The Efimov effect describes that in a three-body system of identical bosons, an accumulation of bound states occurs in the limit of zero energy and diverging scattering length of the two-particle interaction. Recent experimental successes have shown signatures of those bound states, called Efimov trimers. The experiments provide evidence of the existence of Efimov trimers only in an indirect way. The short life-time of the trimers is prohibiting a direct study. One idea of stabilizing the Efimov trimers is to put them into an optical lattice.
As an approximation of three particles on a single lattice site, we study a three-particle system in a harmonic potential. We present a natural extension of the Efimov effect in free space, that unifies the results that were known so far. An accumulation of bound states appears in the limit of zero energy, diverging scattering length and vanishing harmonic oscillator strength. For a fixed strength of the harmonic oscillator, there is no accumulation of bound state energies.