Generally, the three-body recombination (TBR) of the ultracold helium atoms in the zero-collision-energy limit could be described by the original zero-range (Efimov) universal function [E. Braaten, D. Kang, and L. Platter, Phys. Rev. A 75, 052714 (2007)] using the scattering length $a$ of the He-He interaction and a three-body parameter ${a}_{*}$ as input, where ${a}_{*}$ is associated with the positive scattering length at which an interference minimum in the TBR rate occurs at the threshold. This universal property has been reinvestigated by considering various post-Born-Oppenheimer (post-BO) effects on the relevant scattering process. It is found that a linear correction to $1/{a}_{*}$ versus $1/a$ should be introduced to give a better description of these considered TBR cases because of the finite-range effects. Particularly, such a correction may be ascribed not only to the general scattering properties associated with the Efimov channel at the short hyperradial distance, but also to the tunneling probability in the lowest incident channel. In addition, a successful fit of the modified universal function that includes correctly the finite-range effects [E. Garrido, M. Gattobigio, and A. Kievsky, Phys. Rev. A 88, 032701 (2013)] or the zero-range universal function with a linearly variational $1/{a}_{*}$ versus $1/a$ to numerically accurate data also indicates a clear manifestation of the van der Waals universality. Finally, the post-BO effects on the TBR process for the partial wave with the total angular momentum $J>0$ are also discussed.Generally, the three-body recombination (TBR) of the ultracold helium atoms in the zero-collision-energy limit could be described by the original zero-range (Efimov) universal function [E. Braaten, D. Kang, and L. Platter, Phys. Rev. A 75, 052714 (2007)] using the scattering length $a$ of the He-He interaction and a three-body parameter ${a}_{*}$ as input, where ${a}_{*}$ is associated with the positive scattering length at which an interference minimum in the TBR rate occurs at the threshold. This universal property has been reinvestigated by considering various post-Born-Oppenheimer (post-BO) effects on the relevant scattering process. It is found that a linear correction to $1/{a}_{*}$ versus $1/a$ should be introduced to give a better description of these considered TBR cases because of the finite-range effects. Particularly, such a correction may be ascribed not only to the general scattering properties associated with the Efimov channel at the short hyperradial distance, but also to the tunneling probability in the lowest incident channel. In addition, a successful fit of the modified universal function that includes correctly the finite-range effects [E. Garrido, M. Gattobigio, and A. Kievsky, Phys. Rev. A 88, 032701 (2013)] or the zero-range universal function with a linearly variational $1/{a}_{*}$ versus $1/a$ to numerically accurate data also indicates a clear manifestation of the van der Waals universality. Finally, the post-BO effects on the TBR process for the partial wave with the total angular momentum $J>0$ are also discussed.

Physical Review ADec 6, 20231 citation

Scattering models for ultracold atoms

Eric Braaten, Masaoki Kusunoki, Dongqing Zhang

arXiv:0709.0499Annals of PhysicsFeb 20, 200877 citations

Ultra-low energy elastic scattering in a system of three He atoms

Differential Faddeev equations in total angular momentum representation are used for the first time to investigate ultra-low energy elastic scattering of a helium atom on a helium dimer. Six potential models of interatomic interaction are investigated. The results improve and extend the Faddeev equations based results known in literature. The employed method can be applied to investigation of different elastic and inelastic processes in three- and four-atomic weakly bounded systems below three-body threshold. 1Differential Faddeev equations in total angular momentum representation are used for the first time to investigate ultra-low energy elastic scattering of a helium atom on a helium dimer. Six potential models of interatomic interaction are investigated. The results improve and extend the Faddeev equations based results known in literature. The employed method can be applied to investigation of different elastic and inelastic processes in three- and four-atomic weakly bounded systems below three-body threshold. 1

Jan 1, 20020 citations

Two-body scattering in ultracold dilute atom gases

J. Piili

May 28, 20120 citations

Excited Thomas-Efimov levels in ultracold gases

Mark D. Lee, Thorsten Köhler, Paul S. Julienne

Since the early days of quantum physics, the complex behavior of three interacting particles has been the subject of numerous experimental and theoretical studies. In a recent Letter to Nature, Kraemer et al. [Nature (London) 440, 315 (2006)] report on experimental ``evidence for Efimov quantum states'' in an ultracold gas of cesium atoms. Such quantum states refer to an infinite series of energy levels of three identical Bose particles, accumulating at the threshold for dissociation as the scattering length of each pair is tuned to infinity. Whereas the existence of a single Efimov state has been predicted for three helium atoms, earlier experimental studies concluded that this elusive state had not been found. In this paper we show by an intuitive argument and full numerical calculations that the helium and cesium experiments actually provide evidence of the same, ground state of this trimer spectrum, which the helium experimentalists and pioneering theoretical studies had not associated with Efimov's effect. Unlike the helium trimer, the observed $^{133}\mathrm{Cs}_{3}$ resonance refers to a Borromean molecular state. We discuss how as yet unobserved, excited Efimov quantum states might be detected in ultracold gases of $^{85}\mathrm{Rb}$ and of $^{133}\mathrm{Cs}$ at magnetic field strengths in the vicinity of $0.08\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ $(800\phantom{\rule{0.3em}{0ex}}\mathrm{G})$ .Since the early days of quantum physics, the complex behavior of three interacting particles has been the subject of numerous experimental and theoretical studies. In a recent Letter to Nature, Kraemer et al. [Nature (London) 440, 315 (2006)] report on experimental ``evidence for Efimov quantum states'' in an ultracold gas of cesium atoms. Such quantum states refer to an infinite series of energy levels of three identical Bose particles, accumulating at the threshold for dissociation as the scattering length of each pair is tuned to infinity. Whereas the existence of a single Efimov state has been predicted for three helium atoms, earlier experimental studies concluded that this elusive state had not been found. In this paper we show by an intuitive argument and full numerical calculations that the helium and cesium experiments actually provide evidence of the same, ground state of this trimer spectrum, which the helium experimentalists and pioneering theoretical studies had not associated with Efimov's effect. Unlike the helium trimer, the observed $^{133}\mathrm{Cs}_{3}$ resonance refers to a Borromean molecular state. We discuss how as yet unobserved, excited Efimov quantum states might be detected in ultracold gases of $^{85}\mathrm{Rb}$ and of $^{133}\mathrm{Cs}$ at magnetic field strengths in the vicinity of $0.08\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ $(800\phantom{\rule{0.3em}{0ex}}\mathrm{G})$.

arXiv:cond-mat/0702178Physical Review AJul 30, 200769 citations

a

of the He-He interaction and a three-body parameter

{a}_{*}

as input, where

{a}_{*}

is associated with the positive scattering length at which an interference minimum in the TBR rate occurs at the threshold. This universal property has been reinvestigated by considering various post-Born-Oppenheimer (post-BO) effects on the relevant scattering process. It is found that a linear correction to

1/{a}_{*}

versus

1/a

should be introduced to give a better description of these considered TBR cases because of the finite-range effects. Particularly, such a correction may be ascribed not only to the general scattering properties associated with the Efimov channel at the short hyperradial distance, but also to the tunneling probability in the lowest incident channel. In addition, a successful fit of the modified universal function that includes correctly the finite-range effects [E. Garrido, M. Gattobigio, and A. Kievsky, Phys. Rev. A 88, 032701 (2013)] or the zero-range universal function with a linearly variational

1/{a}_{*}

versus

1/a

to numerically accurate data also indicates a clear manifestation of the van der Waals universality. Finally, the post-BO effects on the TBR process for the partial wave with the total angular momentum

J>0

are also discussed.

^{133}\mathrm{Cs}_{3}

resonance refers to a Borromean molecular state. We discuss how as yet unobserved, excited Efimov quantum states might be detected in ultracold gases of

^{85}\mathrm{Rb}

and of

^{133}\mathrm{Cs}

at magnetic field strengths in the vicinity of

0.08\phantom{\rule{0.3em}{0ex}}\mathrm{T}

(800\phantom{\rule{0.3em}{0ex}}\mathrm{G})