Simulation of positronium laser cooling using the Lindblad master equation
We present a formulation and numerical results for positronium (Ps) laser cooling. The formulation is based on the Lindblad master equation and follows the time evolution of the density matrix of Ps atoms. It therefore accounts for atomic coherence, which is necessary to describe the interaction of Ps with the train of short laser pulses generated by the system developed by Shu $\textit{et al.}$ [K. Shu $\textit{et al.}$, Phys. Rev. A $\textbf{109}$, 043520 (2024)]. Using this formulation, we calculate the time evolution of the populations in each internal and momentum state and thereby quantitatively predict the momentum distribution after laser cooling. We present the representative time evolution of the internal-state populations and momentum distribution, together with a comprehensive scan of the laser parameters used to optimize the cooling efficiency. A prominent feature of the simulated distributions is sub-recoil cooling through velocity-selective coherent population trapping, a coherent effect captured by the quantum-mechanical treatment.