  A detection scheme is explored for light dark matter, such as axion dark
matter or dark photon dark matter, using a Paul ion trap system. We first
demonstrate that a qubit, constructed from the ground and first excited states
of vibrational modes of ions in a Paul trap, can serve as an effective sensor
for weak electric fields due to its resonant excitation. As a consequence, a
Paul ion trap allows us to search for weak electric fields induced by light
dark matter with masses around the neV range. Furthermore, we illustrate that
an entangled qubit system involving $N$ ions can enhance the excitation rate by
a factor of $N^2$. The sensitivities of the Paul ion trap system to
axion-photon coupling and gauge kinetic mixing can reach previously unexplored
parameter space.
