Positronium laser cooling in a magnetic field

We study realistic 3D laser cooling of positronium (Ps) in the presence of a magnetic field. Triplet and singlet states mixing due to the magnetic field, and dynamical Stark effect, generally produce higher annihilation rates than in the zero-field case. 3D cooling is efficient only at very low field $B\ensuremath{\lesssim}50\phantom{\rule{0.16em}{0ex}}\mathrm{mT}$ and at high field values $B⪆0.7\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{T}$. Near $100\phantom{\rule{0.16em}{0ex}}\mathrm{ns}$ long laser pulses, spectrally broad enough to cover most of the Ps Doppler profile and with energy in the $\mathrm{mJ}$ range, are required to cool Ps. Simulations based on full diagonalization of the Stark and Zeeman Hamiltonian and a kinetic Monte Carlo algorithm exactly solving the rate equations indicate that an efficient cooling (typically from $300\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ down to below $50\phantom{\rule{0.16em}{0ex}}\mathrm{K}$) is possible even in a magnetic field. We also propose 3D moving molasses cooling that can produce a well-defined monochromatic Ps beam useful for applications.