Absolute frequency measurement of a ⁸⁸Sr⁺ clock by direct comparison to a primary frequency standard

Abstract We report on a measurement of the absolute frequency of the 88 Sr + clock transition via a direct comparison to our cesium fountain clock, National Research Council Canada (NRC)-FCs2. The measurement yield a value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>444</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mn>779</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mn>044</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mn>095</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mn>485.404</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.045</mml:mn> </mml:mrow> </mml:math> Hz. The corresponding fractional uncertainty of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>1.0</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>16</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> is, to our knowledge, the lowest so far reported for an absolute frequency measurement. The low uncertainty obtained is primarily a consequence of improvements to NRC-FCs2, specifically a systematic uncertainty of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>9.3</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>17</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> and a stability of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>6.3</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>14</mml:mn> </mml:mrow> </mml:msup> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:msqrt> <mml:mi>τ</mml:mi> </mml:msqrt> </mml:mrow> </mml:math> . The measurement was made over a period of 37 days with 68% uptime, for a total measurement time of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>2.16</mml:mn> <mml:mo>×</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mrow> <mml:mn>6</mml:mn> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> s. The 88 Sr + frequency was also compared to terrestrial time via a global navigation satellite system (GNSS) link to Universal Coordinated Time, yielding a frequency value of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mn>444</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mn>779</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mn>044</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mn>095</mml:mn> <mml:mstyle scriptlevel="0"/> <mml:mn>485.406</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.089</mml:mn> </mml:mrow> </mml:math> Hz, which is in agreement with the direct comparison with NRC-FCs2.