  We propose a new table-top experimental configuration for the direct
detection of dark matter axions with mass in the $(10^{-6} \rm eV - 10^{-2} \rm
eV)$ range using non-perturbative effects in a system with non-trivial spatial
topology. Different from most experimental setups found in literature on direct
dark matter axion detection, which relies on $\dot{\theta}$ or
$\vec{\nabla}\theta$, we found that our system is in principle sensitive to a
static $\theta\geq 10^{-14}$ and can also be used to set limit on the
fundamental constant $\theta_{\rm QED}$ which becomes the fundamental
observable parameter of the Maxwell system if some conditions are met.
Connection with Witten effect when the induced electric charge $e'$ is
proportional to $\theta$ and the magnetic monopole becomes the dyon with
non-vanishing $e'=-e \frac{\theta}{2\pi}$ is also discussed.
