A Prototype Hybrid Mode Cavity for Heterodyne Axion Detection

Abstract

In the heterodyne approach to axion detection, axion dark matter induces transitions between two modes of a microwave cavity, resulting in a parametrically enhanced signal power. We describe the fabrication and characterization of a prototype normal conducting cavity specifically optimized for heterodyne detection. Corrugations on the cavity walls support linearly polarized hybrid modes which maximize the signal power while strongly suppressing noise. We demonstrate tuning mechanisms which allow one mode's frequency to be scanned across a 4 MHz range, while suppressing cross-coupling noise by at least 80 dB. A future superconducting cavity with identical geometry to our prototype would have the potential to probe orders of magnitude beyond astrophysical bounds.

Figures (11)

• Figure 1: Geometry of the prototype cavity. (a) Interior of the cavity, showing corrugations on the aluminum side walls and the "fixed" copper endplate. (b) The corrugated copper endplates. The "tunable" endplate is open at the back, so that a tuning plate (shown in Fig. \ref{['fig:tuner_fab']}) can be deformed behind it, adjusting the mode frequency difference.
• Figure 2: Original conceptual design of the hybrid mode cavity. (a) The cavity has corrugated side walls which support highly overmoded $\text{HE}_{11}$ modes, and endplate fins shift the modes by $\lambda/4$ relative to each other. (b) Electric and magnetic field profiles of an $\text{HE}_{11}$ mode in a $\lambda/4$ period. The fields are linearly polarized, orthogonal, and suppressed at the cavity side walls. (c) Full mode profiles of both $\text{HE}_{11}$ modes, in units of $\mathrm{m}^{-3/2}$. Here, $\tilde{\mathbf{E}}_0$ and $\tilde{\mathbf{B}}_1$ are both approximately vertical, while $\tilde{\mathbf{E}}_1$ and $\tilde{\mathbf{B}}_0$ are both approximately horizontal. We show the vertical components of $\tilde{\mathbf{E}}_0$ and $\tilde{\mathbf{B}}_1$ at left, and the horizontal components of $\tilde{\mathbf{E}}_1$ and $\tilde{\mathbf{B}}_0$ at right. They overlap almost perfectly within the cavity, giving a high signal form factor.
• Figure 3: The final cavity design, with approximately square cross section. The three subfigures show the same quantities as in Fig. \ref{['fig:cylinder']}, and the same useful features of the $\text{HE}_{11}$ modes.
• Figure 4: Schematic depiction of the waveguide couplers and frequency tuning mechanism.
• Figure 5: Simulations of cross-coupling suppression. Imperfections of the cavity geometry lead to a larger $\chi_{\mathrm{d}}$ and $\chi_{\mathrm{r}}$, which can be simultaneously suppressed by rotating an endplate. Dots show simulated results, and the dashed curve is an interpolation. To demonstrate the point, we consider simulated imperfections of the cavity which are much more severe than what would actually occur. (a) Half of the cavity is twisted by $0.1^\circ$. Rotating the endplate by a similar amount restores a low value of the cross-coupling, $\chi \lesssim 10^{-4}$. (b) The cavity is skewed, so that one diagonal is $0.8 \, \mathrm{mm}$ longer than the other. Rotating the endplate restores $\chi \lesssim 10^{-3}$.