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

TL;DR

This paper analyzes the potential of superfluid helium-3's homogeneous precession domain as a sensitive detector for axion-nucleon interactions, incorporating realistic measurement errors and data analysis strategies to project competitive sensitivity.

Contribution

It provides a detailed statistical and dynamical analysis of the HPD system for axion detection, including a framework for transient resonance analysis and realistic experimental projections.

Findings

Projected sensitivity to $g_{aNN} \\sim 10^{-12}$ GeV$^{-1}$ across a decade in axion mass.

Inclusion of measurement and clock errors in the sensitivity analysis.

Development of a framework for analyzing transient resonances in non-stationary backgrounds.

Abstract

The homogeneous precession domain (HPD) of superfluid $^{3}$He has recently been identified as a detection medium which might provide sensitivity to the axion-nucleon coupling $g_{aNN}$ 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 non-stationary background in a time-series analysis. Incorporating an optimal data-taking and analysis strategy, we project a sensitivity approaching $g_{aNN} \sim 10^{-12}$ GeV$^{-1}$ across a decade in axion mass.