  We study motion and field dynamics of a single-atom laser consisting of a
single incoherently pumped free atom moving in an optical high-{\it Q}
resonator. For sufficient pumping, the system starts lasing whenever the atom
is close to a field antinode. If the field mode eigenfrequency is larger than
the atomic transition frequency, the generated laser light attracts the atom to
the field antinode and cools its motion. Using quantum Monte Carlo wave
function simulations, we investigate this coupled atom-field dynamics including
photon recoil and cavity decay. In the regime of strong coupling, the generated
field shows strong nonclassical features like photon antibunching, and the atom
is spatially confined and cooled to sub-Doppler temperatures.
