We present experimental and theoretical studies of polarization-gradie
nt cooling of metastable neon atoms confined to the dark center of a T
EM01 (doughnut) mode. A slow beam of neon atoms is guided and focused
inside a blue-detuned and focused doughnut-mode laser beam to a spot
size below 10 mu m. The transverse motion inside this doughnut mode is
cooled by means of two-dimensional optical molasses. We observed non-
Gaussian two-component velocity distributions of which the cold compon
ent has a width of down to three recoil velocities. These results are
found to be in qualitative agreement with a quantum Monte Carlo simula
tion of cooling in one dimension in the presence of an external light-
shift potential. For the simulation we apply the recently developed te
chnique of quantum-state diffusion with adaptive noise. [S1050-2947(98
)03710-X].