Simple quantum model of ultracold polar molecule collisions

We present a unified formalism for describing chemical reaction rates of trapped, ultracold molecules. This formalism reduces the scattering to its essential features, namely, a propagation of the reactant molecules through a gauntlet of long-range forces before they ultimately encounter one another, followed by a probability for the reaction to occur once they do. In this way, the electric-field dependence should be readily parametrized in terms of a pair of fitting parameters (along with a $C_6$ coefficient) for each asymptotic value of partial-wave quantum numbers $|L,M_L\rangle$. From this, the electric-field dependence of the collision rates follows automatically. We present examples for reactive species, such as KRb, and nonreactive species, such as RbCs.

Figure 1

Probability to tunnel to short range, vs collision energy, for $s$- and $p$-wave collisions of KRb molecules, assuming zero electric field and $C_6=16130$ a.u. [15]. The dashed lines are the analytic, low-energy approximations $1-\exp (-4k{\beta }_L)$. Inset: Dependence of the $p$-wave transmission probability, evaluated at the height of the centrifugal barrier, as a function of induced dipole moment $d$.

Figure 2

Dependence of chemical reaction rates $K_L^{\mathrm{qu}}$ on dipole moment $d$ for identical (a) fermionic (odd $L$) or (b) bosonic (even $L$) KRb molecules. In the case of unit reaction probability, $y=1$, this variation takes a universal form independent of details of the short-range physics. For $y<1$, nonuniversal resonances appear that reveal more details of the short-range interaction. The data from [5] (points) are well fit by near-universal scattering, $y=0.83$.