  We study a single incoherently pumped atom moving within an optical high-Q
resonator in the strong coupling regime. Using a semiclassical description for
the atom and field dynamics, we derive a closed system of differential
equations to describe this coupled atom-field dynamics. For sufficiently strong
pumping the system starts lasing when the atom gets close to a field antinode,
and the associated light forces provide for self-trapping of the atom. For a
cavity mode blue detuned with respect to the atomic transition frequency this
is combined with cavity induced motional cooling allowing for long term
steady-state operation of such a laser. The analytical results for temperature
and field statistics agree well with our earlier predictions based on Quantum
Monte Carlo simulations. We find sub-Doppler temperatures that decrease with
gain and coupling strength and can even go beyond the limit of passive cavity
cooling. Besides demonstrating the importance of light forces in single-atom
lasers, this result also gives strong evidence to enhance laser cooling through
stimulated emission in resonators.
