Dynamic super Efimov effect

The super Efimov effect is a recently proposed three-body effect characterized by a double-exponential scaling, which has not yet been observed experimentally. Here, we present the general dynamic equations determining the cloud size of a scale-invariant quantum gas in a time-dependent harmonic trap. We show that a double-logarithmic periodicity as the hallmark of the super Efimov effect emerges when the trap frequency is decreased with a specially designed time dependence. We also demonstrate that this dynamic super Efimov effect can be realized with realistic choices of parameters in current experiments.

Figure 1

A schematic plot of the time-varying trapping frequency $\omega \left(t\right)$ for observing the dynamic super Efimov effect.

Figure 2

(a) The mean square of the cloud size ${\mathcal{R}}^2\left(t\right)/{\mathcal{R}}_0^2$, where the dashed line denotes that the trap frequency $\omega \left(t\right)$ decreases from 500 to 50 Hz. (b) ${\mathcal{R}}^2\left(t\right)/[Atln(t/t^{*})]$ as a function of $lnln(t/t^{*})$. Here we have set $\lambda =0.005$, $t^{*}=0.3\mathrm{ms}$. The shaded area corresponds to an error bar of $5\%$ of the cloud size.