Heteronuclear Efimov Scenario with Positive Intraspecies Scattering Length

We investigate theoretically and experimentally the heteronuclear Efimov scenario for a three-body system that consists of two bosons and one distinguishable particle with positive intraspecies scattering lengths. The three-body parameter at the three-body scattering threshold and the scaling factor between consecutive Efimov resonances are found to be controlled by the scattering length between the two bosons, approximately independent of short-range physics. We observe two excited-state Efimov resonances in the three-body recombination spectra of an ultracold mixture of fermionic ${}^6\mathrm{Li}$ and bosonic ${}^{133}\mathrm{Cs}$ atoms close to a Li-Cs Feshbach resonance, where the Cs-Cs interaction is positive. Deviation of the obtained scaling factor of 4.0(3) from the universal prediction of 4.9 and the absence of the ground state Efimov resonance shed new light on the interpretation of the universality and the discrete scaling behavior of heteronuclear Efimov physics.

Figure 1

Adiabatic hyperspherical potentials $U$ for a $BBX$ system with a mass ratio of $m_B/m_X=22.1$ and $a_{BB}=-1$ (left panel) and $a_{BB}=1$ (right panel) in the universal zero-range model. The solid curves correspond to interspecies scattering length $a_{BX}$ with respective values $\infty$, $-10$, $-5$, $-3$ in units of $|a_{BB}|$. The energy unit in this figure is ${\hslash }^2/2\mu a_{BB}^2$, where $\mu$ is the three-body reduced mass.

Figure 2

Calculated CsCsLi energy spectra for the three deepest Efimov states for experimental scattering lengths that correspond to the 843 G (circles, left panel) and 889 G (squares, right panel) Li-Cs Feshbach resonances and $a_{\mathrm{CsCs}}\approx -1500a_0$ and $a_{\mathrm{CsCs}}\approx 190a_0$, respectively [38]. The atom-dimer scattering threshold $\mathrm{CsCs}+\mathrm{Li}$ for the latter case is shown as a dashed blue line. Arrows indicate the positions at which the Efimov states would either cross the $\mathrm{Cs}+\mathrm{Cs}+\mathrm{Li}$ scattering threshold or become predissociative into a $\mathrm{CsCs}+\mathrm{Li}$ state. The error bars represent the width of the corresponding Efimov state. Missing error bars indicate a width that is smaller than the symbol size.

Figure 3

Experimental and theoretical Cs-Cs-Li three-body recombination rate spectra at a temperature of 120 (blue squares, blue solid line) and 320 nK (red circles, red dotted line) for $a_{\mathrm{CsCs}}\approx 190a_0$. The error bars represent the statistical errors from bootstrapping, magnetic field uncertainties, and technical limit due to Cs-Cs-Cs three-body losses. The grayed areas correspond to the zero-temperature Efimov resonance positions, which are extracted from the calculated trimer energy spectra (see text). The arrow in the left panel indicates the approximate position of a possible four-body resonance.