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Collisional losses, decoherence, and frequency shifts in optical lattice clocks with bosons

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 Added by Christian Lisdat
 Publication date 2009
  fields Physics
and research's language is English




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We have quantified collisional losses, decoherence and the collision shift in a one-dimensional optical lattice clock with bosonic 88Sr. The lattice clock is referenced to the highly forbidden transition 1S0 - 3P0 at 698 nm, which becomes weakly allowed due to state mixing in a homogeneous magnetic field. We were able to quantify three decoherence coefficients, which are due to dephasing collisions, inelastic collisions between atoms in the upper and lower clock state, and atoms in the upper clock state only. Based on the measured coefficients, we determine the operation parameters at which a 1D-lattice clock with 88Sr shows no degradation due to collisions on the relative accuracy level of 10-16.



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We analyze both the s- and p-wave collision induced frequency shifts and propose a over-$pi$ pulse scheme to cancel the shifts in optical lattice clocks interrogated by a Rabi pulse. The collisional frequency shifts are analytically solved as a function of the pulse area and the inhomogeneity of the Rabi frequencies. Experimentally measured collisional frequency shifts in an Yb optical lattice clock are in good agreement with the analytical calculations. Based on our analysis, the over-$pi$ pulse combined with a small inhomogeneity below 0.1 allows a fractional uncertainty on a level of $10^{-18}$ in both Sr and Yb optical lattice clocks by canceling the collisional frequency shift.
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Collisions between background gas particles and the trapped ion in an atomic clock can subtly shift the frequency of the clock transition. The uncertainty in the correction for this effect makes a significant contribution to the total systematic uncertainty budget of trapped-ion clocks. Using a non-perturbative analytic framework that was developed for this problem, we estimate the frequency shift in Al$^+$ ion clocks due to collisions with helium and hydrogen. Our calculations significantly improve the uncertainties in the collisional shift coefficients, and show that the collisional frequency shifts for Al$^+$ are zero to within uncertainty.
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