Abstract
In this paper, we report the observation of the higher order 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. We show that at the magic wavelength of the lattice, where the first order term cancels, the higher order shift will not constitute a limitation to the fractional accuracy of the clock at a level of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-18</sup> . We also report an accurate frequency measurement of the clock transition. The frequency is determined to be v <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</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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