Raman Sideband Cooling in presence of Multiple Decay Channels

We have investigated the efficiency of pulsed Raman sideband cooling in the presence of multiple decay and excitation channels. By applying sum rules we identify parameter regimes in which multiple scattering of photons can be described by an effective wave vector. Using this method we determine the rate of heating caused by optical pumping inside and outside the Lamb-Dicke regime. On this basis we discuss also the efficiency of a recently proposed scheme for ground-state cooling outside the Lamb-Dicke regime [G. Morigi, J.I. Cirac, M. Lewenstein, and P. Zoller, Europhys. Lett. {\bf 39}, 13 (1997)].