Simulations Of Laser Cooling In An Ultracold Neutral Plasma*

Ultracold neutral plasmas (UNPs) generated by photoionization of laser-cooled, magneto-optically trapped neutral gases, are useful systems for studying strongly coupled plasmas. Coupling is parameterized by $\Gamma_{i}$, the ratio of the average nearest neighbor Coulomb interaction energy to the ion kinetic energy. For typical UNPs, $\Gamma_{i}$ is currently limited to $\sim3$. For alkaline earth ions, higher $\Gamma_{i}$ can be achieved by laser-cooling. Using Molecular Dynamics and a quantum trajectories approach, we have simulated laser-cooling of Sr$^{+}$ ions interacting through a Yukawa potential. The simulations include re-pumping from two long-lived D-states, and are conducted at experimentally achievable parameters (density $n=2$\,e+14\,m$^{-3}$, size $\sigma_{0}=4$\,mm, $T_{e}$=19\,K). Laser-cooling is shown to both reduce the temperature by a factor of 2 over relevant timescales (tens of $\mu$\,s) and slow the electron thermal-pressure driven radial expansion of the UNP. We also discuss the unique aspects of laser-cooling in a highly collisional system; in particular, the effect of collisions on dark state formation due to the coupling of the P$_{3/2}$ state to both the S$_{1/2}$ (via the cooling transition) and the D$_{5/2}$ (via a re-pump transition) states.