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AIP conference proceedings

Fractional frequency parametric resonances in a Paul trap

M. A. N. Razvi, X. Z. Chu, R. Alheit, R. Blümel, Günther Werth

Published Jan 1, 1999• 0 citations
Publisher

Abstract

Excitation of the motional frequencies of clouds of H2+ and N2+ ions, confined in a Paul trap, by an additionally applied radiofrequency quadrupole field leads to the observation of parametric resonances that are predicted to occur at frequencies 2ωz/n, n=1,2,3…, where ωz is the axial secular frequency. In the case of clouds of N2+ ions resonances up to n=10 are detected. They can be explained by parametric instabilities of the center-of-mass motion in the axial direction. The fractional resonances are observable only if the excitation field surpasses a critical strength. We find an odd-even staggering of the thresholds.

DOI
10.1063/1.57472

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Excitation of the motional frequencies of clouds of H2+ and N2+ ions, confined in a Paul trap, by an additionally applied radiofrequency quadrupole field leads to the observation of parametric resonances that are predicted to occur at frequencies 2ωz/n, n=1,2,3…, where ωz is the axial secular frequency. In the case of clouds of N2+ ions resonances up to n=10 are detected. They can be explained by parametric instabilities of the center-of-mass motion in the axial direction. The fractional resonances are observable only if the excitation field surpasses a critical strength. We find an odd-even staggering of the thresholds.
We report the observation of the first ten collective parametric resonances of an uncooled N2+{N}_{2}^{+}N2+​ ion cloud in a Paul trap driven at simple fractions of twice the secular frequency of the trap by an additionally applied quadrupole field. The fractional resonances are observable only if the excitation field surpasses a critical strength. Odd-even staggering of the thresholds is observed.
In an experiment using a Paul trap, we create a H2+{\mathrm{H}}_{2}^{+}H2+​ ion cloud by electron ionization of the background gas at ${10}^{\ensuremath{-}9}$-mbar residual pressure. Exciting the ions parametrically at twice the frequency of the secular motion of ions in the rrr or zzz 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.
Abstract 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 ωsec\omega _{\text {sec}}ωsec​ ω sec using pairs of opposing electrodes. While excitation near the resonance with the secular frequency ωsec\omega _{\text {sec}}ωsec​ ω sec only leads to a linear increase of the amplitude with excitation duration, parametric excitation near 2 ωsec2\, \omega _{\text {sec}}2ωsec​ 2 ω 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 138Ba+^{138}\text {Ba}^{+}138Ba+ 138 Ba + ions Doppler cooled, corresponding to a mass selectivity of better than Δm/m=1/138\Delta m / m = 1/138Δm/m=1/138 Δ 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.
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 Mg+{\mathrm{Mg}}^{+}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.
We have carried out a molecular-dynamics simulation of hundreds of ions confined in a Paul trap. The simulation includes the trapped particles' micromotion and interparticle Coulomb interactions. We have implemented a random walk in velocity to bring the secular motion to a given temperature which we have numerically measured. When the coupling \ensuremath{\Gamma} is large the ions form concentric shells which undergo a quadrupole oscillation at the rf frequency, while the ions within a shell form a 2D hexagonal lattice. Ion clouds at 5 mK show no rf heating for qz{\mathit{q}}_{\mathit{z}}qz​\ensuremath{\lesssim}0.6, whereas rapid heating is seen for qz{\mathit{q}}_{\mathit{z}}qz​=0.8.