Scattering of ultracold molecules in the highly resonant regime

Compared to purely atomic collisions, ultracold molecular collisions potentially support a much larger number of Fano-Feshbach resonances due to the enormous number of rovibrational states available. In fact, for alkali-metal dimers we find that the resulting density of resonances cannot be resolved at all, even on the sub-$\mu$K temperature scale of ultracold experiments. As a result, all observables become averaged over many resonances and can effectively be described by simpler, nonresonant scattering calculations. Two particular examples are discussed: nonchemically reactive RbCs and chemically reactive KRb. In the former case, the formation of a long-lived collision complex may lead to the ejection of molecules from a trap. In the latter case, chemical reactions broaden the resonances so much that they become unobservable.

Figure 1

Rovibrational density of states of RbCs + RbCs collisions as a function of the maximally allowed end-over-end angular momentum $L_c$ of the collision complex, for a total angular momentum $J=0-4,M=0$ (solid, long-dashed, dashed, dashed-dotted, and dotted line, respectively). The scale on the right axis gives the corresponding RRKM lifetime of the collision complex according to ${\tau }_0=2\pi \hslash \rho$.

Figure 2

Elastic scattering cross sections for RbCs + RbCs collisions in their absolute ground state ($v=n=0$, $M_{\mathrm{Cs}}=7/2$, and $M_{\mathrm{Rb}}=3/2$). Shown is the $s$-wave cross section (yellow shading under the curve), and the $d$-wave cross section (orange shading). The characteristic van der Waals energy $E_{\text{vdW}}$ is indicated by the vertical dashed line.

Figure 3

Quenching rate constants of two indistinguishable bosonic polar ${}^{87}$Rb${}^{133}$Cs molecules as a function of the induced dipole moment for a temperature of $T=1\mu$K. The solid line represents the $M_L=0$ contribution and the dashed line the $M_L=2$ (equal to the $M_L=-2$) contribution.

Figure 4

(a) Time evolution of the RbCs molecular density $n_m\left(t\right)$ for zero field (upper curves) and an applied electric field of 10 kV/cm (lower curves); $s$- and $d$-wave collisions are considered. Dotted ($s$-wave) and dashed ($d$-wave) lines are computed without particle loss due to complex-molecule collisions, that is, $K_{\mathrm{mc}}=0$ in Eqs. (20) and (21). The initial molecular density is $n_0={10}^{10}{\mathrm{cm}}^{-3}$ at an assumed sample temperature of 1 $\mu$K. The arrows indicate the time scale $t^{\prime }$ as given by Eq. (24). (b) Evolution of the ratio of molecules bound in complexes to free molecules. The same set of parameters as in panel (a) is used.

Figure 5

Same as in Fig. 4, but for a higher initial density of $n_0={10}^{11}{\mathrm{cm}}^{-3}$.

Figure 6

Inelastic $p$-wave scattering cross section mimicking ultracold KRb collisions with $N_o=100$ (light gray) and $N_o=1000$ [red (dark gray)] product channels. The dashed line represents the analytic prediction for unit loss probability; cf. Eq. (26).