Efimov Physics and the Three-Body Parameter for Shallow van der Waals Potentials

Abstract

Extremely weakly-bound three-boson systems are predicted to exhibit intriguing universal properties such as discrete scale invariance. Motivated by recent experimental studies of the ground and excited helium trimers, this work analyzes the three-body parameter and the structural properties of three helium atoms as the s-wave scattering length is tuned artificially. Connections with theoretical and experimental studies of the Efimov scenario as it pertains to cold atom systems are made.

Energy and structural properties ofN-boson clusters attached to three-body Efimov states: Two-body zero-range interactions and the role of the three-body regulator

“…This relationship is nowadays being attributed to van der Waals universality. Moreover, the binding momentum spacing of 23.4 between the ground state and the first excited state is quite close to the spacing of 22.6944 exhibited by consective pure Efimov trimers [40]. It is thus interesting to investigate if van der Waals universality exists for N > 3, i.e., to answer the question whether or not the N -body ground state energy depends on the short-range details of the two-body van der Waals potential.…”

“…Specifically, the trimer ground state binding momentum κ at unitarity is, to a good approximation, determined by the van der Waals length L vdW [27,39] and independent of the short-range details. For the two-body Lenard-Jones potential, one finds κ [40], where L vdW = ( √ mc 6 / ) 1/2 /2. This relationship is nowadays being attributed to van der Waals universality.…”

“…(i) For the models 2bG, 2bLJ, 2b10-6, and 2b8-6, the hyperangular and hyperradial degrees of freedom do not separate and the difference between their angular distributions and those for the twobody zero-range models provides valuable insights (see Ref. [40]). (ii) For the N -body clusters, the angular distributions, which depend on both the hyperangles and the N -particle hyperradius, can serve to monitor the three-body correlations.…”

Efimov–van der Waals universality for ultracold atoms with positive scattering lengths

“…[3] for a summary of such experimental findings). Theoretical works then successfully confirmed and interpreted the universality of the a − parameter [15][16][17][18][19][20][21] and consolidated a new universal picture for Efimov physics in atomic systems dominated by van der Waals forces.…”

“…[64], indicating that both sand d-wave mixing and finite-width effects might be at the heart of deviations of the three-body parameters for a > 0 here obtained, as well as the deviations among the currently available experimental data (Table III). A fundamental difference between the physics for a < 0 (where a more robust universal picture was found [15][16][17][18][19][20][21] -see Refs. [3,47] for a summary of such experimental findings) and for a > 0 is that corrections for the energy of the weakly bound s-wave dimer, whether originated from mixing of s-and d-wave interactions or finite-width effects, should already lead to modifications on the a > 0 three-body parameters.…”