Enhanced dimer relaxation in an atomic and molecular Bose-Einstein condensate

We derive a universal formula for the rate constant $\beta$ for relaxation of a shallow dimer into deeply-bound diatomic molecules in the case of atoms with a large scattering length $a$. We show that $\beta$ is determined by $a$ and by 2 three-body parameters that also determine the binding energies and widths of Efimov states. The rate constant $\beta$ scales like $\hslash a∕m$ near the resonance, but the coefficient is a periodic function of $\ln \left(a\right)$ that may have resonant enhancement at values of $a$ that differ by multiples of 22.7.

Figure 1

The hyperspherical potential in the region $l⪡R⪡a$. The evolution of wave functions in the regions $R\sim a$ and $R\sim l$ is described by unitary matrices $s$ and $t$.

Figure 2

The dimer relaxation rate constant $\beta$ in units of $\hslash a∕m$ as a function of $a{\Lambda }_{*}$ for ${\eta }_{*}=0.1,0.5,1.0$, and $\infty$.