Excited Thomas-Efimov levels in ultracold gases

Abstract

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 $0.08\phantom{\rule{0.3em}{0ex}}\mathrm{T}$ $(800\phantom{\rule{0.3em}{0ex}}\mathrm{G})$.