Three-body universality in ultracold $p$-wave resonant mixtures

We study three-body collisions within ultracold mixtures with resonant interspecies $p$-wave interactions. Our results for the three-body effective interaction strength and decay rate are crucial towards understanding the stability and lifetime of these dilute quantum fluids. On resonance, we find that a class of universal scattering pathways emerges, regardless of the details of the short-range interactions. This gives rise quite generally to a remarkable regime where three-body effective interactions dominate over both inelastic decay and two-body effective interactions. Additionally, we find a series of mass-ratio-dependent trimer resonances further from resonance.

Figure 1

Diagrammatic representation of the four distinct three-body scattering processes that result in the $\sqrt{-a_1}$ scaling of ${\mathcal{U}}_0$ due to one resonant $p$-wave interspecies interaction. In these diagrams, individual particles propagate from right to left with identities distinguished by color and line style. The vertices represent the $s$- (circles) or $p$-wave (squares) component of the two-body transition operator.

Figure 2

${\mathcal{U}}_0$ near the first $p$-wave BX dimer resonance of the square-well potential for various mass ratios at (a) $a_1<0$ and (b) $a_1>0$. We have defined the dimensionless quantities ${\overline{\mathcal{U}}}_0\equiv {\mathcal{U}}_0{m}_{\mathrm{X}}{\hslash }^4/R^4$ and ${\overline{a}}_1=a_1/R^3$. The BB interaction is set to zero. The red dashed lines represent Eqs. (8) and (9) with $a_{\mathrm{BB}}/R=0$, $a_{\mathrm{BX}}/R=1$, and ${\tilde{r}}_{1}R=3$. The parameters $a_{\mathrm{BX}}$ and ${\tilde{r}}_1$ can be regarded as constants for $|{\overline{a}}_1|\gtrsim 10$. For $a_1>0$, $\mathrm{Im}\left({\mathcal{U}}_0\right)$ is determined by the three-body recombination rate into one deep $s$-wave dimer state ($l=0$) and one shallow $p$-wave dimer state ($l=1$). These two contributions to $\mathrm{Im}\left({\mathcal{U}}_0\right)$ are presented in the inset for $\chi =0$. The inset for $\mathrm{Re}\left({\mathcal{U}}_0\right)$ at $a_1>0$ demonstrates its logarithmic behavior at large $a_1$ for $\chi =0.1$.

Figure 3

(a) $-\mathrm{Im}\left({\mathcal{U}}_0\right)$ near the first $p$-wave BX dimer resonance of the square-well potential for various mass ratios $\chi \ll 1$ at $a_1<0$. The BB interaction is set to zero. (b) The $p$-wave scattering volumes $a_{1,\mathrm{res}}$ that locate the local maxima in $-\mathrm{Im}\left({\mathcal{U}}_0\right)$ for $0.025\le \chi \le 0.4$.