Three Body Recombination of Ultracold Dipoles to Weakly Bound Dimers

We use universality in two-body dipolar physics to study three-body recombination. We present results for the universal structure of weakly bound two-dipole states that depend only on the $s$-wave scattering length ($a$). We study threshold three-body recombination rates into weakly bound dimer states as a function of the scattering length. A Fermi golden rule analysis is used to estimate rates for different events mediated by the dipole-dipole interaction and a phenomenological contact interaction. The three-body recombination rate in the limit where $a\gg D$ contains terms which scale as $a^4$, $a^2{D}^2$, and $D^4$, where $D$ is the dipolar length. When $a\ll D$, the three-body recombination rate scales as $D^4$.

Figure 1

Universal properties of two-body dipolar scattering. (a) The binding energy (symbols with curves) of the dipolar dimer as a function of the $s$-wave scattering length for the first (black circles), second (blue diamonds), and eighth (red square) resonance. (b) The partial wave molecular populations are shown for the $s$-wave (solid), $d$-wave (dashed), and $g$-wave (dotted) populations for the first (black) and second (blue) resonance.

Figure 2

The three-body recombination rate of three identical bosonic dipoles is shown in dipole units as a function of the scattering length. The total recombination rate (solid curves) is universal and independent of the resonance used. The sS (dashed red), dS (dotted red), and higher order (dot-dashed red curves) partial wave contributions are shown as well. The $a^4$ (blue square) and $D^2{a}^2$ (blue circle) terms from the asymptotic results of Eq. (6) are shown as well. Inset: The total recombination rate is shown compared to the result of Eq. (6) for the large $a$ limit (green dashed curve).