Monte-Carlo simulations of the capture and cooling of alkali-metal atoms by a supersonic helium jet

Abstract

We present three-dimensional Monte-Carlo simulations of the capture of 1000 K ${}^7$Li or 500 K ${}^{87}$Rb atoms by a continuous supersonic ${}^4$He jet and show that intense alkali-metal beams form with narrow transverse and longitudinal velocity distributions. The nozzle creating the ${}^4$He jet is held at approximately 4 K. These conditions are similar to those in the cold ${}^7$Li source developed by some of us as described in [Phy. Rev. A 107, 013302 (2023)]. The simulations use differential cross-sections obtained from quantum scattering calculations of ${}^7$Li or ${}^{87}$Rb atoms with ${}^4$He atoms for relative collision energies between $k\times 1$ mK to $k\times 3000$ K, where $k$ is the Boltzmann constant. For collision energies larger than $\approx k\times 4$ K the collisions favor forward scattering, deflecting the ${}^7$Li or ${}^{87}$Rb atoms by no more than a few degrees. From the simulations, we find that about 1$\%$ of the lithium atoms are captured into the ${}^4$He jet, resulting in a lithium beam with a most probable velocity of about $210$ m/s and number densities on the order of $10^8$ cm${}^{-3}$. Simulations predict narrow yet asymmetric velocity distributions which are verified by comparing to fluorescence measurements of the seeded ${}^7$Li atoms. We find agreement between simulated and experimentally measured seeded ${}^7$Li densities to be better than 50$\%$ across a range of ${}^4$He flow rates. We make predictions for capture efficiency and cooling of ${}^{87}$Rb by a supersonic ${}^4$He jet. The capture efficiency for ${}^{87}$Rb is expected to be similar to ${}^7$Li.