Sympathetic Cooling and Slowing of Molecules with Rydberg Atoms

We propose to sympathetically slow and cool polar molecules in a cold, low-density beam using laser-cooled Rydberg atoms. The elastic collision cross sections between molecules and Rydberg atoms are large enough to efficiently thermalize the molecules even in a low-density environment. Molecules traveling at $100\mathrm{m}/\mathrm{s}$ can be stopped in under 30 collisions with little inelastic loss. Our method does not require photon scattering from the molecules and can be generically applied to complex species for applications in precision measurement, quantum information science, and controlled chemistry.

Figure 1

(a) Interaction potential between the CH molecule and the Li Rydberg atom. The state labels indicate the asymptotic states when the molecule is far away from the Rydberg atom. When they are close, all atom-molecule pair states are hybridized. The dashed vertical line marks the classic radius of the $\mathrm{Li}(3{0S}_{1/2})$ state. When the pair state density is high near the degenerate manifold of high angular momentum Rydberg states, the interaction potential depth is larger than $\sim 10\mathrm{GHz}$. (b) The scattering cross section for the potential of the $3{0S}_{1/2},J=1/2^{-}$ pair state, compared with the half of the cross section of a hard sphere with radius $R_n$ ($\pi R_n^2$).

Figure 2

(a) and (b) Laser coupling scheme for Rydberg excitation and cooling. ${\mathrm{\Omega }}_2$ (red arrow) couples $|e⟩\leftrightarrow |r⟩$ off resonantly, and ${\mathrm{\Omega }}_1$ (purple arrow) couples $|g⟩$ to the dressed Rydberg state $|\tilde{r}⟩$ with an effective coupling strength $\mathrm{\Omega }\approx 2\pi \times 1\mathrm{MHz}$ (orange arrow in [b]). (c) Mean free path of the collision, as well as the diffusion distance (in the atom cloud) to stop a molecule initially at $100\mathrm{m}/\mathrm{s}$, as a function of the total atom density (Rydberg and ground states) and principal quantum number, when the system is in a steady state with the laser couplings in (a). We use 25 as the number of collisions needed to stop the molecules, as described in the main text. The blue dashed line marks the parameters above which the blockade effect starts to limit the Rydberg population density.

Figure 3

Proposed experimental setup and sequence. A beam (blue) of atoms and molecules comes out from a buffer gas cell (brown box). The plots qualitatively illustrate the expected temperature (T) and velocity (v) profiles of the atoms and molecules. In (a), atoms and molecules are both relatively hot (typically $\sim 4\mathrm{K}$) and fast (typically $\sim 100\mathrm{m}/\mathrm{s}$ [33]). Laser cooling is applied to the atoms in the moving frame. The frequencies of the beams along the $x$ direction are shifted for cooling in the moving frame. Two beams in the $y$ direction are not shown in the figure. After cooling, in (b), atoms are cold ($<100\mathrm{\mu }\mathrm{K}$), but molecules are still hot. In the Zeeman slower (orange), atoms are excited to the dressed Rydberg state $|\tilde{r}⟩$ by two counterpropagating beams. In (c), molecules collide and thermalize with the Rydberg atoms and are cooled to the steady state temperature ($\sim 100\mathrm{mK}$). After slowing, magneto-optical force and position-dependent Rydberg excitation are applied to compress the density of the molecules and load them into a trap. (d) The magneto-optical trap where the molecules are pushed by the Rydberg atoms toward the center of the trap.