Universalities in ultracold reactions of alkali-metal polar molecules

We consider ultracold collisions of ground-state heteronuclear alkali-metal dimers that are susceptible to four-center chemical reactions $2AB\to A_2+B_2$ even at submicrokelvin temperatures. These reactions depend strongly on species, temperature, electric field, and confinement in an optical lattice. We calculate ab initio van der Waals coefficients for these interactions and use a quantum formalism to study the scattering properties of such molecules under an external electric field and optical lattice. We also apply a quantum threshold model to explore the dependence of reaction rates on the various parameters. We find that, among the heteronuclear alkali-metal fermionic species, LiNa is the least reactive, whereas LiCs is the most reactive. For the bosonic species, LiK is the most reactive in zero field, but all species considered, LiNa, LiK, LiRb, LiCs, and KRb, share a universal reaction rate once a sufficiently high electric field is applied. For indistinguishable bosons, the inelastic/reactive rate increases as $d^2$ in the quantum regime, where $d$ is the dipole moment induced by the electric field. This is a weaker power-law dependence than for indistinguishable fermions, for which the rate behaves as $d^6$.

Figure 1

Solid lines: Loss rate coefficient ${\beta }_{L=1}$ divided by $T$ in free three-dimensional (3D) space, of the reaction $AB+AB\to A_2+B_2$ for different reactive fermionic polar molecules ($AB=\text{LiNa,}\text{KRb,}\text{LiK,}\text{LiRb,}\text{LiCs}$), as a function of the electric dipole moment. The fermions are considered in the same indistinguishable quantum state. In the van der Waals regime, the rate coefficient is constant, while in the electric field regime, the rate coefficient behaves as $d^6$ (see text for details). Dashed lines: ${\beta }_{L=1,M_L=0}$ and ${\beta }_{L=1,|M_L|=1}$ components of $L=1$, shown here for $AB=\text{LiNa}$.

Figure 2

As Fig. 1 for different reactive bosonic polar molecules. The rate coefficient ${\beta }_{L=0}$ is plotted as a function of the electric dipole moment for $T\to 0$ (Wigner regime). The bosons are considered in the same indistinguishable quantum state. In the van der Waals regime, the rate is constant, while in the electric field regime, the rate coefficient behaves as $d^2$ (see text for details).

Figure 3

Top panel: Van der Waals regime for $M_L=0$ and $|M_L|=1$. The quantity ${\beta }_{1,0}^{6,2}={\beta }_{1,1}^{6,2}$ divided by $T$ is plotted as a function of ${\left(\mu C_6\right)}^{3/4}$. Middle panel: Electric field regime for $M_L=0$. The quantity ${\beta }_{1,0}^{3,2}$ divided by $d^{6}T$ is plotted as a function of ${\mu }^3$. Bottom panel: Electric field regime for $|M_L|=1$. The quantity ${\beta }_{1,1}^{4,3}$ divided by $d^{6}T$ is plotted as a function of ${\mu }^3$.

Figure 4

Top panel: van der Waals regime. The quantity ${\beta }_{0,0}^6$ is plotted as a function of ${(C_6/{\mu }^3)}^{1/4}$. Bottom panel: Electric field regime. The quantity ${\beta }_{0,0}^4$ divided by $d^2$ is plotted for the five different colliding species.

Figure 5

Loss rate coefficients for different reactive polar molecules in confined 2D space, for indistinguishable fermions (top panel) and indistinguishable bosons (bottom panel). The frequency of the 1D trap is $\nu =20$ kHz and the temperature is $T=500$ nK. The dashed lines represent a model based on the rescaled 3D rate coefficients for $a_{\mathrm{dd}}\ll a_{\mathrm{ho}}$, and the dotted lines represent a model based on a functional form (Ref. [40] for example) for $a_{\mathrm{dd}}\gg a_{\mathrm{ho}}$.