For alkali atoms, $\ell$ is given by the van der Waals length $\ell_{vdW}$ which quantifies the range of the interaction. Examples of universal two-body states can be found in different branches of physics such as atomic physics, nuclear physics, and high-energy physics [@Hammer:2010kp; @Platter:2009gz]. Universal properties also exist for more than two particles. Systems of three identical bosons have an infinite number of geometrically spaced low-energy bound states ([*Efimov trimers*]{}) with an accumulation point at zero energy when the scattering length is taken to infinity and the range of the interaction is taken to zero [@Efimov]. In this so-called [*unitary limit*]{}, the binding energies of two successive trimers are related by a multiplicative factor of approximately $22.7^2\approx 515$. This remarkable feature is the consequence of a discrete scaling symmetry with a scaling factor $e^{\pi/s_0}\approx22.7$ where $s_0\approx 1.00624$ for identical bosons. For more complicated systems, the scaling factor depends on the mass ratios and the spin of the components. We will refer to phenomena that result from the discrete scale invariance in the three-body sector as [*Efimov physics*]{} [@Braaten:2004rn]. Corrections to Efimov physics in a process with typical wave number $k$ are suppressed by $\ell/a$ and by $ka$.

Efimov trimers in 