to the experimental data.…”

“…This implies that there is some generic universality even in the three-body parameter which cannot be captured by simple zero-range models that need the ρ 0 supplied from elsewhere. A number of theoretical works have presented various models that explain the observations (Naidon et al 2012, Chin 2011, Wang, D'Incao, Esry & Greene 2012, Schmidt et al 2012 and it seems clear that the two-body inter-atomic potential is the culprit since it has a large repulsion at short distance which will naturally provide a threebody cut-off (Sørensen et al 2012a, Sørensen et al 2012b. However, there is still a question of how the number of bound two-body states in the inter-atomic potential influences a − (Wang, D'Incao, Esry & Greene 2012, Sørensen et al 2012a).…”