Abstract : 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.
A configuration of magnetic fields is exhibited which can harmonically trap paramagnetic particles in a shallow field minimum, superposed on a nearly uniform field which simplifies spectroscopic interactions with the particles. The potential energy of a trapped neutral particle depends on the particle's internal quantum number, as well as its position in the trap, permitting a combined rf-laser optical pumping cycle which can cool particles by a factor of 2 per cycle. Application of these ideas to the trapping of Na atoms is discussed.