Spin-dependent optical potentials allow us to use microwave radiation to
manipulate the motional state of trapped neutral atoms (
Förster et al. 2009 Phys. Rev.
Lett. 103, 233001). Here, we discuss this method in greater detail, comparing it to the
widely-employed Raman sideband coupling method. We provide a simplified model for sideband
cooling in a spin-dependent potential, and we discuss it in terms of the generalized
Lamb-Dicke parameter. Using a master equation formalism, we present a quantitative analysis of
the cooling performance for our experiment, which can be generalized to other experimental
settings. We additionally use microwave sideband transitions to engineer motional Fock states
and coherent states, and we devise a technique for measuring the population distribution of the
prepared states.