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 mode
l 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.
The $^1mathrm{S}_0$-$^3mathrm{P}_0$ clock transition frequency $ u_text{Sr}$ in neutral $^{87}$Sr has been measured relative to the Cs standard by three independent laboratories in Boulder, Paris, and Tokyo over the last three years. The agreement on
the $1times 10^{-15}$ level makes $ u_text{Sr}$ the best agreed-upon optical atomic frequency. We combine periodic variations in the $^{87}$Sr clock frequency with $^{199}$Hg$^+$ and H-maser data to test Local Position Invariance by obtaining the strongest limits to date on gravitational-coupling coefficients for the fine-structure constant $alpha$, electron-proton mass ratio $mu$ and light quark mass. Furthermore, after $^{199}$Hg$^+$, $^{171}$Yb$^+$ and H, we add $^{87}$Sr as the fourth optical atomic clock species to enhance constraints on yearly drifts of $alpha$ and $mu$.
