Theory of a single-atom laser including light forces

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.