Axion detection via topological Casimir effect

We propose a new table-top experimental configuration for the direct detection of dark matter QCD axions in the traditional open mass window ${10}^{-6}\mathrm{eV}\lesssim m_a\lesssim {10}^{-2}\mathrm{eV}$ using nonperturbative effects in a system with nontrivial spatial topology. Different from most experimental setups found in literature on direct dark matter axion detection, which relies on $\dot{\theta }$ or $\overrightarrow{\nabla }\theta$, we found that our system is in principle sensitive to a static $\theta \ge {10}^{-14}$ and can also be used to set limit on the fundamental constant ${\theta }_{\mathrm{QED}}$ which becomes the fundamental observable parameter of the Maxwell system if some conditions are met. Furthermore, the proposed experiments can probe entire open mass window ${10}^{-6}\mathrm{eV}\lesssim m_a\lesssim {10}^{-2}\mathrm{eV}$ with the same design, which should be contrasted with conventional cavity-type experiments being sensitive to a specific axion mass. Connection with Witten effect when the induced electric charge $e^{\prime }$ is proportional to $\theta$ and the magnetic monopole becomes the dyon with nonvanishing $e^{\prime }=-e\frac{\theta }{2\pi }$ is also discussed.