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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 𝑔𝑎⁢𝑁⁢𝑁 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 𝑔𝑎⁢𝑁⁢𝑁 ∼10−12  GeV−1 across a decade in axion mass. 

The hypothetical axion particle (of unknown mass) is a leading candidate for dark matter (DM). Many experiments search for axions with microwave cavities, where an axion may convert into a cavity photon, leading to a feeble excess in the output power of the cavity. Recent work [Backes et al., Nature 590, 238 (2021)] has demonstrated that injecting squeezed vacuum into the cavity can substantially accelerate the axion search. Here, we go beyond and provide a theoretical framework to leverage the benefits of quantum squeezing in a network setting consisting of many sensor cavities. By forming a local sensor network, the signals among the cavities can be combined coherently to boost the axion search. Furthermore, injecting multipartite entanglement across the cavities—generated by splitting a squeezed vacuum—enables a global noise reduction. We explore the performance advantage of such a local, entangled sensor network, which enjoys both coherence between the axion signals and entanglement between the sensors. Our analyses are pertinent to next-generation DM-axion searches aiming to leverage a network of sensors and quantum resources in an optimal way. Finally, we assess the possibility of using a more exotic quantum state, the Gottesman-Kitaev-Preskill (GKP) state. Despite a constant-factor improvement in the scan time relative to a single-mode squeezed state in the ideal case, the advantage of employing a GKP state disappears when a practical measurement scheme is considered.