Long-distance chronometric leveling with a portable optical clock

We have measured the geopotential difference between two locations separated by 457 km by comparison of two optical lattice clocks via an interferometric fiber link, utilizing the gravitational redshift of the clock transition frequency. The <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><a:msup><a:mi/><a:mn>87</a:mn></a:msup><a:mi>Sr</a:mi></a:math> clocks have been compared side-by-side before and after one of the clocks was moved to the remote location. The chronometrically measured geopotential difference of <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><d:mn>3918.1</d:mn><d:mo stretchy="false">(</d:mo><d:mn>2.6</d:mn><d:mo stretchy="false">)</d:mo><d:mspace width="0.2em"/><d:msup><d:mrow><d:mi mathvariant="normal">m</d:mi></d:mrow><d:mn>2</d:mn></d:msup><d:mspace width="0.2em"/><d:msup><d:mrow><d:mi mathvariant="normal">s</d:mi></d:mrow><d:mrow><d:mrow><d:mo>−</d:mo><d:mn>2</d:mn></d:mrow></d:mrow></d:msup></d:math> agrees with an independent geodetic determination of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><m:mn>3915.88</m:mn><m:mo stretchy="false">(</m:mo><m:mn>0.30</m:mn><m:mo stretchy="false">)</m:mo><m:mspace width="0.2em"/><m:msup><m:mrow><m:mi mathvariant="normal">m</m:mi></m:mrow><m:mn>2</m:mn></m:msup><m:mspace width="0.2em"/><m:msup><m:mrow><m:mi mathvariant="normal">s</m:mi></m:mrow><m:mrow><m:mo>−</m:mo><m:mn>2</m:mn></m:mrow></m:msup></m:math>. The uncertainty of the chronometric geopotential difference is equivalent to an uncertainty of <v:math xmlns:v="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"><v:mn>27</v:mn><v:mspace width="0.2em"/><v:mi>cm</v:mi></v:math> in height.