Cosmic Axion Background Detection Using Resonant Cavity Arrays

Abstract

The axion is a well-motivated and generic extension of the Standard Model. If produced in the early universe, axions may still be relativistic today, forming a Cosmic Axion Background (C$a$B) potentially detectable in direct detection experiments. Although C$a$B is expected to be broadband, which makes it challenging to be detected, a high-quality-factor microwave cavity acts as a narrowband filter with response peaked at its resonant frequency. We propose a new strategy using multi-cavity arrays to distinguish signal from background noise by exploiting spatial correlations of the axion-induced electric field which are set by the cavity quality factor. We compute the two-point correlation function for electric fields in spatially separated cavities sourced by an isotropic C$a$B. Analyzing various cavity geometries, we find that stacked, wide-base cavity arrays offer coherent enhancement of the axion signal. We apply our formalism to prospective upgrades of the ADMX experiment, including configurations with four and eighteen coupled cavities. Although these arrays do not achieve a coherent enhancement, optimizing the geometry could potentially yield an $\mathcal{O}(1)$ improvement in the sensitivity to the C$a$B.

Figures (5)

• Figure 1: Geometry of the vectors involved in calculating the correlation function between the electric fields produced in two cavities.
• Figure 2: Left: Self-correlation $\mathcal{F}_{ii}$ as a function of $\omega_0L$, illustrating the limiting behavior of Eq. \ref{['eq:self_correlation_limits']}. Right: Ratio of the inter-cavity correlation ($i \neq j$) to the self-correlation ($i = j$) as a function of separation normalized by the radius, for $L/R = 1/2$ (green line) and $L/R = 12$ (blue line). Blue curves correspond to coplanar cavities; green curves correspond to vertically aligned cavities. Dashed lines indicate unphysical overlapping cavity configurations. Both cases show oscillatory decay with increasing separation, with correlation potentially vanishing at specific distances.
• Figure 3: $\bar{I}(\mathcal{N})$ versus $\mathcal{N}$ for a vertically stacked linear array in Section \ref{['vertically stacked fat cavities']} (green) and a coplanar $\mathcal{N}\times 1$ array (blue). Each cavity has a dimension of $R= 25~\mathrm{cm}$ and $L = 5~\mathrm{cm}$ and is touching the neighboring cavities. The green line shows a coherent configuration with $\bar{I}(\mathcal{N})$ increasing linearly and then approaching a constant. On the other hand, $\bar{I}(\mathcal{N})$ of an incoherent configuration is effectively constant regardless of the size of the array.
• Figure 4: Normalized $g_{a\gamma\gamma}$ (with respect to the CAST limit $g_{a\gamma\gamma}^{\mathrm{SE}}=6.6\times 10^{-11}\,\mathrm{GeV}^{-1}$) versus the 95% upper limit on $\Omega_0$ for a $1~\mathrm{m}$-tall cavity partitioned into different numbers of stacked segments. All other parameters match those in Section \ref{['The statistics of a multi-cavity array']}. The black line shows $g_{a\gamma\gamma}/g_{a\gamma\gamma}^{\mathrm{SE}}=1$, and the shaded regions denote sensitivity bands.
• Figure 5: Normalized $g_{a\gamma\gamma}$ (with respect to the CAST limit $g_{a\gamma\gamma}^{\mathrm{SE}}=6.6\times 10^{-11}\,\mathrm{GeV}^{-1}$) versus the 95% upper limit on $\Omega_0$ for existing and future ADMX proposals. The black line indicates the CAST limit, $g_{a\gamma\gamma}/g_{a\gamma\gamma}^{\mathrm{SE}}=1$. The colored regions denote sensitivity bands. The blue and green lines correspond to ADMX run-2A and ADMX-EFR, respectively. All other parameters are as in Section \ref{['The statistics of a multi-cavity array']}, with the magnetic field for ADMX-EFR taken to be 9.4 T and $Q = 1.8\times 10^5$.