Abstract
The authors report the observation of the hyperpolarizability frequency shift due to the trapping field in a <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">87</sup> Sr optical lattice clock. The authors show that at the magic wavelength of the lattice, where the first order term cancels, this higher order shift will not constitute a limitation to the fractional accuracy of the clock down to the 10 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-18</sub> level. This result is achieved by operating the clock at very high trapping intensity up to 400 kW/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and by a specific study of the effect of the two two-photon transitions near the magic wavelength. The authors also report an accurate frequency measurement of the clock transition. The frequency is determined to be v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1S0</sub> - <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> = 429 228 004 229 879 (5) Hz with a fractional uncertainty that is comparable to state-of-the-art optical clocks with neutral atoms in free fall
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