Theory of Laser Cooling and Spectroscopy of Harmonically Trapped Single Atoms.

The problem of laser cooling of a single ion or atom in a harmonic trap was considered. A simple theory of sideband cooling has been developed. In the limit that the particle's secular motion can be treated semiclassically, the theory allows the calculation of a logarithmic cooling rate either numerically or, for two special cases, analytically. The theory could be used to optimize the parameters of a cooling experiment. The spectroscopy of a single atom in the ladder configuration has been treated theoretically. A dressed atom approach was used to provide qualitative information about the system. The optical Bloch equations for a four -level system in the rotating wave approximation were developed and solved for steady state. The Bloch equations were also solved in the adiabatic approximation and upward and downward transition rates were extracted from this treatment.