Statistics and sensitivity of axion wind detection with the homogeneous precession domain of superfluid helium-3

The homogeneous precession domain (HPD) of superfluid <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mmultiscripts><a:mrow><a:mi>He</a:mi></a:mrow><a:mprescripts/><a:none/><a:mrow><a:mn>3</a:mn></a:mrow></a:mmultiscripts></a:mrow></a:math> has recently been identified as a detection medium which might provide sensitivity to the axion-nucleon coupling <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>g</c:mi><c:mrow><c:mi>a</c:mi><c:mi>N</c:mi><c:mi>N</c:mi></c:mrow></c:msub></c:math> competitive with, or surpassing, existing experimental proposals. In this work, we make a detailed study of the statistical and dynamical properties of the HPD system in order to make realistic projections for a full-fledged experimental program. We include the effects of clock error and measurement error in a concrete readout scheme using superconducting qubits and quantum metrology. This work also provides a more general framework to describe the statistics associated with the axion gradient coupling through the treatment of a transient resonance with a nonstationary background in a time-series analysis. Incorporating an optimal data-taking and analysis strategy, we project a sensitivity approaching <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>g</e:mi><e:mrow><e:mi>a</e:mi><e:mi>N</e:mi><e:mi>N</e:mi></e:mrow></e:msub><e:mo>∼</e:mo><e:msup><e:mn>10</e:mn><e:mrow><e:mo>−</e:mo><e:mn>12</e:mn></e:mrow></e:msup><e:mtext> </e:mtext><e:mtext> </e:mtext><e:mrow><e:msup><e:mrow><e:mi>GeV</e:mi></e:mrow><e:mrow><e:mo>−</e:mo><e:mn>1</e:mn></e:mrow></e:msup></e:mrow></e:math> across a decade in axion mass. Published by the American Physical Society 2024