Symmetry Breaking in Sticky Collisions between Ultracold Molecules

Ultracold molecules undergo “sticky collisions” that result in loss even for chemically nonreactive molecules. Sticking times can be enhanced by orders of magnitude by interactions that lead to nonconservation of nuclear spin or total angular momentum. We present a quantitative theory of the required strength of such symmetry-breaking interactions based on classical simulation of collision complexes. We find static electric fields as small as $10\mathrm{V}/\mathrm{cm}$ can lead to nonconservation of angular momentum, while we find nuclear spin is conserved during collisions. We also compute loss of collision complexes due to spontaneous emission and absorption of black-body radiation, which are found to be slow.

Figure 1

Classical simulations of ultracold sticky collisions. Panel (a) shows schematically the classical simulations on a simple but realistic high-dimensional potential energy surface. After a typical time, ${\tau }_S^{\mathrm{traj}}$, the classical trajectory crosses the dividing surface $R=R_S$. At this surface, $N_S\gg 1$ collision channels are energetically accessible. We estimate the physical sticking time in ultracold collisions, where only a single collision channel is open, by correcting as ${\tau }_{\text{stick}}^{\mathrm{traj}}=N_S{\tau }_S^{\mathrm{traj}}$. Panel (b) demonstrates quantitatively the steep dependence of ${\tau }_S^{\mathrm{traj}}$ and $N_S$ on the position of the dividing surface $R_S$ and that the sticking time estimated from classical trajectories ${\tau }_{\text{stick}}^{\mathrm{traj}}$ is independent of $R_S$ and in quantitative agreement with sticking times obtained from phase-space integrals ${\tau }_{\text{stick}}^{\mathrm{RRKM}}$.

Figure 2

Autocorrelation functions (ACFs). Dipole and spherical-harmonic ACFs for $\mathrm{NaK}+\mathrm{K}$, $\mathrm{NaK}+\mathrm{NaK}$, and $\mathrm{RbCs}+\mathrm{RbCs}$ sticky collisions.

Figure 3

Effective density of states as determined by fitting the distribution of sticking times, see Supplemental Material [43]. The dimensionless parameter $\mathrm{\Omega }$ represents the Stark interaction in units of the level spacing, and hence effectively represents the electric field. The total density of states increases as $(1+J_{\max }{)}^2$ for large $\mathrm{\Omega }$, but the transition to $J$ conservation consistently occurs around $\mathrm{\Omega }=1$ irrespective of the value of $J_{\max }$.

Figure 4

Spectrum of spontaneous emission and absorption of black-body radiation at 293 K. The integrated intensity yields the loss rate, which is in the order of $0.1{\mathrm{s}}^{-1}$ and can essentially be excluded during sticky collisions, see Table 1.