  We study a method for mass-selective removal of ions from a Paul trap by
parametric excitation. This can be achieved by applying an oscillating electric
quadrupole field at twice the secular frequency $\omega_{\text{sec}}$ using
pairs of opposing electrodes. While excitation near the resonance with the
frequency $\omega_{\text{sec}}$ only leads to a linear increase of the
amplitude with excitation duration, parametric excitation near $2\,
\omega_{\text{sec}}$ results in an exponential increase of the amplitude. This
enables efficient removal of ions from the trap with modest excitation voltages
and narrow bandwidth, therefore substantially reducing the disturbance of ions
with other charge-to-mass ratios. We numerically study and compare the mass
selectivity of the two methods. In addition, we experimentally show that the
barium isotopes with 136 and 137 nucleons can be removed from small ion
crystals and ejected out of the trap while keeping $^{138}\text{Ba}^{+}$ ions
Doppler cooled, corresponding to a mass selectivity of better than $\Delta m /
m = 1/138$. This method can be widely applied to ion trapping experiments
without major modifications, since it only requires modulating the potential of
the ion trap.
