The parametric resonant behavior of ions inside a linear rf ion trap is studied both theoretically and experimentally. Theoretically, the resonant motion of ions inside an ideal ion trap is described by approximating the trapping rf field as a harmonic pseudopotential with the ions being excited by an additional quadrupolar ac voltage. The resulting damped Mathieu equation is studied and the regions of resonant instability are predicted by investigating the solutions. Experimentally, the parametric excitation of ${\mathrm{Mg}}^{+}$ ions is observed by subjecting the cloud of trapped ions to an additional quadrupolar ac field. The various ion motion resonances are detected through the disappearance of the laser-induced fluorescence signal. Weak damping is introduced by the presence of a low-pressure buffer gas. The experimental results are compared with the theoretical predictions.

• Received 1 August 2002

DOI:https://doi.org/10.1103/PhysRevA.66.063414