We investigate the influence of atomic motion on precision Rabi spectroscopy of ultracold fermionic atoms confined in a deep, one dimensional (1D) optical lattice. We analyze the spectral components of longitudinal sideband spectra and present a model to extract information about the transverse motion and sample temperature from their structure. Rabi spectroscopy of the clock transition itself is also influenced by atomic motion in the weakly confined transverse directions of the optical lattice. By deriving Rabi flopping and Rabi lineshapes of the carrier transition, we obtain a model to quantify trap state dependent excitation inhomogeneities. The inhomogeneously excited ultracold fermions become distinguishable, which allows s-wave collisions. We derive a detailed model of this process and explain observed density shift data in terms of a dynamic mean field shift of the clock transition.
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