Role of the intraspecies scattering length in the Efimov scenario with large mass difference

We experimentally and theoretically study the effect of the intraspecies scattering length onto the heteronuclear Efimov scenario, following up on our earlier observation of Efimov resonances in an ultracold Cs-Li mixture for negative [Pires et al., Phys. Rev. Lett. 112, 250404 (2014)] and positive Cs-Cs scattering length [Ulmanis et al., Phys. Rev. Lett. 117, 153201 (2016)]. Three theoretical models of increasing complexity are employed to quantify its influence on the scaling factor and the three-body parameter: a simple Born-Oppenheimer picture, a zero-range theory, and a spinless van der Waals model. These models are compared to Efimov resonances observed in an ultracold mixture of bosonic ${}^{133}\mathrm{Cs}$ and fermionic ${}^6\mathrm{Li}$ atoms close to two Cs-Li Feshbach resonances located at 843 G and 889 G, characterized by different sign and magnitude of the Cs-Cs interaction. By changing the sign and magnitude of the intraspecies scattering length different scaling behaviors of the three-body loss rate are identified, in qualitative agreement with theoretical predictions. The three-body loss rate is strongly influenced by the intraspecies scattering length.

Figure 1

Born-Oppenheimer energy spectrum for the Cs-Cs-Li system vs the intraspecies scattering length $a_{\mathrm{CsCs}}$. The spectrum is obtained for $a_{\mathrm{CsLi}}\to \infty$ (black solid lines). For comparison the energies of the two least bound ${\mathrm{Cs}}_2$ states are displayed (red dashed lines).

Figure 2

Adiabatic hyperspherical potentials $U$ for a $BBX$ system with a mass ratio of $m_B/m_X=22.1$ and $a_{BB}<0$ (left panel) and $a_{BB}>0$ (right panel) in the universal zero-range model. The curves correspond to interspecies scattering lengths $a_{BX}$ with respective values $\infty$, $-10$, $-5$, $-3$ in units of $\left|a_{BB}\right|$. Figure taken from [8].

Figure 3

Cs-Cs-Li adiabatic hyperspherical potentials $U$ within the spinless vdW theory for intraspecies scattering lenths $a_{\mathrm{CsCs}}=-1500a_0$ (left panel) and $a_{\mathrm{CsCs}}=+200a_0$ (right panel) in units of the Cs-Li vdW energy $E_{\mathrm{vdW}}^{\mathrm{CsLi}}$. In both cases the interspecies scattering length is $a_{\mathrm{CsLi}}=-400a_0$.

Figure 4

Interspecies scattering lengths $a_{\mathrm{CsLi}}$ for the channels $\mathrm{Li}\left|1/2,+1/2\right.〉\oplus \mathrm{Cs}\left|3,3\right.〉$ (upper panel, black line), $\mathrm{Li}\left|1/2,-1/2\right.〉\oplus \mathrm{Cs}\left|3,3\right.〉$ (upper panel, blue dash dotted line), and intraspecies scattering length $a_{\mathrm{CsCs}}$ for Cs atoms in the ground state $\mathrm{Cs}\left|3,3\right.〉\oplus \mathrm{Cs}\left|3,3\right.〉$ (lower panel, red dashed line). Scattering lengths taken from [36, 37].

Figure 5

(a),(c) Cs-Cs-Li three-body recombination rate spectra at temperatures of (a) 120 nK (blue diamonds and squares, blue solid line) and 450 nK (red circles, red dash-dotted line) close to the 843 G Cs-Li Feshbach resonance and Cs-Cs scattering length $a_{\mathrm{CsCs}}\approx -1500a_0$ and (c) 120 nK (blue squares, blue solid line) and 320 nK (red circles, red dash-dotted line) close to the 889 G Cs-Li Feshbach resonance and Cs-Cs scattering length $a_{\mathrm{CsCs}}\approx +190a_0$. The experimental data are taken from [6, 8, 20]. The insets show a zoom into the region of the two excited Efimov resonances. The error bars represent statistical errors from bootstrapping, magnetic-field uncertainties, and the technical limit due to Cs-Cs-Cs three-body losses. The blue solid lines and red dash-dotted lines show the calculated three-body loss rates from the spinless vdW theory for the lower and higher temperature, respectively. Experimental data have been scaled by a numerical constant, well within the absolute error, to fit the theory (see Ref. [20]). (b),(d) Calculated CsCsLi energy spectra for the three deepest bound Efimov states for experimental scattering lengths that correspond to the (b) 843 G and (d) 889 G Cs-Li Feshbach resonances, respectively. The atom-dimer scattering threshold $\mathrm{CsCs}+\mathrm{Li}$ for the latter case is shown as a dashed blue line. The error bars represent the width of the corresponding Efimov state. Missing error bars indicate a width that is smaller than the symbol size. The grayed areas correspond to the positions at which the Efimov states cross the $\mathrm{Cs}+\mathrm{Cs}+\mathrm{Li}$ scattering threshold and their widths represent their uncertainty.

Figure 6

Cs-Cs-Li three-body recombination rate spectra with positive (squares) and negative (circles) intraspecies interaction. The power laws $\propto a_{\mathrm{CsLi}}^4$ (dotted line) and $\propto a_{\mathrm{CsLi}}^2$ (dashed line) are drawn as guides to the eye. The error bars represent the statistical errors from bootstrapping, magnetic-field uncertainties, and technical limit due to Cs-Cs-Cs three-body losses. The data were taken close to the 889 G Cs-Li Feshbach resonance at a temperature of 320 nK, where $a_{\mathrm{CsCs}}\approx +190a_0$, and close to the 843 G Cs-Li Feshbach resonance at a temperature of 450 nK, where $a_{\mathrm{CsCs}}\approx -1500a_0$.