Nonlinear collective oscillations of an ion cloud in a Paul trap

In an experiment using a Paul trap, we create a ${\mathrm{H}}_2^{+}$ ion cloud by electron ionization of the background gas at ${10}^{-9}$-mbar residual pressure. Exciting the ions parametrically at twice the frequency of the secular motion of ions in the $r$ or $z$ direction, we observe a narrow resonance at some distance from the motional resonance center if the amplitude of the exciting field exceeds a threshold value. The threshold value decreases with increasing ion number. Since the narrow resonance does not shift with ion number, we interpret it as a collective resonance of the center of mass of the ion cloud. The resonance shape exhibits the typical form of a driven anharmonic oscillator. The conclusions drawn from the experiments are supported by detailed analytical and numerical computations.