Axion Haloscope Array With $\mathcal{PT}$ Symmetry.

We generalize the recently proposed $\mathcal{PT}$-symmetric axion haloscope to a larger array with more $\mathcal{PT}$-symmetric structures. The optimized signal-to-noise ratio (SNR) has a greater enhancement, as well as the signal power. Furthermore, we show that the robustness of the detector towards the variations of the array coupling is the strongest when a binary tree structure is introduced which contains a largely enhanced $\mathcal{PT}$ symmetry. The multiple allowed probing sensors can further increase the SNR by a factor of sensors' number due to the correlation of the signals. This type of array can strongly boost the search for axion compared to single mode resonant detection. The enhancement to the SNR becomes the most manifest when applied to the newly proposed detection using superconducting radiofrequency caivty with AC magnetic field where most of the parameter space of the QCD axion above kHz can be probed.